Research ArticleA Removal of Eye Movement and Blink Artifacts from EEG DataUsing Morphological Component Analysis

Balbir Singh1 and Hiroaki Wagatsuma123

1Graduate School of Life Science and Systems Engineering Kyushu Institute of Technology (KYUTECH) Kitakyushu Japan2RIKEN Brain Science Institute Wako Japan3Artificial Intelligence Research Center National Institute of Advanced Industrial Science and Technology (AIST) Tsukuba Japan

Correspondence should be addressed to Balbir Singh awana-balbir-singhedubrainkyutechacjp

Received 3 October 2016 Revised 25 November 2016 Accepted 15 December 2016 Published 17 January 2017

Academic Editor Michele Migliore

Copyright copy 2017 Balbir Singh and Hiroaki Wagatsuma This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

EEG signals contain a large amount of ocular artifacts with different time-frequency properties mixing together in EEGs of interestThe artifact removal has been substantially dealt with by existing decomposition methods known as PCA and ICA based onthe orthogonality of signal vectors or statistical independence of signal components We focused on the signal morphology andproposed a systematic decomposition method to identify the type of signal components on the basis of sparsity in the time-frequency domain based on Morphological Component Analysis (MCA) which provides a way of reconstruction that guaranteesaccuracy in reconstruction by using multiple bases in accordance with the concept of ldquodictionaryrdquo MCAwas applied to decomposethe real EEG signal and clarified the best combination of dictionaries for this purpose In our proposed semirealistic biologicalsignal analysis with iEEGs recorded from the brain intracranially those signals were successfully decomposed into original typesby a linear expansion ofwaveforms such as redundant transformsUDWTDCT LDCTDST andDIRACOur result demonstratedthat the most suitable combination for EEG data analysis was UDWT DST and DIRAC to represent the baseline envelopemultifrequency wave-forms and spiking activities individually as representative types of EEG morphologies

1 Introduction

The electrophysiological mechanism of how EEG signals aregenerated and information of what they represent still remainunclear and the most plausible hypothesis is that the signalsare composed of synchronous spiking activities with respectto the oscillatory modulation of the local field potential [1]Therefore EEGs have been used as an index to representthe brain state such as being awake sleeping and selectiveattention and to estimate which brain regions are active incomparison with other regions if they are located on thesuperior surface of the brain close to the cranial bone likepart of the cerebrum The most difficult issue in the dataanalysis of EEGs is the uncertainty of the discriminationof the signal and noise Biological signals contain multipletypes of the signals caused by different internal mechanismssuch as EOG (electrooculogram) generated by the move-ment of eyeballs and eyelids and EMG (electromyogram)

generated by muscular movements of body parts Unlessindividual electrophysiological mechanisms can be isolatedthe problem of the impossibility in pursuit of the true signal isinevitableThe EEG has been known as the most noninvasivetool in particular for clinical diagnosis and neuroscienceresearch while medical professionals and researchers in therelated fields have the difficulty of the signal contaminationIn the engineering field EEGs are used practically in brain-computer-interface technology [2ndash10] In those cases themost serious artifact is ocular related potential for exampleeye movements and eye blinks and thus methods of artifactremoval have been proposed [11ndash13] The proposed methodmostly dealt with linear and stationary signal decompositionfor artifact removals However there are a few methods totreat nonlinear andnonstationary properties in EEGs [14ndash16]EEG signals decomposition indicates that traditional meth-ods are not simply applicable to nonlinear and nonstationarysignals in the purpose of artifact removals [17]

HindawiComputational and Mathematical Methods in MedicineVolume 2017 Article ID 1861645 17 pageshttpsdoiorg10115520171861645

2 Computational and Mathematical Methods in Medicine

Recently signal decomposition by focusing morpho-logical components is attracting more and more attentiondue to its applicability to nonlinear and nonstationary sig-nal properties [18ndash20] Originally signal feature extractionsusing linear analysis in time-frequency domains had beenstudied via Fourier and wavelet transforms or eigenvectorsand subspace theories in the simplest manner [21] The blindsource separation [22] has been discussed widely on theissue of a linearmixture signal and Independent ComponentAnalysis (ICA) and Principal Component Analysis (PCA)are representative methods In the case of the EEG signaldecomposition those methods were frequently applied [2324] especially in the offline analysis In PCA the EEGcomponents are decomposed on spacetime basis whileas disadvantage it is difficult to reconstruct overall signalsby the linear combination of principal components (PCs)because of the ignorance of signals with small amplitudesand irregular changesTherefore the accurate reconstructionin those methods requires the prior and detailed knowledgeto identify PCs corresponding to artifacts [25 26] Thelimitation led a shift of the research trends from PCA toICA with high order statics to specify independence inthe signal On the other hand since the ICA is restrictedto the measure of statistical independence ICA faces thedifficulty of detecting signal components if Gaussian noise iscontaminated in the manner that the noise spreads over in anundesired way into the signal components [11ndash13 27 28]

In plausible EEG decomposition [29] the key role isthe effectiveness in analyzation enhancement and syntheti-zation of signal properties including the nonlinear andnonstationary changes Blind source separation such asICA has demonstrated the decomposition performance evenin complex signals however the sparsity is getting to behighlighted as an extended concept because of the consis-tency between signal analysis and synthesis in a systematicmanner [30] and then the methodology based on the sparsityby using redundant transforms was introduced for signaldecomposition in various applications [31] MCA is oneof the methods In terms of MCA the sparsity plays avital role in separating different timefrequency propertiesor morphologies of individual signal components whichwere demonstrated in the recent studies [18 32 33] Theeffectiveness of the MCA based noise removal was mostlyclarified in image processing [19 20 31 34] However wehypothesized that the MCA decomposition is effective inthe EEG artifact removal and it clarifies which kinds ofsignal morphologies contaminate the signal as true biologicalsignals by using redundant transformormixed overcompletedictionary in the sense of MCA [35] Different dictionarieswhich mean different types of mathematical basis functionrepresent evoked potentials generated by different electro-physiological mechanisms Yong et al [36] preliminarilyreported the effectiveness in the EEG artifact removal andprovided a less comprehensive analysis with MCA in theframework of verification of how EEG true signal preservedafter noise removals even with various EOGfluctuations [37]

In the present study we proposed an EEG decompo-sition method based on the sparsity and overcompletenessdictionary by specifying the best combination of dictionaries

[31] and discussed the reason in the sense of the EEGfrequency properties Depending on the set of dictionariesreconstructed signals were highly different in the represen-tation of timefrequency features in signal [35 38 39] Inthe computer experiment we used the Block-Coordinate-Relaxation (BCR) algorithm to minimize error in signalreconstruction and obtain the sparsest representation ofdesired features The goal of this study is to propose thesystematic way of the artifact removal in EEG signals byemploying MCA and specify timefrequency properties torepresent signal components by verifying the appropriatecombination of the dictionaries

2 Methods and Materials

21 Decomposition Method Numerous methods have beencommonly formulated as the linear combination to suppressor remove the artifacts from EEGs If a signal and a noise arelinearly independent the noise can be removed by replacingcoefficients representing the noise part with zero when thewhole signal is reconstructed The blind source separationmethods like ICA and PCA commonly used the BCI systemto decompose the EEG signal [11ndash13 23 27ndash29 40ndash42] asfollows

119878 = Φ times 119883119884 = 119882 times 119878

(1)

The recorded EEGs from electrodes attached to the scalp(abbreviated as scalp EEG) 119878 can be given by (1) where119883(119905) = [1199091(119905) 1199092(119905) 119909119896(119905)] is time series of coefficientscalled signal components or components simply and Φ isthe mixing matrix to determine the way to split 119878 betweenthe signal and noise In ICA decomposition the final targetis to find the mutual independence 119882 matrix that satisfies119882 = Φminus1 and each row vector in 119884 unmixing matrix isapproximately equal to a scaled value of one row vector in119883The signal then is decomposed into EEGs assumed as the setof true signals and artifacts components The decompositionmethods conventionally require prior knowledge about prop-erties of the target components coupling with the constraints[29] as discussed in the Introduction A heuristic factorremains to be an obstacle for the full automation of the signaldecomposition

22 EEG-EOG Component Morphology The cerebral cortexis located in the outer region of brain hemispheres justbeneath the skull bone and therefore the activities areaccessible by electrical potentials recorded evenly on thescalp These cortical regions are locally separated dependingon functions such as decision-making function (frontalcortex) motor control (premotor cortex) body sensations(somatosensory cortex) and the processing of the sensoryinputs in vision and audition (primary visual and auditorycortex) and then potentials from different positions on thescalp contain information of neuronal activities in differentcortices if signals are clearly separated from each other andfrom artifacts The production of other electric potentialsfrom muscular eyeball and eyelid movements contaminates

Computational and Mathematical Methods in Medicine 3

120578

+

component 1

component k

separationComponentsDenoising

Morphological ComponentAnalysis (MCA)

Separated

Separated

Record

Noise

(EEG)Signal

Eye source components

Eyelidmovement Blink

(Vertical)

(Horizontal)

Figure 1 A schematic diagram of the proposed method for morphological component analysis for the EEG-EOG signal separation

the scalp EEG in an evitable manner of leaking potentialsin the electrophysiological system connecting the brainand muscular-skeletal system On the other hand differentbiological systems have different electrophysiological prop-erties and the nature will be the key to solve the complexdecomposition problem As the traditional knowledge in themedical field [43] it is known that EEG signals have specificcharacteristics on the shape of the waveform called mor-phology ldquomonomorphicrdquo ldquopolymorphicrdquo ldquosinusoidalrdquo andldquotransientrdquo types are recognized differently based on charac-teristics of a single dominant activity multiple frequenciesforming complex activity sine wave-like activity and spikesandor sharp waves (spikes in a duration of 20ndash70msec andsharp waves with a pointed peak and 70ndash200msec duration)If it is possible to decompose the recorded EEG with respectto thosemorphologies of interest this brings us a large benefitbecause it leads the way to the ldquotruerdquo EEGs

According to the electrophysiological mechanism in thenervous system coupled with myogenic potential evoked byocular movements [44 45] the rotation of an eyeball gen-erates potential with an amplitude depending on the degreeof the rotation [46] which is known as the corneoretinaldipole and observed as the staying potential of approximately500120583V asmaximum from the EOG recording in the 4ndash20Hzrange [47] The phenomena had been investigated via thestudies of saccade movements [28 48ndash50] As mentionedabove EEG and EOGs potential have specific morphologiesMorphologies of eye movements and eye blinks can beconsidered as slow change with respect to the EEG time scaleand have a bump shape with a large peak amplitude [51 52]Since the presence of repetitive peaks frequently appears inthe diagnosis of epilepsy [53] we assumed the single bump isthe typical eye blink and assumed the multiple types of slowbaseline changes are eyeball rotations as schematically shownin Figure 1

23 Decomposition Using Morphological Component Analy-sis Recently decomposition of components in image andtime series has a large expectation in applications such asminimizing of the data size for transferring the data via the

Internet MCA based methods fit for the purpose and havethe advantage in the accurate reconstruction of the originaldata after noise removal which relies on the sparsity andovercompleteness of the dictionary In the theory of MCAthe overcomplete dictionary is represented by Φ isin 119877119899times119896where 119896 is themorphological component of signal for 120601119896119896isinΓwhere Γ is the index set of dictionaries A mixed EEG signal119878 isin 119877119899 can be represented as a sparse linear combinationof the coefficient According to Chen et al (2001) [38] theovercomplete dictionary Φ is a set of redundant transformswhich are defined by a set of mathematical functions torepresent the specific morphologies In the process to obtainthe final set of coefficients for accurate reconstruction ofthe original signal the sparseness of the coefficient matrixis crucial In the theory there exists a dictionary thatcan reproduce the specific features of the signal if theappropriate iteration method is introduced to pursue theunique sparse representation The concept of sparsity andthe overcompleteness dictionary has theoretically extendedthe traditional signal decomposition to feature extractionsfocusing on multiple types of morphologies simultaneouslyDue to selection freedom of dictionaries the signal can bedecomposed with explicit dictionary [38] and sometimes itcannot be decomposed in the other form of dictionaries Adictionary is defined as collection of waveforms 120601119896119896isinΓ andthe input signal 119878 is assumed to be reconstructed by a linearcombination of a set of basesrsquo elements 120601119896 and then the signal119878 is expressed as a single vector of 119878 isin 119877119873 and satisfies119878 = 1199041 + 1199042 119904119870 where 1199041 1199042 119904119896 are subcomponentsthat is different morphologies We employed this system torecord EEG signal 119878 as shown in Figure 1 The approximatedecomposition of signal 1198781015840 into its building components canbe expressed as

119878 =119896

sum119894=1

120573119894120601119894 + 120577 = 12057311206011 + 12057321206012 + sdot sdot sdot + 120573119896120601119896 + 120577

cong 1199041 + 1199042 + sdot sdot sdot + 119904119896 (120577 ≪ 1)

= 1198781015840

(2)

4 Computational and Mathematical Methods in Medicine

Decomposition

middot middot middot

component 12057311206011

1st morphological

component 12057321206012

2nd morphological

component 120573k120601k

kth morphological

+

1206011 1206012 120601k

dictionary ΦOvercomplete

Arbitrary EEGsignal

Figure 2 A schematic diagram for EEG signal decomposition using explicit dictionary

Therefore 120573 is the target coefficients for reconstruction ofthe original EEG signal based on the assumption 120577 ≪ 1which means that the remainder 120577 is negligibly small In theconsideration that 120577 represents the noise part (2) withoutnoise can be written as

1198781015840 =119896

sum119894=1

120573119894120601119894 = 120573Φ (3)

Equation (3) is consistent with (1)The problem to solve ishow optimized coefficients can be derived and the equationis rewritten as follows

120573opt1 120573opt2 120573opt

119896 = argmin1205731120573119896

119896

sum119894=1

100381710038171003817100381712057311989410038171003817100381710038170

subject to 1198781015840 =119896

sum119894=1

120573119894120601119894(4)

The problem is how the MCA concept can be embeddedin the systems to decompose biomedical signal especiallyfor EEG signal In this formulation time-frequency param-eters are totally consistent with traditional decompositionmethods which can be applied to the biomedical signaldecomposition such as PCA wavelets and ICA in the senseof the single set of bases One advantage of MCA is theavailability of the combination of multiple basis functionsincluding traditional basis like wavelet decomposition as apart of the component called redundant transforms ThusMCA is expected to reveal what kind of the specificityexists in time-frequency properties of EEG data Concreteproblems in this viewpoint can be addressed as (a) what isthe best combination of dictionaries of MCA for the EEGdecomposition and (b) what is the true EEG signal in theform of obtained sparsest representation based on selecteddictionaries 120601119896

Figure 2 schematically illustrates the MCA decomposi-tion process of arbitrary EEG signal that is assumed to bea linear combination of 119896 morphological component to bedecomposed using explicit dictionaries

In the assumption of three types of dictionaries (119896 = 3)the following three cases are considerable by focusing onindividual dictionaries

Case 1 An overcomplete dictionary 1206011 is representing thecomponent 1199041 1206011 isin 119872119873times1198711 where 119873 ≫ 1198711 119873 being thenumber of samples that is the number of time points in therecorded data

(i) For 1199041 120573opt1 = argmin1205731205730 subject to 1199041 = 1206011120573

while solving this equation leads to the sparse solution(120573opt1 0 lt 120573opt

12 0 120573opt13 0)

(ii) For 1199042 120573opt12 = argmin1205731205730 subject to 1199042 = 1206011120573 while

solving this equation leads to nonsparse solution

(iii) For 1199043 120573opt13 = argmin1205731205730 subject to 1199043 = 1206011120573 while

solving this equation also leads to nonsparse solution

Case 2 An overcomplete dictionary 1206012 is representing thecomponent 1199042 1206012 isin 119872119873times1198712 where119873 ≫ 1198712

(i) For 1199042 120573opt2 = argmin1205731205730 subject to 1199042 = 1206012120573

while solving this equation leads to the sparse solution(120573opt2 0 lt 120573opt

23 0 120573opt21 0)

(ii) For 1199043 120573opt23 = argmin1205731205730 subject to 1199043 = 1206012120573 while

this equation also has nonsparse solution(iii) For 1199041 120573opt

21 = argmin1205731205730 subject to 1199041 = 1206012120573 whilethis equation also has nonsparse solution

Case 3 An overcomplete dictionary 1206013 is representing thecomponent 1199043 1206013 isin 119872119873times1198713 where119873 ≫ 1198713

(i) For 1199043 120573opt3 = argmin1205731205730 subject to 1199043 = 1206013120573

while solving this equation leads to the sparse solution(120573opt3 0 lt 120573opt

32 0 120573opt31 0)

(ii) For 1199042 120573opt32 = argmin1205731205730 subject to 1199042 = 1206013120573 while

solving this equation leads to nonsparse solution

(iii) For 1199041 120573opt31 = argmin1205731205730 subject to 1199041 = 1206013120573 while

solving this equation leads to nonsparse solution

Computational and Mathematical Methods in Medicine 5

Theoretically speaking by using three dictionaries MCAcan divide the signal into components depending on eachdictionary of 1206011 1206012 and 1206013 as the sparest representation of allsignalsThe sparse components are describedmathematicallyas

120573opt1 120573opt2 120573opt3 = argmin

120573112057321205733

1003817100381710038171003817120573110038171003817100381710038170 +

1003817100381710038171003817120573210038171003817100381710038170 +

1003817100381710038171003817120573310038171003817100381710038170

subject to 119878 = 12057311206011 + 12057321206012 + 12057331206013(5)

This formulation states a nonconvex optimization problemto separate the components of the signal However each 120601119896needs to be efficient in a specific component while it remainsnoneffective in other signal components The nonconvexoptimization problem indicated that it is difficult to solve (5)in a simple manner and then the Basis Pursuit (BP) method[54] was proposed based on the idea that the replacementof 1198970 norm by 1198971 norm results in the error minimizationAccording to the improvement the BP [54] was successfullyformulated into an accurate method to represent the sparestof components which is described as

120573opt1 120573opt2 120573opt3 = argmin

120573112057321205733

3

sum119894=1

100381710038171003817100381712057311989410038171003817100381710038171 + 120582

1003817100381710038171003817100381710038171003817100381710038171003817119878 minus3

sum119894=1

1206011198941205731198941003817100381710038171003817100381710038171003817100381710038171003817

2

2

(6)

In this system 1198972 norm is considered to be the errornorm based on the assumption that the residual acts asa white zero-mean Gaussian noise and another importantfinding is the representation of noise models 1198971 Laplaciannoise with the consideration of 119897infin uniformly distributednoise in the form of the optimization problem 120582 representsthe stopping criterion or threshold By using the Block-Coordinate-Relaxation (BCR) method [55] the optimizationproblem can be solved in finite computation time Theprocedure is given below

(1) Initialize = 119868max number of iterations = 119871 threshold120575 = 120582 lowast 119868max

(2) Perform 119871 timesPart (1) update 1199041 assuming 1199042 and 1199043 are fixed

(a) Calculate the residual 119877 = 119878 minus 1199042 minus 1199043(b) Calculate 1205731 = 1206011198791119877(c) Threshold the coefficient of 1205731 and obtain 1205731(d) Reconstruct 1199041 by 1199041 = 12060111205731

Part (2) update 1199042 assuming 1199041 and 1199043 are fixed

(a) Calculate the residual 119877 = 119878 minus 1199041 minus 1199043(b) Calculate 1205732 = 1206011198792119877(c) Threshold the coefficient of 1205732 and obtain 1205732(d) Reconstruct 1199042 by 1199042 = 12060121205732

Part (3) update 1199043 assuming 1199041 and 1199042 are fixed

(a) Calculate the residual 119877 = 119878 minus 1199041 minus 1199042(b) Calculate 1205733 = 1206011198793119877

(c) Threshold the coefficient of 1205733 and obtain 1205733(d) Reconstruct 1199043 by 1199043 = 12060131205733

(3) Update the threshold by 120575 = 120575 minus 120582(4) If 120575 gt 120582 return to Step (2) else finish

3 Hypothesis

In the present study we hypothesized that appropriate threedictionaries of MCA specifically for EEG recording datawere undecimated wavelet transform (UDWT) discrete sinetransform (DST) andDIRAC (aka standard unit vector basisor Kronecker basis) Fadili et al [17] UDWT contributes toseparating slow and bump morphologies for EOG and EEGtransient slow changes DST is for monomorphic and poly-morphic EEG components (major EEG parts) and DIRAC isfor spike type activities in transient EEGs In comparison inthe simulated experiment we used the discrete cosine trans-form (DCT) discrete sine transform (DST) [56 57] and localdiscrete cosine transform (LDCT) dictionaries formajor EEGparts For the verification of the hypothesis the intracranialEEG (iEEG) data was assumed to be ldquotrue EEGrdquo signal whichwas recorded from the real brain activity and artificial EOGsincluding bump and slow changes were introduced and theperformance of the accurate reconstruction of the true EEGswas examined In iEEG there are two types of the data underthe conditions of eye-closing and eye-opening 42 Accordingto the neuroscientific evidence EEGs have a clear peakin the low-frequency range around 10Hz in the frequencyspectrum under the eye-closing condition 42 In the Resultscorrelation coefficient (cc) was used for the validation ofaccuracy in reconstruction and the frequency spectrum wasfor the validation of the nature of the information containedin EEGs

4 Results

For verification of our hypothesis in the computer experi-ments three types of the data were used (1) all simulateddata (2) a combination of real iEEG and simulated EOGand (3) recording of real EEG-EOG data and our proposedmethod was validated

41 Simulated Data In the first place two simulated signalsources were prepared for the simple test of the proposedmethod Initially Yong et al [36] proposed a combinationof the wavelet DCT and DIRAC for EEG artifact removalswhile their results could not tell how effective the methodwas in a qualitative manner In our experiment the firstsource signal consisted of a cosine wave which was assumedto be a monomorphic EEG signal and the second sourceconsisted of blinks component with three bumps designedas usual EOG signals The simulated signal as a mixture ofthe two sources and white noise (120578 = 20) was shownin Figure 3(a) where 120578 was defined as the percentage ofthe maximum amplitude of the input signal Our proposedMCA method was applied to separate the components fromthe simulated signal with the explicit dictionaries UDWT

6 Computational and Mathematical Methods in Medicine

02

0

1

2

024

1000 20000

minus2

minus2

Samples

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)1st signal source

2nd signal source

Combined signal (source)

(a)

0

15

0

2

0

1

1000 20000

minus2

Samples

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

1st separated component (UDWT)

2nd separated component (DCT)

3rd separated component (DIRAC)

(b)

0

2

4

1000 20000

minus2

Samples

Pote

ntia

l (V

)

Combined signal (source)Combination of separated component (reconstructed)

(c)

Figure 3 An example of simulated signal for decomposition and (a) the cosine with bump and spikes signals and combined signal withwhite noise (120578 = 20) (b) separated components with explicit dictionaries UDWT-DCT-DIRAC and (c) comparison between combinedsignal and sum of separated components (cc = 099)

DCT and DIRAC as shown in Figure 3(b) as a replicationtest The correlation coefficient between the simulated signaland the sum of all components was higher than 099 andthe simulated result proved the accuracy of decomposedcomponents byMCAwithUDWTDCT andDIRAC explicitdictionaries (Figure 3(c))

42 Simulated EOGContaminated iEEG Signal Theprevioussection was a simple example of the simulated data In thissection we introduced a new validation way to test theproposed method in a qualitative manner The real iEEGsignals were obtained under the closing eye condition Thelinear combination of simulated EOG and real iEEG signalswas used for the test In this case we assumed that iEEGhad already included a usual level of the white noise andthen did not add further noise additionallyThe iEEG datasetwas given by Andrzejak et al [58] with 100 trials andthe sampling rate was at 17361Hz (000576 ssample) and210(=1024) samples took about 6 s (589824 s) The linearcombination of simulated EOG and iEEG signals was appliedfor the validation

There were different combinations for simulated EOG asassumed artificial eye movement which was considered asthe step function and eye blinks by bump signalThe flatnesssignals with elevations with slow time scales compared with

the EEG time scale represent the gaze-type eyeball rotationsThe signals can be reconstructed by a mathematical methoddefined by the rate of change ()1015840 of which satisfies that119905 | ()1015840 gt 0 should be 0 Thus the definition of the EOGsmoothness is described as

()1015840119868 =

()1015840 (119905) ()1015840 (119905) = 00 ()1015840 (119905) gt 0

(7)

where 119868 = 119905 | ()1015840 = 0 leads to ()1015840119868 equiv 0 according toits definition as shown in Figure 4(b) In addition the bumpssignal was considered as the blink type EOG signal shownin Figure 4(c) Figure 4(d) showed the schematic examplefor the semisimulated signal In the same way 100 datasetsof semisimulated signals with a random combination ofcomponents in time series were used for the validation

Figures 5(a) 5(b) and 5(c) demonstrated a set of resultsfor the decomposition of the semisimulated signal by explicitdictionaries depending on the combination of dictionariesAsmentioned in Section 23 the stopping criterion dependedon 120582 lowast threshold and the parameters in this comparativestudy used a different combination of explicit dictionaries(UDWT-DCT-DIRAC UDWT-DST-DIRAC and UDWT-LDCT-DIRAC) and different type of thresholds either hardand soft and 120582 value varied from 3 to 5

Computational and Mathematical Methods in Medicine 7

200

0

minus200Pote

ntia

l (V

)

Samples40003000200010000

Intracranial real EEG signal

(a)

500

0

minus500Pote

ntia

l (V

)

Samples40003000200010000

Artificial eye movement-related EOG signal

(b)

500

0

minus500Pote

ntia

l (V

)

Samples40003000200010000

Artificial blink EOG signal

(c)

Samples

1000

0

minus1000Pote

ntia

l (V

)

40003000200010000

Combined signal (EEG + EOG)

(d)

Figure 4 A systemic representation of differentmorphological signals (a) intracranial EEG signal (b) artificial block EOG signal (c) artificialblink EOG signal and (d) combined signal

Figures 6(a) and 6(b) showed the averaged cc of decom-posed component by a respective combination of explicitdictionaries with hard and soft thresholds For EEG signaldecomposition performance cc between iEEG and eitherDST DCT or LDCT component was evaluated dependingon the three combination types (Figure 6(a)) For EOGsignal decomposition performance cc between EOG andUDWT component was evaluated (Figure 6(b)) In compari-son between hard and soft thresholds the average value of thehard threshold is around 06 which is larger than that in thesoft threshold while the average value of the soft threshold isaround 095 demonstrating fewer variances than those in thehard thresholdThismethod indicates thatUDWTdictionarywith a soft threshold is the stable performance according tothe fitness of the morphological property in this case

There were similar variances and average values in theevaluation of EEG signal decomposition using the timedomain and then we introduced a measure in the frequencydomain As mentioned in Section 22 EEG signals carryinformation to represent the current brain stage in thespecific tendency in the frequency domain such as having asynchronized neural activities by showing the existence of apeak in the frequency spectrum The EEG data used in theevaluation showed a peak around 10Hz under the closingeye condition and a peak around 50Hz under the openingeye condition Therefore in the frequency analysis a 10Hzpeak will be an index to tell how much the reconstructedsignal preserves the original information contained in theoriginal iEEG data under closing eye condition Figure 7showed the averaged normalized FFT as the comparisonbetween three combinations of the dictionaries InterestinglyalthoughDSTDCT and LDCT single components seemed toreconstruct the EEGs because of a high cc value in the timedomain the frequency spectrum analysis clarified the factthat the single component cannot reproduce the necessarytendency of EEG signals peak Meanwhile the combination

of 2nd and 3rd components which means oscillatory andspike components successfully reproduced the EEG signaltendency suggesting the importance of the spike informa-tion that presumably synchronizes background oscillatorybehaviors The 10Hz peak can be reproduced according toparameter conditions easily However 50Hz peak is difficultto be reproduced especially for LDCT-DIRAC componentin every case In the viewpoint of the tolerance in thechange of the threshold value the soft threshold methodshowed the robust performance of the signal informationpreservation which is consistent with the result of EOGsshown in Figure 6 As shown in Figure 8 the reconstructionaccuracy of the frequency profile by two dictionaries wasproved by a significant difference between the results of twomorphological and single morphological components (119905-test119901 lt 001 in both hard and soft thresholds) This evidencesuggests the importance of the DIRAC component for EEGsignals which was not equivalent to the noise or rathercarrying some information

43 Decomposition of EOG from Real EEG Data

431 EEG Data The real scalp EEG and EOG data wereobtained from the data demonstrated in the paper writtenby Ai et al (2016) [50] These data were recorded from23 EEG channels (FP1 FP2 F7 F3 Fz F4 F8 FC5 FC1FC2 FC4 T7 C3 Cz C4 T8 CP1 CP2 P3 Pz P4 O1and O2) and 7 EOG channels (V1u V1d V2u and V2dvertical EOG ⟨VEOG⟩ electrodeswere placed on supraorbitaland infraorbital rims of each eye HL and HR horizontalEOG ⟨HEOG⟩ electrodes were on the left and right outercanthi Vz was on the forehead approximately 25mm abovethe nasion) respectively according to 10ndash20 InternationalSystem (BrainAmp amplifier Brain Products GmbH) fromthe 8 participants seated in a comfortable armchair withthe base adjusted according to a participant height Theeyes of the participants were fixed straightly to the fixation

8 Computational and Mathematical Methods in Medicine

UDWT DST DIRAC400

0

minus400

Pote

ntia

l (V

)

200

0

minus200

0

100

minus100

Samples400020000

Samples400020000

Samples400020000

(a)

DCTUDWT DIRAC

400

0

minus400

Pote

ntia

l (V

)

200

0

minus200

0

100

minus100

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Samples400020000

Samples400020000

(b)

UDWT LDCT DIRAC400

0

minus400

Pote

ntia

l (V

)

200

0

200

0

minus200

Samples400020000

Samples400020000

Samples400020000

(c)

Figure 5 Components separation byMCA (a) explicit dictionaries are UDWT DST andDIRAC (b) UDWT DCT andDIRAC (c) UDWTLDCT and DIRAC respectively at 120582 = 4 The original signal for decomposition was shown in Figure 4(d) as combined signal

cross in the center of the monitor screen The stimulus wasdisplayed by a CRT monitor A chin support frame wasused to keep the participantrsquos head position fixed and fixtheir head to the supporting frame without laying their chinson the supporting bar to avoid the jaw clenching artifactThe distance between eyes and monitor was set to 70 cmThe sampling rate was 500Hz The whole details of theexperiment protocols were given in Ai et al (2016) [50]

432 Results with Real EEG-EOG According toAi et al [50]the real EEG-EOG data were divided into 4 sessions Eachsession had 12 tasks of eye movement The two EOG signalswere collected from ldquoV1d-V1urdquo and ldquoV2d-V2urdquo at right andleft sides of the eye as shown in Figure 9 and both signalsshowed the same kind of tendency because vertical EOG

propagated symmetrically in an anterior-posterior directionFigure 10 showed the real EEG signals were taken from someelectrodes for example Fp1 Fp2 Cz O1 and O2 whichrepresent EOG influence depending on the frontal centraland occipital parts of the brain

The selected explicit dictionaries were used to representthe targeted component for the EEG and EOG signal EEGand EOG were distinguished based on the morphologythat was observed in the EEG and EOG The lateral eyemovements mostly affect frontal electrodes [45] ThereforeFp1 electrode was used to decompose and demonstratethe effectiveness of our proposed method with MCA asshowed in Figure 11 and the same method was applied toall the 23 electrodes All EEG signals were morphologicallydecomposed with redundant transform

Computational and Mathematical Methods in Medicine 9

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

Aver

aged

corr

elat

ion

coeffi

cien

t

06

04

08

1

(a) cc between iEEG and 2nd comp (hard)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5Av

erag

ed co

rrel

atio

n co

effici

ent

06

04

08

1

(b) cc between iEEG and 2nd comp (soft)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

06

04

08

1

Aver

aged

corr

elat

ion

coeffi

cien

t

(c) cc between EOG and UDWT (hard)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

Aver

aged

corr

elat

ion

coeffi

cien

t

06

04

08

1

(d) cc between EOG and UDWT (soft)

Figure 6 A comparison between cc of decomposed morphological component with iEEG signal and artificial EOG with hard and softthresholds The mean value and standard deviation were calculated from all 100 decomposed datasets by explicit dictionaries (a) Secondmorphological component was decomposed by DST DCT and LDCT with hard and (b) soft threshold respectively (c) First morphologicalcomponent was decomposed by UDWT with a hard threshold and (d) soft threshold respectively 100 trials of iEEG and artificial EOG wereused

10 Computational and Mathematical Methods in Medicine

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

0 20 40 60 80

0

2

4

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(a) Hard (120582 = 3)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(b) Hard (120582 = 4)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(c) Hard (120582 = 5)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(d) Soft (120582 = 3)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(e) Soft (120582 = 4)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Nor

mal

ized

pow

er (d

B)

Frequency (Hz)

minus2

(f) Soft (120582 = 5)

Figure 7 An averaged normalized FFT obtained from 100 of iEEG and combination of two morphological components and singlemorphological component at 120582 varies from 3 to 5 with hard and soft thresholds

Figure 11(a) demonstrated the decomposition of compo-nents by the first explicit dictionary it was divided into threedifferent morphologies of the EEG signal Figures 11(b) and11(c) showed the second and the third explicit dictionary ofredundant transform respectively The overcomplete dictio-nary was a combination of redundant transforms that char-acterized the component in a different morphology Accord-ingly one of redundant transforms can be differentiated intodecomposed components by overcomplete dictionaries Thefirst component was decomposed by ldquoUDWTrdquo of each over-complete dictionary and was analyzed via the slow and blinktype morphology The second component was decomposedby ldquoDCTrdquo ldquoDSTrdquo and ldquoLDCTrdquo and was analyzed via thebackground of the signal which was similar to the EEG signal

and the third component was decomposed by ldquoDIRACrdquo andwas analyzed via the unexpected spikeThe first overcompletedictionary decomposed the EEG signal without changingthe monomorphic polymorphic and transient propertiesThe cc between the original signal and the summation of alldecomposed components was close to one Figure 12 showedthe raw EOG signal taken from the vertical and horizontalchannel and first decomposed component taken from Fp1Fp2 Cz O1 and O2 respectively

Table 1 showed individual cc of original EEG signals andrecomposed EEG signals from the combination of compo-nents with respect to different channels and combinationsof dictionaries Table 2 showed the cc between filter rawEOG signal taken from vertical and horizontal channels and

Computational and Mathematical Methods in Medicine 11

3 4 5

02

03

04

05

06

07

08

09

Aver

aged

FFT

corr

elat

ion

coeffi

cien

t

01

1

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

lowast lowast lowast

(a) Hard threshold

3 4 5

Aver

aged

FFT

corr

elat

ion

coeffi

cien

t02

03

04

05

06

07

08

09

01

1

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

lowast lowast lowast

(b) Soft threshold

Figure 8 A comparison of FFT correlation coefficients between iEEG data and morphological component decomposed by explicitdictionaries lowastSignificant differences (119901 lt 005) (a) Combined two morphological components and (b) single morphological componentMean value and standard deviation calculated from all 100 decomposed datasets by explicit dictionaries with hard and soft thresholds

400

Pote

ntia

l (V

)

200

0

minus200

400

Pote

ntia

l (V

)

200

0

minus200

Samples20000 1000

EOG (V1u-V1d)

EOG (V2u-V2d)

Figure 9 An example of EOG signal taken from right and left sideof eyes

decomposed first component from Fp1 Fp2 Cz O1 and O2respectively

5 Discussion

Artifact contamination in EEG signal has been a com-mon important issue in neurobiological event diagnosis and

Table 1 cc of original signal and sum of the decomposed compo-nents

EEG channelCorrelation coefficient

UDWT-DST-DIRAC

UDWT-DCT-DIRAC

UDWT-LDCT-DIRAC

Fp1 09921 plusmn 0014 09921 plusmn 0014 09932 plusmn 0013Fp2 0992 plusmn 017 09919 plusmn 018 09932 plusmn 014Cz 09898 plusmn 01 09899 plusmn 01 09908 plusmn 009O1 09836 plusmn 015 09836 plusmn 016 09869 plusmn 012O2 09855 plusmn 013 09856 plusmn 013 09849 plusmn 015

neuroscientific researchThevariousmethodswere applied toremove the artifacts from EEG [2 11ndash13 21 23 24 26ndash28 52]The decomposition based analysis was used in removal ofEOG artifacts in EEG [22 27 28 30 40 42] Howeverthose methods lack the elucidation of what the nature ofEEG signals is in the viewpoint of the signal analysis and asystematic approach was required by treating the sparsity andnonlinearity of the signal in the time domain

12 Computational and Mathematical Methods in Medicine

0

0

50

Fp1

Fp2

Cz

O1

O2

100

0

minus100

minus50

minus40

Pote

ntia

l (V

)

0

50

minus50

Pote

ntia

l (V

)

050

minus50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

Figure 10 An example of real EEG signal taken from Fp1 Fp2 Cz O1 and O2 electrode channels

Table 2 cc between filtered EOG and UDWT component decomposed by UDWT dictionary

EOG channels EEG channelsFp1 Fp2 Cz O1 O2

Correlation coefficientUDWT-DST-DIRACV1d 06777 0657 07267 09223 06445V1u 06814 0646 06606 09419 06354V2d 0916 0906 09402 0882 05402V2u 02332 02268 02353 06388 08494H1 08582 0847 08444 06902 05839H2 09419 09468 09559 07476 04752

UDWT-DCT-DIRACV1d 06792 06595 068 09213 06352V1u 06835 06396 06424 09581 06585V2d 09193 0902 09362 08764 05145V2u 02331 02183 02316 06639 08919H1 08593 08507 08626 06759 05376H2 09442 09465 09662 07266 04346

UDWT-LDCT-DIRACV1d 06794 06403 07219 08892 065V1u 06443 06279 06459 08196 05381V2d 09142 09072 09395 09592 06506V2u 02351 02235 02383 03747 06804H1 08637 08449 08471 07638 05734H2 09586 09558 09577 08826 05598

Computational and Mathematical Methods in Medicine 13

0

50

0

20

UDWT

DCT

DIRAC

0

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus30

(a)

UDWT

DST

DIRAC

0

0

20

0

50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus20

minus20

(b)

0

0

50

100

0

UDWT

LDCT

DIRAC

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus20

minus40

minus80

(c)

Figure 11 Component separated fromEEG (Fp1 electrode) signal by explicit dictionaries (a)UDWT-DCT-DIRAC (b)UDWT-DST-DIRACand (c) UDWT-LDCT-DIRAC respectively

This study revealed the nature of EEG signals in the senseof morphologies contained in the original signal by usingMCA The UDWT was used to decompose the slow andbump morphology The DCT DST and LDCT transformwere used to decompose the EEG signal Spike typemorphol-ogy was decomposed by DIRAC Redundant transforms ofDCT and DST have a similar capability in representing themorphology of oscillatory activities Therefore we used theDCT LDCT and DST dictionaries for validations of EEGsignal The detailed significant differences in morphology ofDCT and DST were given in past studies [56 57] while inour analysis there were no significant differences The rightcombination of redundant transforms to form overcompletedictionary revealed the desired decomposition in principle

In Section 42 ldquoBlocksrdquo ldquoBumpsrdquo similar to simulatedEOG signal defined in past studies [59ndash61] as shown in

Figure 4 and EEG data [58] were used to validate ourpurposed method The ldquoBlocksrdquo with abrupt changes weresimilar to the horizontal and vertical eye movements sim-ply as described by past studies [25 51] For the sake ofsimplicity in the present study ldquoBumpsrdquo were used as arepresentative signal form as eye blinks that happens inunexpected timings as illustrated in Figure 5 The separationof components by given dictionary works well in this evalu-ation but the further analysis is necessary for the evaluationof the signal decomposition with complex eye movementswhich requires presumably various redundant dictionariesIn the verification of the component discrimination as shownin Figures 6 and 7 the accuracy of the averaged EOGcomponent decomposition was above 90 which suggests aplausible performance even in the complex eye movementsThe combined DST and DIRAC dictionaries had better

14 Computational and Mathematical Methods in Medicine

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

Samples20000 1000

V1u

H1

(a) UDWT components separated by UDWT-DST-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(b) UDWT components separated by UDWT-DCT-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(c) UDWT components separated by UDWT-LDCT-DIRAC

Figure 12 UDWT component taken from Fp1 Fp2 Cz O1 and O2 separated by UDWT-DCT-DIRAC UDWT-DST-DIRAC and UDWT-LDCT-DIRAC respectively

decomposition performance than others while DST andDCT theoretically have no meaningful difference The usageof iEEG as the true EEG signal had a large benefit whichcan be used for the performance test for past proposedmethods like ICA and PCA consistently Our proposedmethod successfully demonstrated the performance in cc andthe frequency profile especially in Section 42 while in theserious discussion of the real EEG and EOG signals the DSTor DCT component exhibited a baseline fluctuation of thesignal which denotes the persistence of the EOG componentor other slow frequency artifacts noises and the factor willbe improved by the fine-tuned design of the DST or DCTdictionary with a band pass filter function In addition thethreshold problem exits in the optimization algorithm andnumber of iterations [37]

The EEG decomposition had not mark with a combi-nation of a second and a third component of EEG signal

decomposed by ldquoDST DCT and LDCTrdquo andDIRAC respec-tively based on the morphology Therefore the accuratecombination in the further perspective will be considerableEven the combination of all components and the mixedsignal or real EEG signal had cc above 97 for all redundanttransforms as is analyzed in the frequency spectrum thesignal morphology has further meaning in the viewpointof the signal transmission The MCA method has such anextended and flexible availability for signal analyses

6 Conclusion

Morphological Component Analysis methodology wasapplied to the simulated semisimulated and real EOGand EEG signal The successful decomposition of the EOGand EEG signal into their morphological component wasdemonstrated It seems to be that the EEG signals and

Computational and Mathematical Methods in Medicine 15

artifacts in EEG have been represented by different explicitdictionaries We analyzed the EEG signals involved with theEOG artifacts which were influenced by task conditionsTheDIRAC explicit dictionary decomposed the EEG signal intospike-like activities which may be related to the transientproperty of EEG UDWT explicit dictionary representsslow movement or bumps DCT DST and LDCT explicitdictionaries represent dominant signal that represents EEGsor pure tones signals as monomorphic and polymorphicactivities These results suggested that the effectivenessof MCA in ocular artifacts removal from the EEG rawsignal was derived from signal morphology characterizedas slow and smooth change of EOG time series In thefurther analysis the MCA is required to compare withother competing methods for the EEG and EOG signaldecomposition

Competing Interests

The authors have declared that no competing interests exist

Acknowledgments

This work was partly supported by JSPS KAKENHI 16H01616and 26240032 and theNewEnergy and Industrial TechnologyDevelopment Organization (NEDO) ldquoNext-Generation Arti-ficial Intelligence (3) Base Technology for Next-GenerationAIrdquo (Automated Driving Task) and the collaborative researchproject with Fujitsu Ten Limited

References

[1] J P Donoghue J N Sanes N G Hatsopoulos and G GaalldquoNeural discharge and local field potential oscillations in pri-mate motor cortex during voluntary movementsrdquo Journal ofNeurophysiology vol 79 no 1 pp 159ndash173 1998

[2] J A Uriguen and B Garcia-Zapirain ldquoEEG artifact removalmdashstate-of-the-art and guidelinesrdquo Journal of Neural Engineeringvol 12 no 3 Article ID 031001 2015

[3] C Kamarajan and B Porjesz ldquoAdvances in electrophysiologicalresearchrdquoAlcohol Research Current Reviews vol 37 no 1 article53 2015

[4] L F Nicolas-Alonso and J Gomez-Gil ldquoBrain computer inter-faces a reviewrdquo Sensors vol 12 no 2 pp 1211ndash1279 2012

[5] L Mayaud M Congedo A Van Laghenhove et al ldquoA compar-ison of recording modalities of P300 event-related potentials(ERP) for brain-computer interface (BCI) paradigmrdquo Neuro-physiologie CliniqueClinical Neurophysiology vol 43 no 4 pp217ndash227 2013

[6] X-Y Wang J Jin Y Zhang and B Wang ldquoBrain controlhuman-computer integration control based on brain-computerinterfacerdquo Acta Automatica Sinica vol 39 no 3 pp 208ndash2212013

[7] G Al-Hudhud ldquoAffective command-based control system inte-grating brain signals in commands control systemsrdquo Computersin Human Behavior vol 30 pp 535ndash541 2014

[8] J L Sirvent Blasco E Ianez A Ubeda and JM Azorın ldquoVisualevoked potential-based brain-machine interface applications toassist disabled peoplerdquo Expert Systems with Applications vol 39no 9 pp 7908ndash7918 2012

[9] H Cecotti ldquoSpelling with non-invasive Brain-Computer Inter-facesmdashcurrent and future trendsrdquo Journal of Physiology Parisvol 105 no 1ndash3 pp 106ndash114 2011

[10] I S Kotchetkov B Y Hwang G Appelboom C P Kellnerand E S Connolly Jr ldquoBrain-computer interfaces militaryneurosurgical and ethical perspectiverdquo Neurosurgical Focusvol 28 no 5 article no E25 2010

[11] R N Vigario ldquoExtraction of ocular artefacts from EEG usingindependent component analysisrdquo Electroencephalography andClinical Neurophysiology vol 103 no 3 pp 395ndash404 1997

[12] W Zhou and J Gotman ldquoAutomatic removal of eye movementartifacts from the EEG using ICA and the dipole modelrdquoProgress in Natural Science vol 19 no 9 pp 1165ndash1170 2009

[13] R Sameni andCGouy-Pailler ldquoAn iterative subspace denoisingalgorithm for removing electroencephalogram ocular artifactsrdquoJournal of Neuroscience Methods vol 225 pp 97ndash105 2014

[14] M Breakspear and J R Terry ldquoDetection and description ofnon-linear interdependence in normal multichannel humanEEG datardquo Clinical Neurophysiology vol 113 no 5 pp 735ndash7532002

[15] U R Acharya O Faust N Kannathal T Chua and S Laxmin-arayan ldquoNon-linear analysis of EEG signals at various sleepstagesrdquo Computer Methods and Programs in Biomedicine vol80 no 1 pp 37ndash45 2005

[16] L I Aftanas and S A Golocheikine ldquoNon-linear dynamiccomplexity of the human EEGduringmeditationrdquoNeuroscienceLetters vol 330 no 2 pp 143ndash146 2002

[17] M J Fadili J-L Starck J Bobin and Y Moudden ldquoImagedecomposition and separation using sparse representations anoverviewrdquo Proceedings of the IEEE vol 98 no 6 pp 983ndash9942010

[18] K J Blinowska and P J Durka ldquoUnbiased high resolutionmethod of EEG analysis in time-frequency spacerdquo Acta Neuro-biologiae Experimentalis vol 61 no 3 pp 157ndash174 2001

[19] E Imani H-R Pourreza and T Banaee ldquoFully automateddiabetic retinopathy screening usingmorphological componentanalysisrdquo Computerized Medical Imaging and Graphics vol 43pp 78ndash88 2015

[20] E Imani M Javidi and H-R Pourreza ldquoImprovement ofretinal blood vessel detection using morphological componentanalysisrdquo Computer Methods and Programs in Biomedicine vol118 no 3 pp 263ndash279 2016

[21] A S Al-Fahoum and A A Al-Fraihat ldquoMethods of EEG signalfeatures extraction using linear analysis in frequency and time-frequency domainsrdquo ISRN Neuroscience vol 2014 Article ID730218 7 pages 2014

[22] M Zibulevsky and B A Pearlmutter ldquoBlind source separationby sparse decomposition in a signal dictionaryrdquoNeural Compu-tation vol 13 no 4 pp 863ndash882 2001

[23] N P Castellanos andVAMakarov ldquoRecovering EEGbrain sig-nals artifact suppression with wavelet enhanced independentcomponent analysisrdquo Journal of Neuroscience Methods vol 158no 2 pp 300ndash312 2006

[24] J Hou K Morgan D M Tucker et al ldquoAn improved artifactsremoval method for high dimensional EEGrdquo Journal of Neuro-science Methods vol 268 pp 31ndash42 2016

[25] P Berg and M Scherg ldquoA multiple source approach to thecorrection of eye artifactsrdquo Electroencephalography and ClinicalNeurophysiology vol 90 no 3 pp 229ndash241 1994

[26] P K Sadasivan and D Narayana Dutt ldquoSVD based techniquefor noise reduction in electroencephalographic signalsrdquo SignalProcessing vol 55 no 2 pp 179ndash189 1996

16 Computational and Mathematical Methods in Medicine

[27] C A Joyce I F Gorodnitsky andMKutas ldquoAutomatic removalof eye movement and blink artifacts from EEG data using blindcomponent separationrdquo Psychophysiology vol 41 no 2 pp 313ndash325 2004

[28] G L Wallstrom R E Kass A Miller J F Cohn and N A FoxldquoAutomatic correction of ocular artifacts in the EEG a com-parison of regression-based and component-based methodsrdquoInternational Journal of Psychophysiology vol 53 no 2 pp 105ndash119 2004

[29] S M Gordon V Lawhern A D Passaro and K McDowellldquoInformed decomposition of electroencephalographic datardquoJournal of Neuroscience Methods vol 256 pp 41ndash55 2015

[30] D StuderUHoffmann andTKoenig ldquoFromEEGdependencymultichannel matching pursuit to sparse topographic EEGdecompositionrdquo Journal of Neuroscience Methods vol 153 no2 pp 261ndash275 2006

[31] J-L Starck M Elad and D Donoho ldquoRedundant multiscaletransforms and their application for morphological componentseparationrdquo Advances in Imaging and Electron Physics vol 132pp 287ndash348 2004

[32] P J Franaszczuk G K Bergey P J Durka andHM EisenbergldquoTime-frequency analysis using thematching pursuit algorithmapplied to seizures originating from the mesial temporal loberdquoElectroencephalography and Clinical Neurophysiology vol 106no 6 pp 513ndash521 1998

[33] P J Durka A Matysiak E M Montes P V Sosa and K JBlinowska ldquoMultichannel matching pursuit and EEG inversesolutionsrdquo Journal of Neuroscience Methods vol 148 no 1 pp49ndash59 2005

[34] J Bobin J-L Starck J Fadili and Y Moudden ldquoSparsityand morphological diversity in blind source separationrdquo IEEETransactions on Image Processing vol 16 no 11 pp 2662ndash26742007

[35] P J Durka D Ircha and K J Blinowska ldquoStochastic time-frequency dictionaries formatching pursuitrdquo IEEE Transactionson Signal Processing vol 49 no 3 pp 507ndash510 2001

[36] X Yong R K Ward and G E Birch ldquoGeneralized morpholog-ical component analysis for EEG source separation and artifactremovalrdquo in Proceedings of the 4th International IEEEEMBSConference on Neural Engineering (NER rsquo09) pp 343ndash346Antalya Turkey May 2009

[37] B Singh G Ai and H Wagatsuma ldquoAn electrooculographyanalysis in the time-frequency domain using morphologicalcomponent analysis toward the development of mobile BCIsystemsrdquo in Universal Access in Human-Computer InteractionAccess to Interaction 9th International Conference UAHCI 2015Held as Part of HCI International 2015 Los Angeles CA USAAugust 2ndash7 2015 Proceedings Part II vol 9176 of Lecture Notesin Computer Science pp 528ndash537 Springer Berlin Germany2015

[38] S S Chen D L Donoho and M A Saunders ldquoAtomicdecomposition by basis pursuitrdquo SIAM Review vol 43 no 1pp 129ndash159 2001

[39] D L Donoho and X Huo ldquoUncertainty principles and idealatomic decompositionrdquo IEEE Transactions on InformationThe-ory vol 47 no 7 pp 2845ndash2862 2001

[40] F Miwakeichi E Martınez-Montes P A Valdes-Sosa NNishiyama H Mizuhara and Y Yamaguchi ldquoDecomposingEEG data into spacendashtimendashfrequency components using par-allel factor analysisrdquo NeuroImage vol 22 no 3 pp 1035ndash10452004

[41] K J Friston C D Frith P F Liddle and R S J FrackowiakldquoFunctional connectivity the principal-component analysis oflarge (PET) data setsrdquo Journal of Cerebral Blood Flow andMetabolism vol 13 no 1 pp 5ndash14 1993

[42] S Makeig T-P Jung A J Bell D Ghahremani and T JSejnowski ldquoBlind separation of auditory event-related brainresponses into independent componentsrdquo Proceedings of theNational Academy of Sciences of the United States of Americavol 94 no 20 pp 10979ndash10984 1997

[43] Biomedical Signal httpwwwmedicinemcgillcaphysiovlabbiomed signalseeg nhtm

[44] S E G Nilsson and B E Andersson ldquoCorneal DC recordingsof slow ocular potential changes such as the ERG c-wave and thelight peak in clinical workmdashequipment and examples of resultsrdquoDocumenta Ophthalmologica vol 68 no 3-4 pp 313ndash325 1988

[45] OG Lins TW Picton P Berg andM Scherg ldquoOcular artifactsin EEG and event-related potentials I scalp topographyrdquo BrainTopography vol 6 no 1 pp 51ndash63 1993

[46] T W Picton P Van Roon M L Armilio P Berg N Ille andM Scherg ldquoThe correction of ocular artifacts a topographicperspectiverdquo Clinical Neurophysiology vol 111 no 1 pp 53ndash652000

[47] A S Keren S Yuval-Greenberg and L Y Deouell ldquoSaccadicspike potentials in gamma-band EEG characterization detec-tion and suppressionrdquo NeuroImage vol 49 no 3 pp 2248ndash2263 2010

[48] M Plochl J P Ossandon and P Konig ldquoCombining EEG andeye tracking identification characterization and correctionof eye movement artifacts in electroencephalographic datardquoFrontiers in Human Neuroscience vol 6 article 278 2012

[49] S Dandekar C Privitera T Carney and S A Klein ldquoNeuralsaccadic response estimation during natural viewingrdquo Journalof Neurophysiology vol 107 no 6 pp 1776ndash1790 2012

[50] G Ai N Sato B Singh and H Wagatsuma ldquoDirection andviewing area-sensitive influence of EOGartifacts revealed in theEEG topographic pattern analysisrdquo Cognitive Neurodynamicsvol 10 no 4 pp 301ndash314 2016

[51] P Berg and M Scherg ldquoDipole models of eye movements andblinksrdquo Electroencephalography and Clinical Neurophysiologyvol 79 no 1 pp 36ndash44 1991

[52] R J Croft and R J Barry ldquoRemoval of ocular artifact from theEEG a reviewrdquo Neurophysiologie Clinique vol 30 no 1 pp 5ndash19 2000

[53] I J Rampil ldquoA primer for EEG signal processing in anesthesiardquoAnesthesiology vol 89 no 4 pp 980ndash1002 1998

[54] J L Starck Y Moudden J Bobin M Elad and D DonoholdquoMorphological component analysisrdquo in Optics amp Photonics2005 p 59140Q International Society forOptics and Photonics2005

[55] S Sardy A Bruce and P Tseng ldquoBlock coordinate relaxationmethods for nonparametric signal denoising with waveletdictionariesrdquo Journal of Computational and Graphical Statisticsvol 9 pp 361ndash379 2000

[56] M Puschel and J M F Moura ldquoThe algebraic approach to thediscrete cosine and sine transforms and their fast algorithmsrdquoSIAM Journal on Computing vol 32 no 5 pp 1280ndash1316 2003

[57] X Shao and S G Johnson ldquoType-IV DCT DST and MDCTalgorithms with reduced numbers of arithmetic operationsrdquoSignal Processing vol 88 no 6 pp 1313ndash1326 2008

[58] R G Andrzejak K Lehnertz F Mormann C Rieke P Davidand C E Elger ldquoIndications of nonlinear deterministic and

Computational and Mathematical Methods in Medicine 3

120578

+

component 1

component k

separationComponentsDenoising

Morphological ComponentAnalysis (MCA)

Separated

Separated

Record

Noise

(EEG)Signal

Eye source components

Eyelidmovement Blink

(Vertical)

(Horizontal)

Figure 1 A schematic diagram of the proposed method for morphological component analysis for the EEG-EOG signal separation

the scalp EEG in an evitable manner of leaking potentialsin the electrophysiological system connecting the brainand muscular-skeletal system On the other hand differentbiological systems have different electrophysiological prop-erties and the nature will be the key to solve the complexdecomposition problem As the traditional knowledge in themedical field [43] it is known that EEG signals have specificcharacteristics on the shape of the waveform called mor-phology ldquomonomorphicrdquo ldquopolymorphicrdquo ldquosinusoidalrdquo andldquotransientrdquo types are recognized differently based on charac-teristics of a single dominant activity multiple frequenciesforming complex activity sine wave-like activity and spikesandor sharp waves (spikes in a duration of 20ndash70msec andsharp waves with a pointed peak and 70ndash200msec duration)If it is possible to decompose the recorded EEG with respectto thosemorphologies of interest this brings us a large benefitbecause it leads the way to the ldquotruerdquo EEGs

According to the electrophysiological mechanism in thenervous system coupled with myogenic potential evoked byocular movements [44 45] the rotation of an eyeball gen-erates potential with an amplitude depending on the degreeof the rotation [46] which is known as the corneoretinaldipole and observed as the staying potential of approximately500120583V asmaximum from the EOG recording in the 4ndash20Hzrange [47] The phenomena had been investigated via thestudies of saccade movements [28 48ndash50] As mentionedabove EEG and EOGs potential have specific morphologiesMorphologies of eye movements and eye blinks can beconsidered as slow change with respect to the EEG time scaleand have a bump shape with a large peak amplitude [51 52]Since the presence of repetitive peaks frequently appears inthe diagnosis of epilepsy [53] we assumed the single bump isthe typical eye blink and assumed the multiple types of slowbaseline changes are eyeball rotations as schematically shownin Figure 1

23 Decomposition Using Morphological Component Analy-sis Recently decomposition of components in image andtime series has a large expectation in applications such asminimizing of the data size for transferring the data via the

Internet MCA based methods fit for the purpose and havethe advantage in the accurate reconstruction of the originaldata after noise removal which relies on the sparsity andovercompleteness of the dictionary In the theory of MCAthe overcomplete dictionary is represented by Φ isin 119877119899times119896where 119896 is themorphological component of signal for 120601119896119896isinΓwhere Γ is the index set of dictionaries A mixed EEG signal119878 isin 119877119899 can be represented as a sparse linear combinationof the coefficient According to Chen et al (2001) [38] theovercomplete dictionary Φ is a set of redundant transformswhich are defined by a set of mathematical functions torepresent the specific morphologies In the process to obtainthe final set of coefficients for accurate reconstruction ofthe original signal the sparseness of the coefficient matrixis crucial In the theory there exists a dictionary thatcan reproduce the specific features of the signal if theappropriate iteration method is introduced to pursue theunique sparse representation The concept of sparsity andthe overcompleteness dictionary has theoretically extendedthe traditional signal decomposition to feature extractionsfocusing on multiple types of morphologies simultaneouslyDue to selection freedom of dictionaries the signal can bedecomposed with explicit dictionary [38] and sometimes itcannot be decomposed in the other form of dictionaries Adictionary is defined as collection of waveforms 120601119896119896isinΓ andthe input signal 119878 is assumed to be reconstructed by a linearcombination of a set of basesrsquo elements 120601119896 and then the signal119878 is expressed as a single vector of 119878 isin 119877119873 and satisfies119878 = 1199041 + 1199042 119904119870 where 1199041 1199042 119904119896 are subcomponentsthat is different morphologies We employed this system torecord EEG signal 119878 as shown in Figure 1 The approximatedecomposition of signal 1198781015840 into its building components canbe expressed as

119878 =119896

sum119894=1

120573119894120601119894 + 120577 = 12057311206011 + 12057321206012 + sdot sdot sdot + 120573119896120601119896 + 120577

cong 1199041 + 1199042 + sdot sdot sdot + 119904119896 (120577 ≪ 1)

= 1198781015840

(2)

4 Computational and Mathematical Methods in Medicine

Decomposition

middot middot middot

component 12057311206011

1st morphological

component 12057321206012

2nd morphological

component 120573k120601k

kth morphological

+

1206011 1206012 120601k

dictionary ΦOvercomplete

Arbitrary EEGsignal

Figure 2 A schematic diagram for EEG signal decomposition using explicit dictionary

Therefore 120573 is the target coefficients for reconstruction ofthe original EEG signal based on the assumption 120577 ≪ 1which means that the remainder 120577 is negligibly small In theconsideration that 120577 represents the noise part (2) withoutnoise can be written as

1198781015840 =119896

sum119894=1

120573119894120601119894 = 120573Φ (3)

Equation (3) is consistent with (1)The problem to solve ishow optimized coefficients can be derived and the equationis rewritten as follows

120573opt1 120573opt2 120573opt

119896 = argmin1205731120573119896

119896

sum119894=1

100381710038171003817100381712057311989410038171003817100381710038170

subject to 1198781015840 =119896

sum119894=1

120573119894120601119894(4)

The problem is how the MCA concept can be embeddedin the systems to decompose biomedical signal especiallyfor EEG signal In this formulation time-frequency param-eters are totally consistent with traditional decompositionmethods which can be applied to the biomedical signaldecomposition such as PCA wavelets and ICA in the senseof the single set of bases One advantage of MCA is theavailability of the combination of multiple basis functionsincluding traditional basis like wavelet decomposition as apart of the component called redundant transforms ThusMCA is expected to reveal what kind of the specificityexists in time-frequency properties of EEG data Concreteproblems in this viewpoint can be addressed as (a) what isthe best combination of dictionaries of MCA for the EEGdecomposition and (b) what is the true EEG signal in theform of obtained sparsest representation based on selecteddictionaries 120601119896

Figure 2 schematically illustrates the MCA decomposi-tion process of arbitrary EEG signal that is assumed to bea linear combination of 119896 morphological component to bedecomposed using explicit dictionaries

In the assumption of three types of dictionaries (119896 = 3)the following three cases are considerable by focusing onindividual dictionaries

Case 1 An overcomplete dictionary 1206011 is representing thecomponent 1199041 1206011 isin 119872119873times1198711 where 119873 ≫ 1198711 119873 being thenumber of samples that is the number of time points in therecorded data

(i) For 1199041 120573opt1 = argmin1205731205730 subject to 1199041 = 1206011120573

while solving this equation leads to the sparse solution(120573opt1 0 lt 120573opt

12 0 120573opt13 0)

(ii) For 1199042 120573opt12 = argmin1205731205730 subject to 1199042 = 1206011120573 while

solving this equation leads to nonsparse solution

(iii) For 1199043 120573opt13 = argmin1205731205730 subject to 1199043 = 1206011120573 while

solving this equation also leads to nonsparse solution

Case 2 An overcomplete dictionary 1206012 is representing thecomponent 1199042 1206012 isin 119872119873times1198712 where119873 ≫ 1198712

(i) For 1199042 120573opt2 = argmin1205731205730 subject to 1199042 = 1206012120573

while solving this equation leads to the sparse solution(120573opt2 0 lt 120573opt

23 0 120573opt21 0)

(ii) For 1199043 120573opt23 = argmin1205731205730 subject to 1199043 = 1206012120573 while

this equation also has nonsparse solution(iii) For 1199041 120573opt

21 = argmin1205731205730 subject to 1199041 = 1206012120573 whilethis equation also has nonsparse solution

Case 3 An overcomplete dictionary 1206013 is representing thecomponent 1199043 1206013 isin 119872119873times1198713 where119873 ≫ 1198713

(i) For 1199043 120573opt3 = argmin1205731205730 subject to 1199043 = 1206013120573

while solving this equation leads to the sparse solution(120573opt3 0 lt 120573opt

32 0 120573opt31 0)

(ii) For 1199042 120573opt32 = argmin1205731205730 subject to 1199042 = 1206013120573 while

solving this equation leads to nonsparse solution

(iii) For 1199041 120573opt31 = argmin1205731205730 subject to 1199041 = 1206013120573 while

solving this equation leads to nonsparse solution

Computational and Mathematical Methods in Medicine 5

Theoretically speaking by using three dictionaries MCAcan divide the signal into components depending on eachdictionary of 1206011 1206012 and 1206013 as the sparest representation of allsignalsThe sparse components are describedmathematicallyas

120573opt1 120573opt2 120573opt3 = argmin

120573112057321205733

1003817100381710038171003817120573110038171003817100381710038170 +

1003817100381710038171003817120573210038171003817100381710038170 +

1003817100381710038171003817120573310038171003817100381710038170

subject to 119878 = 12057311206011 + 12057321206012 + 12057331206013(5)

This formulation states a nonconvex optimization problemto separate the components of the signal However each 120601119896needs to be efficient in a specific component while it remainsnoneffective in other signal components The nonconvexoptimization problem indicated that it is difficult to solve (5)in a simple manner and then the Basis Pursuit (BP) method[54] was proposed based on the idea that the replacementof 1198970 norm by 1198971 norm results in the error minimizationAccording to the improvement the BP [54] was successfullyformulated into an accurate method to represent the sparestof components which is described as

120573opt1 120573opt2 120573opt3 = argmin

120573112057321205733

3

sum119894=1

100381710038171003817100381712057311989410038171003817100381710038171 + 120582

1003817100381710038171003817100381710038171003817100381710038171003817119878 minus3

sum119894=1

1206011198941205731198941003817100381710038171003817100381710038171003817100381710038171003817

2

2

(6)

In this system 1198972 norm is considered to be the errornorm based on the assumption that the residual acts asa white zero-mean Gaussian noise and another importantfinding is the representation of noise models 1198971 Laplaciannoise with the consideration of 119897infin uniformly distributednoise in the form of the optimization problem 120582 representsthe stopping criterion or threshold By using the Block-Coordinate-Relaxation (BCR) method [55] the optimizationproblem can be solved in finite computation time Theprocedure is given below

(1) Initialize = 119868max number of iterations = 119871 threshold120575 = 120582 lowast 119868max

(2) Perform 119871 timesPart (1) update 1199041 assuming 1199042 and 1199043 are fixed

(a) Calculate the residual 119877 = 119878 minus 1199042 minus 1199043(b) Calculate 1205731 = 1206011198791119877(c) Threshold the coefficient of 1205731 and obtain 1205731(d) Reconstruct 1199041 by 1199041 = 12060111205731

Part (2) update 1199042 assuming 1199041 and 1199043 are fixed

(a) Calculate the residual 119877 = 119878 minus 1199041 minus 1199043(b) Calculate 1205732 = 1206011198792119877(c) Threshold the coefficient of 1205732 and obtain 1205732(d) Reconstruct 1199042 by 1199042 = 12060121205732

Part (3) update 1199043 assuming 1199041 and 1199042 are fixed

(a) Calculate the residual 119877 = 119878 minus 1199041 minus 1199042(b) Calculate 1205733 = 1206011198793119877

(c) Threshold the coefficient of 1205733 and obtain 1205733(d) Reconstruct 1199043 by 1199043 = 12060131205733

(3) Update the threshold by 120575 = 120575 minus 120582(4) If 120575 gt 120582 return to Step (2) else finish

3 Hypothesis

In the present study we hypothesized that appropriate threedictionaries of MCA specifically for EEG recording datawere undecimated wavelet transform (UDWT) discrete sinetransform (DST) andDIRAC (aka standard unit vector basisor Kronecker basis) Fadili et al [17] UDWT contributes toseparating slow and bump morphologies for EOG and EEGtransient slow changes DST is for monomorphic and poly-morphic EEG components (major EEG parts) and DIRAC isfor spike type activities in transient EEGs In comparison inthe simulated experiment we used the discrete cosine trans-form (DCT) discrete sine transform (DST) [56 57] and localdiscrete cosine transform (LDCT) dictionaries formajor EEGparts For the verification of the hypothesis the intracranialEEG (iEEG) data was assumed to be ldquotrue EEGrdquo signal whichwas recorded from the real brain activity and artificial EOGsincluding bump and slow changes were introduced and theperformance of the accurate reconstruction of the true EEGswas examined In iEEG there are two types of the data underthe conditions of eye-closing and eye-opening 42 Accordingto the neuroscientific evidence EEGs have a clear peakin the low-frequency range around 10Hz in the frequencyspectrum under the eye-closing condition 42 In the Resultscorrelation coefficient (cc) was used for the validation ofaccuracy in reconstruction and the frequency spectrum wasfor the validation of the nature of the information containedin EEGs

4 Results

For verification of our hypothesis in the computer experi-ments three types of the data were used (1) all simulateddata (2) a combination of real iEEG and simulated EOGand (3) recording of real EEG-EOG data and our proposedmethod was validated

41 Simulated Data In the first place two simulated signalsources were prepared for the simple test of the proposedmethod Initially Yong et al [36] proposed a combinationof the wavelet DCT and DIRAC for EEG artifact removalswhile their results could not tell how effective the methodwas in a qualitative manner In our experiment the firstsource signal consisted of a cosine wave which was assumedto be a monomorphic EEG signal and the second sourceconsisted of blinks component with three bumps designedas usual EOG signals The simulated signal as a mixture ofthe two sources and white noise (120578 = 20) was shownin Figure 3(a) where 120578 was defined as the percentage ofthe maximum amplitude of the input signal Our proposedMCA method was applied to separate the components fromthe simulated signal with the explicit dictionaries UDWT

6 Computational and Mathematical Methods in Medicine

02

0

1

2

024

1000 20000

minus2

minus2

Samples

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)1st signal source

2nd signal source

Combined signal (source)

(a)

0

15

0

2

0

1

1000 20000

minus2

Samples

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

1st separated component (UDWT)

2nd separated component (DCT)

3rd separated component (DIRAC)

(b)

0

2

4

1000 20000

minus2

Samples

Pote

ntia

l (V

)

Combined signal (source)Combination of separated component (reconstructed)

(c)

Figure 3 An example of simulated signal for decomposition and (a) the cosine with bump and spikes signals and combined signal withwhite noise (120578 = 20) (b) separated components with explicit dictionaries UDWT-DCT-DIRAC and (c) comparison between combinedsignal and sum of separated components (cc = 099)

DCT and DIRAC as shown in Figure 3(b) as a replicationtest The correlation coefficient between the simulated signaland the sum of all components was higher than 099 andthe simulated result proved the accuracy of decomposedcomponents byMCAwithUDWTDCT andDIRAC explicitdictionaries (Figure 3(c))

42 Simulated EOGContaminated iEEG Signal Theprevioussection was a simple example of the simulated data In thissection we introduced a new validation way to test theproposed method in a qualitative manner The real iEEGsignals were obtained under the closing eye condition Thelinear combination of simulated EOG and real iEEG signalswas used for the test In this case we assumed that iEEGhad already included a usual level of the white noise andthen did not add further noise additionallyThe iEEG datasetwas given by Andrzejak et al [58] with 100 trials andthe sampling rate was at 17361Hz (000576 ssample) and210(=1024) samples took about 6 s (589824 s) The linearcombination of simulated EOG and iEEG signals was appliedfor the validation

There were different combinations for simulated EOG asassumed artificial eye movement which was considered asthe step function and eye blinks by bump signalThe flatnesssignals with elevations with slow time scales compared with

the EEG time scale represent the gaze-type eyeball rotationsThe signals can be reconstructed by a mathematical methoddefined by the rate of change ()1015840 of which satisfies that119905 | ()1015840 gt 0 should be 0 Thus the definition of the EOGsmoothness is described as

()1015840119868 =

()1015840 (119905) ()1015840 (119905) = 00 ()1015840 (119905) gt 0

(7)

where 119868 = 119905 | ()1015840 = 0 leads to ()1015840119868 equiv 0 according toits definition as shown in Figure 4(b) In addition the bumpssignal was considered as the blink type EOG signal shownin Figure 4(c) Figure 4(d) showed the schematic examplefor the semisimulated signal In the same way 100 datasetsof semisimulated signals with a random combination ofcomponents in time series were used for the validation

Figures 5(a) 5(b) and 5(c) demonstrated a set of resultsfor the decomposition of the semisimulated signal by explicitdictionaries depending on the combination of dictionariesAsmentioned in Section 23 the stopping criterion dependedon 120582 lowast threshold and the parameters in this comparativestudy used a different combination of explicit dictionaries(UDWT-DCT-DIRAC UDWT-DST-DIRAC and UDWT-LDCT-DIRAC) and different type of thresholds either hardand soft and 120582 value varied from 3 to 5

Computational and Mathematical Methods in Medicine 7

200

0

minus200Pote

ntia

l (V

)

Samples40003000200010000

Intracranial real EEG signal

(a)

500

0

minus500Pote

ntia

l (V

)

Samples40003000200010000

Artificial eye movement-related EOG signal

(b)

500

0

minus500Pote

ntia

l (V

)

Samples40003000200010000

Artificial blink EOG signal

(c)

Samples

1000

0

minus1000Pote

ntia

l (V

)

40003000200010000

Combined signal (EEG + EOG)

(d)

Figure 4 A systemic representation of differentmorphological signals (a) intracranial EEG signal (b) artificial block EOG signal (c) artificialblink EOG signal and (d) combined signal

Figures 6(a) and 6(b) showed the averaged cc of decom-posed component by a respective combination of explicitdictionaries with hard and soft thresholds For EEG signaldecomposition performance cc between iEEG and eitherDST DCT or LDCT component was evaluated dependingon the three combination types (Figure 6(a)) For EOGsignal decomposition performance cc between EOG andUDWT component was evaluated (Figure 6(b)) In compari-son between hard and soft thresholds the average value of thehard threshold is around 06 which is larger than that in thesoft threshold while the average value of the soft threshold isaround 095 demonstrating fewer variances than those in thehard thresholdThismethod indicates thatUDWTdictionarywith a soft threshold is the stable performance according tothe fitness of the morphological property in this case

There were similar variances and average values in theevaluation of EEG signal decomposition using the timedomain and then we introduced a measure in the frequencydomain As mentioned in Section 22 EEG signals carryinformation to represent the current brain stage in thespecific tendency in the frequency domain such as having asynchronized neural activities by showing the existence of apeak in the frequency spectrum The EEG data used in theevaluation showed a peak around 10Hz under the closingeye condition and a peak around 50Hz under the openingeye condition Therefore in the frequency analysis a 10Hzpeak will be an index to tell how much the reconstructedsignal preserves the original information contained in theoriginal iEEG data under closing eye condition Figure 7showed the averaged normalized FFT as the comparisonbetween three combinations of the dictionaries InterestinglyalthoughDSTDCT and LDCT single components seemed toreconstruct the EEGs because of a high cc value in the timedomain the frequency spectrum analysis clarified the factthat the single component cannot reproduce the necessarytendency of EEG signals peak Meanwhile the combination

of 2nd and 3rd components which means oscillatory andspike components successfully reproduced the EEG signaltendency suggesting the importance of the spike informa-tion that presumably synchronizes background oscillatorybehaviors The 10Hz peak can be reproduced according toparameter conditions easily However 50Hz peak is difficultto be reproduced especially for LDCT-DIRAC componentin every case In the viewpoint of the tolerance in thechange of the threshold value the soft threshold methodshowed the robust performance of the signal informationpreservation which is consistent with the result of EOGsshown in Figure 6 As shown in Figure 8 the reconstructionaccuracy of the frequency profile by two dictionaries wasproved by a significant difference between the results of twomorphological and single morphological components (119905-test119901 lt 001 in both hard and soft thresholds) This evidencesuggests the importance of the DIRAC component for EEGsignals which was not equivalent to the noise or rathercarrying some information

43 Decomposition of EOG from Real EEG Data

431 EEG Data The real scalp EEG and EOG data wereobtained from the data demonstrated in the paper writtenby Ai et al (2016) [50] These data were recorded from23 EEG channels (FP1 FP2 F7 F3 Fz F4 F8 FC5 FC1FC2 FC4 T7 C3 Cz C4 T8 CP1 CP2 P3 Pz P4 O1and O2) and 7 EOG channels (V1u V1d V2u and V2dvertical EOG ⟨VEOG⟩ electrodeswere placed on supraorbitaland infraorbital rims of each eye HL and HR horizontalEOG ⟨HEOG⟩ electrodes were on the left and right outercanthi Vz was on the forehead approximately 25mm abovethe nasion) respectively according to 10ndash20 InternationalSystem (BrainAmp amplifier Brain Products GmbH) fromthe 8 participants seated in a comfortable armchair withthe base adjusted according to a participant height Theeyes of the participants were fixed straightly to the fixation

8 Computational and Mathematical Methods in Medicine

UDWT DST DIRAC400

0

minus400

Pote

ntia

l (V

)

200

0

minus200

0

100

minus100

Samples400020000

Samples400020000

Samples400020000

(a)

DCTUDWT DIRAC

400

0

minus400

Pote

ntia

l (V

)

200

0

minus200

0

100

minus100

Samples400020000

Samples400020000

Samples400020000

(b)

UDWT LDCT DIRAC400

0

minus400

Pote

ntia

l (V

)

200

0

200

0

minus200

Samples400020000

Samples400020000

Samples400020000

(c)

Figure 5 Components separation byMCA (a) explicit dictionaries are UDWT DST andDIRAC (b) UDWT DCT andDIRAC (c) UDWTLDCT and DIRAC respectively at 120582 = 4 The original signal for decomposition was shown in Figure 4(d) as combined signal

cross in the center of the monitor screen The stimulus wasdisplayed by a CRT monitor A chin support frame wasused to keep the participantrsquos head position fixed and fixtheir head to the supporting frame without laying their chinson the supporting bar to avoid the jaw clenching artifactThe distance between eyes and monitor was set to 70 cmThe sampling rate was 500Hz The whole details of theexperiment protocols were given in Ai et al (2016) [50]

432 Results with Real EEG-EOG According toAi et al [50]the real EEG-EOG data were divided into 4 sessions Eachsession had 12 tasks of eye movement The two EOG signalswere collected from ldquoV1d-V1urdquo and ldquoV2d-V2urdquo at right andleft sides of the eye as shown in Figure 9 and both signalsshowed the same kind of tendency because vertical EOG

propagated symmetrically in an anterior-posterior directionFigure 10 showed the real EEG signals were taken from someelectrodes for example Fp1 Fp2 Cz O1 and O2 whichrepresent EOG influence depending on the frontal centraland occipital parts of the brain

The selected explicit dictionaries were used to representthe targeted component for the EEG and EOG signal EEGand EOG were distinguished based on the morphologythat was observed in the EEG and EOG The lateral eyemovements mostly affect frontal electrodes [45] ThereforeFp1 electrode was used to decompose and demonstratethe effectiveness of our proposed method with MCA asshowed in Figure 11 and the same method was applied toall the 23 electrodes All EEG signals were morphologicallydecomposed with redundant transform

Computational and Mathematical Methods in Medicine 9

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

Aver

aged

corr

elat

ion

coeffi

cien

t

06

04

08

1

(a) cc between iEEG and 2nd comp (hard)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5Av

erag

ed co

rrel

atio

n co

effici

ent

06

04

08

1

(b) cc between iEEG and 2nd comp (soft)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

06

04

08

1

Aver

aged

corr

elat

ion

coeffi

cien

t

(c) cc between EOG and UDWT (hard)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

Aver

aged

corr

elat

ion

coeffi

cien

t

06

04

08

1

(d) cc between EOG and UDWT (soft)

Figure 6 A comparison between cc of decomposed morphological component with iEEG signal and artificial EOG with hard and softthresholds The mean value and standard deviation were calculated from all 100 decomposed datasets by explicit dictionaries (a) Secondmorphological component was decomposed by DST DCT and LDCT with hard and (b) soft threshold respectively (c) First morphologicalcomponent was decomposed by UDWT with a hard threshold and (d) soft threshold respectively 100 trials of iEEG and artificial EOG wereused

10 Computational and Mathematical Methods in Medicine

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

0 20 40 60 80

0

2

4

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(a) Hard (120582 = 3)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(b) Hard (120582 = 4)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(c) Hard (120582 = 5)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(d) Soft (120582 = 3)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(e) Soft (120582 = 4)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Nor

mal

ized

pow

er (d

B)

Frequency (Hz)

minus2

(f) Soft (120582 = 5)

Figure 7 An averaged normalized FFT obtained from 100 of iEEG and combination of two morphological components and singlemorphological component at 120582 varies from 3 to 5 with hard and soft thresholds

Figure 11(a) demonstrated the decomposition of compo-nents by the first explicit dictionary it was divided into threedifferent morphologies of the EEG signal Figures 11(b) and11(c) showed the second and the third explicit dictionary ofredundant transform respectively The overcomplete dictio-nary was a combination of redundant transforms that char-acterized the component in a different morphology Accord-ingly one of redundant transforms can be differentiated intodecomposed components by overcomplete dictionaries Thefirst component was decomposed by ldquoUDWTrdquo of each over-complete dictionary and was analyzed via the slow and blinktype morphology The second component was decomposedby ldquoDCTrdquo ldquoDSTrdquo and ldquoLDCTrdquo and was analyzed via thebackground of the signal which was similar to the EEG signal

and the third component was decomposed by ldquoDIRACrdquo andwas analyzed via the unexpected spikeThe first overcompletedictionary decomposed the EEG signal without changingthe monomorphic polymorphic and transient propertiesThe cc between the original signal and the summation of alldecomposed components was close to one Figure 12 showedthe raw EOG signal taken from the vertical and horizontalchannel and first decomposed component taken from Fp1Fp2 Cz O1 and O2 respectively

Table 1 showed individual cc of original EEG signals andrecomposed EEG signals from the combination of compo-nents with respect to different channels and combinationsof dictionaries Table 2 showed the cc between filter rawEOG signal taken from vertical and horizontal channels and

Computational and Mathematical Methods in Medicine 11

3 4 5

02

03

04

05

06

07

08

09

Aver

aged

FFT

corr

elat

ion

coeffi

cien

t

01

1

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

lowast lowast lowast

(a) Hard threshold

3 4 5

Aver

aged

FFT

corr

elat

ion

coeffi

cien

t02

03

04

05

06

07

08

09

01

1

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

lowast lowast lowast

(b) Soft threshold

Figure 8 A comparison of FFT correlation coefficients between iEEG data and morphological component decomposed by explicitdictionaries lowastSignificant differences (119901 lt 005) (a) Combined two morphological components and (b) single morphological componentMean value and standard deviation calculated from all 100 decomposed datasets by explicit dictionaries with hard and soft thresholds

400

Pote

ntia

l (V

)

200

0

minus200

400

Pote

ntia

l (V

)

200

0

minus200

Samples20000 1000

EOG (V1u-V1d)

EOG (V2u-V2d)

Figure 9 An example of EOG signal taken from right and left sideof eyes

decomposed first component from Fp1 Fp2 Cz O1 and O2respectively

5 Discussion

Artifact contamination in EEG signal has been a com-mon important issue in neurobiological event diagnosis and

Table 1 cc of original signal and sum of the decomposed compo-nents

EEG channelCorrelation coefficient

UDWT-DST-DIRAC

UDWT-DCT-DIRAC

UDWT-LDCT-DIRAC

Fp1 09921 plusmn 0014 09921 plusmn 0014 09932 plusmn 0013Fp2 0992 plusmn 017 09919 plusmn 018 09932 plusmn 014Cz 09898 plusmn 01 09899 plusmn 01 09908 plusmn 009O1 09836 plusmn 015 09836 plusmn 016 09869 plusmn 012O2 09855 plusmn 013 09856 plusmn 013 09849 plusmn 015

neuroscientific researchThevariousmethodswere applied toremove the artifacts from EEG [2 11ndash13 21 23 24 26ndash28 52]The decomposition based analysis was used in removal ofEOG artifacts in EEG [22 27 28 30 40 42] Howeverthose methods lack the elucidation of what the nature ofEEG signals is in the viewpoint of the signal analysis and asystematic approach was required by treating the sparsity andnonlinearity of the signal in the time domain

12 Computational and Mathematical Methods in Medicine

0

0

50

Fp1

Fp2

Cz

O1

O2

100

0

minus100

minus50

minus40

Pote

ntia

l (V

)

0

50

minus50

Pote

ntia

l (V

)

050

minus50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

Figure 10 An example of real EEG signal taken from Fp1 Fp2 Cz O1 and O2 electrode channels

Table 2 cc between filtered EOG and UDWT component decomposed by UDWT dictionary

EOG channels EEG channelsFp1 Fp2 Cz O1 O2

Correlation coefficientUDWT-DST-DIRACV1d 06777 0657 07267 09223 06445V1u 06814 0646 06606 09419 06354V2d 0916 0906 09402 0882 05402V2u 02332 02268 02353 06388 08494H1 08582 0847 08444 06902 05839H2 09419 09468 09559 07476 04752

UDWT-DCT-DIRACV1d 06792 06595 068 09213 06352V1u 06835 06396 06424 09581 06585V2d 09193 0902 09362 08764 05145V2u 02331 02183 02316 06639 08919H1 08593 08507 08626 06759 05376H2 09442 09465 09662 07266 04346

UDWT-LDCT-DIRACV1d 06794 06403 07219 08892 065V1u 06443 06279 06459 08196 05381V2d 09142 09072 09395 09592 06506V2u 02351 02235 02383 03747 06804H1 08637 08449 08471 07638 05734H2 09586 09558 09577 08826 05598

Computational and Mathematical Methods in Medicine 13

0

50

0

20

UDWT

DCT

DIRAC

0

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus30

(a)

UDWT

DST

DIRAC

0

0

20

0

50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus20

minus20

(b)

0

0

50

100

0

UDWT

LDCT

DIRAC

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus20

minus40

minus80

(c)

Figure 11 Component separated fromEEG (Fp1 electrode) signal by explicit dictionaries (a)UDWT-DCT-DIRAC (b)UDWT-DST-DIRACand (c) UDWT-LDCT-DIRAC respectively

This study revealed the nature of EEG signals in the senseof morphologies contained in the original signal by usingMCA The UDWT was used to decompose the slow andbump morphology The DCT DST and LDCT transformwere used to decompose the EEG signal Spike typemorphol-ogy was decomposed by DIRAC Redundant transforms ofDCT and DST have a similar capability in representing themorphology of oscillatory activities Therefore we used theDCT LDCT and DST dictionaries for validations of EEGsignal The detailed significant differences in morphology ofDCT and DST were given in past studies [56 57] while inour analysis there were no significant differences The rightcombination of redundant transforms to form overcompletedictionary revealed the desired decomposition in principle

In Section 42 ldquoBlocksrdquo ldquoBumpsrdquo similar to simulatedEOG signal defined in past studies [59ndash61] as shown in

Figure 4 and EEG data [58] were used to validate ourpurposed method The ldquoBlocksrdquo with abrupt changes weresimilar to the horizontal and vertical eye movements sim-ply as described by past studies [25 51] For the sake ofsimplicity in the present study ldquoBumpsrdquo were used as arepresentative signal form as eye blinks that happens inunexpected timings as illustrated in Figure 5 The separationof components by given dictionary works well in this evalu-ation but the further analysis is necessary for the evaluationof the signal decomposition with complex eye movementswhich requires presumably various redundant dictionariesIn the verification of the component discrimination as shownin Figures 6 and 7 the accuracy of the averaged EOGcomponent decomposition was above 90 which suggests aplausible performance even in the complex eye movementsThe combined DST and DIRAC dictionaries had better

14 Computational and Mathematical Methods in Medicine

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

Samples20000 1000

V1u

H1

(a) UDWT components separated by UDWT-DST-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(b) UDWT components separated by UDWT-DCT-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(c) UDWT components separated by UDWT-LDCT-DIRAC

Figure 12 UDWT component taken from Fp1 Fp2 Cz O1 and O2 separated by UDWT-DCT-DIRAC UDWT-DST-DIRAC and UDWT-LDCT-DIRAC respectively

decomposition performance than others while DST andDCT theoretically have no meaningful difference The usageof iEEG as the true EEG signal had a large benefit whichcan be used for the performance test for past proposedmethods like ICA and PCA consistently Our proposedmethod successfully demonstrated the performance in cc andthe frequency profile especially in Section 42 while in theserious discussion of the real EEG and EOG signals the DSTor DCT component exhibited a baseline fluctuation of thesignal which denotes the persistence of the EOG componentor other slow frequency artifacts noises and the factor willbe improved by the fine-tuned design of the DST or DCTdictionary with a band pass filter function In addition thethreshold problem exits in the optimization algorithm andnumber of iterations [37]

The EEG decomposition had not mark with a combi-nation of a second and a third component of EEG signal

decomposed by ldquoDST DCT and LDCTrdquo andDIRAC respec-tively based on the morphology Therefore the accuratecombination in the further perspective will be considerableEven the combination of all components and the mixedsignal or real EEG signal had cc above 97 for all redundanttransforms as is analyzed in the frequency spectrum thesignal morphology has further meaning in the viewpointof the signal transmission The MCA method has such anextended and flexible availability for signal analyses

6 Conclusion

Morphological Component Analysis methodology wasapplied to the simulated semisimulated and real EOGand EEG signal The successful decomposition of the EOGand EEG signal into their morphological component wasdemonstrated It seems to be that the EEG signals and

Computational and Mathematical Methods in Medicine 15

artifacts in EEG have been represented by different explicitdictionaries We analyzed the EEG signals involved with theEOG artifacts which were influenced by task conditionsTheDIRAC explicit dictionary decomposed the EEG signal intospike-like activities which may be related to the transientproperty of EEG UDWT explicit dictionary representsslow movement or bumps DCT DST and LDCT explicitdictionaries represent dominant signal that represents EEGsor pure tones signals as monomorphic and polymorphicactivities These results suggested that the effectivenessof MCA in ocular artifacts removal from the EEG rawsignal was derived from signal morphology characterizedas slow and smooth change of EOG time series In thefurther analysis the MCA is required to compare withother competing methods for the EEG and EOG signaldecomposition

Competing Interests

The authors have declared that no competing interests exist

Acknowledgments

This work was partly supported by JSPS KAKENHI 16H01616and 26240032 and theNewEnergy and Industrial TechnologyDevelopment Organization (NEDO) ldquoNext-Generation Arti-ficial Intelligence (3) Base Technology for Next-GenerationAIrdquo (Automated Driving Task) and the collaborative researchproject with Fujitsu Ten Limited

References

[1] J P Donoghue J N Sanes N G Hatsopoulos and G GaalldquoNeural discharge and local field potential oscillations in pri-mate motor cortex during voluntary movementsrdquo Journal ofNeurophysiology vol 79 no 1 pp 159ndash173 1998

[2] J A Uriguen and B Garcia-Zapirain ldquoEEG artifact removalmdashstate-of-the-art and guidelinesrdquo Journal of Neural Engineeringvol 12 no 3 Article ID 031001 2015

[3] C Kamarajan and B Porjesz ldquoAdvances in electrophysiologicalresearchrdquoAlcohol Research Current Reviews vol 37 no 1 article53 2015

[4] L F Nicolas-Alonso and J Gomez-Gil ldquoBrain computer inter-faces a reviewrdquo Sensors vol 12 no 2 pp 1211ndash1279 2012

[5] L Mayaud M Congedo A Van Laghenhove et al ldquoA compar-ison of recording modalities of P300 event-related potentials(ERP) for brain-computer interface (BCI) paradigmrdquo Neuro-physiologie CliniqueClinical Neurophysiology vol 43 no 4 pp217ndash227 2013

[6] X-Y Wang J Jin Y Zhang and B Wang ldquoBrain controlhuman-computer integration control based on brain-computerinterfacerdquo Acta Automatica Sinica vol 39 no 3 pp 208ndash2212013

[7] G Al-Hudhud ldquoAffective command-based control system inte-grating brain signals in commands control systemsrdquo Computersin Human Behavior vol 30 pp 535ndash541 2014

[8] J L Sirvent Blasco E Ianez A Ubeda and JM Azorın ldquoVisualevoked potential-based brain-machine interface applications toassist disabled peoplerdquo Expert Systems with Applications vol 39no 9 pp 7908ndash7918 2012

[9] H Cecotti ldquoSpelling with non-invasive Brain-Computer Inter-facesmdashcurrent and future trendsrdquo Journal of Physiology Parisvol 105 no 1ndash3 pp 106ndash114 2011

[10] I S Kotchetkov B Y Hwang G Appelboom C P Kellnerand E S Connolly Jr ldquoBrain-computer interfaces militaryneurosurgical and ethical perspectiverdquo Neurosurgical Focusvol 28 no 5 article no E25 2010

[11] R N Vigario ldquoExtraction of ocular artefacts from EEG usingindependent component analysisrdquo Electroencephalography andClinical Neurophysiology vol 103 no 3 pp 395ndash404 1997

[12] W Zhou and J Gotman ldquoAutomatic removal of eye movementartifacts from the EEG using ICA and the dipole modelrdquoProgress in Natural Science vol 19 no 9 pp 1165ndash1170 2009

[13] R Sameni andCGouy-Pailler ldquoAn iterative subspace denoisingalgorithm for removing electroencephalogram ocular artifactsrdquoJournal of Neuroscience Methods vol 225 pp 97ndash105 2014

[14] M Breakspear and J R Terry ldquoDetection and description ofnon-linear interdependence in normal multichannel humanEEG datardquo Clinical Neurophysiology vol 113 no 5 pp 735ndash7532002

[15] U R Acharya O Faust N Kannathal T Chua and S Laxmin-arayan ldquoNon-linear analysis of EEG signals at various sleepstagesrdquo Computer Methods and Programs in Biomedicine vol80 no 1 pp 37ndash45 2005

[16] L I Aftanas and S A Golocheikine ldquoNon-linear dynamiccomplexity of the human EEGduringmeditationrdquoNeuroscienceLetters vol 330 no 2 pp 143ndash146 2002

[17] M J Fadili J-L Starck J Bobin and Y Moudden ldquoImagedecomposition and separation using sparse representations anoverviewrdquo Proceedings of the IEEE vol 98 no 6 pp 983ndash9942010

[18] K J Blinowska and P J Durka ldquoUnbiased high resolutionmethod of EEG analysis in time-frequency spacerdquo Acta Neuro-biologiae Experimentalis vol 61 no 3 pp 157ndash174 2001

[19] E Imani H-R Pourreza and T Banaee ldquoFully automateddiabetic retinopathy screening usingmorphological componentanalysisrdquo Computerized Medical Imaging and Graphics vol 43pp 78ndash88 2015

[20] E Imani M Javidi and H-R Pourreza ldquoImprovement ofretinal blood vessel detection using morphological componentanalysisrdquo Computer Methods and Programs in Biomedicine vol118 no 3 pp 263ndash279 2016

[21] A S Al-Fahoum and A A Al-Fraihat ldquoMethods of EEG signalfeatures extraction using linear analysis in frequency and time-frequency domainsrdquo ISRN Neuroscience vol 2014 Article ID730218 7 pages 2014

[22] M Zibulevsky and B A Pearlmutter ldquoBlind source separationby sparse decomposition in a signal dictionaryrdquoNeural Compu-tation vol 13 no 4 pp 863ndash882 2001

[23] N P Castellanos andVAMakarov ldquoRecovering EEGbrain sig-nals artifact suppression with wavelet enhanced independentcomponent analysisrdquo Journal of Neuroscience Methods vol 158no 2 pp 300ndash312 2006

[24] J Hou K Morgan D M Tucker et al ldquoAn improved artifactsremoval method for high dimensional EEGrdquo Journal of Neuro-science Methods vol 268 pp 31ndash42 2016

[25] P Berg and M Scherg ldquoA multiple source approach to thecorrection of eye artifactsrdquo Electroencephalography and ClinicalNeurophysiology vol 90 no 3 pp 229ndash241 1994

[26] P K Sadasivan and D Narayana Dutt ldquoSVD based techniquefor noise reduction in electroencephalographic signalsrdquo SignalProcessing vol 55 no 2 pp 179ndash189 1996

16 Computational and Mathematical Methods in Medicine

[27] C A Joyce I F Gorodnitsky andMKutas ldquoAutomatic removalof eye movement and blink artifacts from EEG data using blindcomponent separationrdquo Psychophysiology vol 41 no 2 pp 313ndash325 2004

[28] G L Wallstrom R E Kass A Miller J F Cohn and N A FoxldquoAutomatic correction of ocular artifacts in the EEG a com-parison of regression-based and component-based methodsrdquoInternational Journal of Psychophysiology vol 53 no 2 pp 105ndash119 2004

[29] S M Gordon V Lawhern A D Passaro and K McDowellldquoInformed decomposition of electroencephalographic datardquoJournal of Neuroscience Methods vol 256 pp 41ndash55 2015

[30] D StuderUHoffmann andTKoenig ldquoFromEEGdependencymultichannel matching pursuit to sparse topographic EEGdecompositionrdquo Journal of Neuroscience Methods vol 153 no2 pp 261ndash275 2006

[31] J-L Starck M Elad and D Donoho ldquoRedundant multiscaletransforms and their application for morphological componentseparationrdquo Advances in Imaging and Electron Physics vol 132pp 287ndash348 2004

[32] P J Franaszczuk G K Bergey P J Durka andHM EisenbergldquoTime-frequency analysis using thematching pursuit algorithmapplied to seizures originating from the mesial temporal loberdquoElectroencephalography and Clinical Neurophysiology vol 106no 6 pp 513ndash521 1998

[33] P J Durka A Matysiak E M Montes P V Sosa and K JBlinowska ldquoMultichannel matching pursuit and EEG inversesolutionsrdquo Journal of Neuroscience Methods vol 148 no 1 pp49ndash59 2005

[34] J Bobin J-L Starck J Fadili and Y Moudden ldquoSparsityand morphological diversity in blind source separationrdquo IEEETransactions on Image Processing vol 16 no 11 pp 2662ndash26742007

[35] P J Durka D Ircha and K J Blinowska ldquoStochastic time-frequency dictionaries formatching pursuitrdquo IEEE Transactionson Signal Processing vol 49 no 3 pp 507ndash510 2001

[36] X Yong R K Ward and G E Birch ldquoGeneralized morpholog-ical component analysis for EEG source separation and artifactremovalrdquo in Proceedings of the 4th International IEEEEMBSConference on Neural Engineering (NER rsquo09) pp 343ndash346Antalya Turkey May 2009

[37] B Singh G Ai and H Wagatsuma ldquoAn electrooculographyanalysis in the time-frequency domain using morphologicalcomponent analysis toward the development of mobile BCIsystemsrdquo in Universal Access in Human-Computer InteractionAccess to Interaction 9th International Conference UAHCI 2015Held as Part of HCI International 2015 Los Angeles CA USAAugust 2ndash7 2015 Proceedings Part II vol 9176 of Lecture Notesin Computer Science pp 528ndash537 Springer Berlin Germany2015

[38] S S Chen D L Donoho and M A Saunders ldquoAtomicdecomposition by basis pursuitrdquo SIAM Review vol 43 no 1pp 129ndash159 2001

[39] D L Donoho and X Huo ldquoUncertainty principles and idealatomic decompositionrdquo IEEE Transactions on InformationThe-ory vol 47 no 7 pp 2845ndash2862 2001

[40] F Miwakeichi E Martınez-Montes P A Valdes-Sosa NNishiyama H Mizuhara and Y Yamaguchi ldquoDecomposingEEG data into spacendashtimendashfrequency components using par-allel factor analysisrdquo NeuroImage vol 22 no 3 pp 1035ndash10452004

[41] K J Friston C D Frith P F Liddle and R S J FrackowiakldquoFunctional connectivity the principal-component analysis oflarge (PET) data setsrdquo Journal of Cerebral Blood Flow andMetabolism vol 13 no 1 pp 5ndash14 1993

[42] S Makeig T-P Jung A J Bell D Ghahremani and T JSejnowski ldquoBlind separation of auditory event-related brainresponses into independent componentsrdquo Proceedings of theNational Academy of Sciences of the United States of Americavol 94 no 20 pp 10979ndash10984 1997

[43] Biomedical Signal httpwwwmedicinemcgillcaphysiovlabbiomed signalseeg nhtm

[44] S E G Nilsson and B E Andersson ldquoCorneal DC recordingsof slow ocular potential changes such as the ERG c-wave and thelight peak in clinical workmdashequipment and examples of resultsrdquoDocumenta Ophthalmologica vol 68 no 3-4 pp 313ndash325 1988

[45] OG Lins TW Picton P Berg andM Scherg ldquoOcular artifactsin EEG and event-related potentials I scalp topographyrdquo BrainTopography vol 6 no 1 pp 51ndash63 1993

[46] T W Picton P Van Roon M L Armilio P Berg N Ille andM Scherg ldquoThe correction of ocular artifacts a topographicperspectiverdquo Clinical Neurophysiology vol 111 no 1 pp 53ndash652000

[47] A S Keren S Yuval-Greenberg and L Y Deouell ldquoSaccadicspike potentials in gamma-band EEG characterization detec-tion and suppressionrdquo NeuroImage vol 49 no 3 pp 2248ndash2263 2010

[48] M Plochl J P Ossandon and P Konig ldquoCombining EEG andeye tracking identification characterization and correctionof eye movement artifacts in electroencephalographic datardquoFrontiers in Human Neuroscience vol 6 article 278 2012

[49] S Dandekar C Privitera T Carney and S A Klein ldquoNeuralsaccadic response estimation during natural viewingrdquo Journalof Neurophysiology vol 107 no 6 pp 1776ndash1790 2012

[50] G Ai N Sato B Singh and H Wagatsuma ldquoDirection andviewing area-sensitive influence of EOGartifacts revealed in theEEG topographic pattern analysisrdquo Cognitive Neurodynamicsvol 10 no 4 pp 301ndash314 2016

[51] P Berg and M Scherg ldquoDipole models of eye movements andblinksrdquo Electroencephalography and Clinical Neurophysiologyvol 79 no 1 pp 36ndash44 1991

[52] R J Croft and R J Barry ldquoRemoval of ocular artifact from theEEG a reviewrdquo Neurophysiologie Clinique vol 30 no 1 pp 5ndash19 2000

[53] I J Rampil ldquoA primer for EEG signal processing in anesthesiardquoAnesthesiology vol 89 no 4 pp 980ndash1002 1998

[54] J L Starck Y Moudden J Bobin M Elad and D DonoholdquoMorphological component analysisrdquo in Optics amp Photonics2005 p 59140Q International Society forOptics and Photonics2005

[55] S Sardy A Bruce and P Tseng ldquoBlock coordinate relaxationmethods for nonparametric signal denoising with waveletdictionariesrdquo Journal of Computational and Graphical Statisticsvol 9 pp 361ndash379 2000

[56] M Puschel and J M F Moura ldquoThe algebraic approach to thediscrete cosine and sine transforms and their fast algorithmsrdquoSIAM Journal on Computing vol 32 no 5 pp 1280ndash1316 2003

[57] X Shao and S G Johnson ldquoType-IV DCT DST and MDCTalgorithms with reduced numbers of arithmetic operationsrdquoSignal Processing vol 88 no 6 pp 1313ndash1326 2008

[58] R G Andrzejak K Lehnertz F Mormann C Rieke P Davidand C E Elger ldquoIndications of nonlinear deterministic and

4 Computational and Mathematical Methods in Medicine

Decomposition

middot middot middot

component 12057311206011

1st morphological

component 12057321206012

2nd morphological

component 120573k120601k

kth morphological

+

1206011 1206012 120601k

dictionary ΦOvercomplete

Arbitrary EEGsignal

Figure 2 A schematic diagram for EEG signal decomposition using explicit dictionary

Therefore 120573 is the target coefficients for reconstruction ofthe original EEG signal based on the assumption 120577 ≪ 1which means that the remainder 120577 is negligibly small In theconsideration that 120577 represents the noise part (2) withoutnoise can be written as

1198781015840 =119896

sum119894=1

120573119894120601119894 = 120573Φ (3)

Equation (3) is consistent with (1)The problem to solve ishow optimized coefficients can be derived and the equationis rewritten as follows

120573opt1 120573opt2 120573opt

119896 = argmin1205731120573119896

119896

sum119894=1

100381710038171003817100381712057311989410038171003817100381710038170

subject to 1198781015840 =119896

sum119894=1

120573119894120601119894(4)

The problem is how the MCA concept can be embeddedin the systems to decompose biomedical signal especiallyfor EEG signal In this formulation time-frequency param-eters are totally consistent with traditional decompositionmethods which can be applied to the biomedical signaldecomposition such as PCA wavelets and ICA in the senseof the single set of bases One advantage of MCA is theavailability of the combination of multiple basis functionsincluding traditional basis like wavelet decomposition as apart of the component called redundant transforms ThusMCA is expected to reveal what kind of the specificityexists in time-frequency properties of EEG data Concreteproblems in this viewpoint can be addressed as (a) what isthe best combination of dictionaries of MCA for the EEGdecomposition and (b) what is the true EEG signal in theform of obtained sparsest representation based on selecteddictionaries 120601119896

Figure 2 schematically illustrates the MCA decomposi-tion process of arbitrary EEG signal that is assumed to bea linear combination of 119896 morphological component to bedecomposed using explicit dictionaries

In the assumption of three types of dictionaries (119896 = 3)the following three cases are considerable by focusing onindividual dictionaries

Case 1 An overcomplete dictionary 1206011 is representing thecomponent 1199041 1206011 isin 119872119873times1198711 where 119873 ≫ 1198711 119873 being thenumber of samples that is the number of time points in therecorded data

(i) For 1199041 120573opt1 = argmin1205731205730 subject to 1199041 = 1206011120573

while solving this equation leads to the sparse solution(120573opt1 0 lt 120573opt

12 0 120573opt13 0)

(ii) For 1199042 120573opt12 = argmin1205731205730 subject to 1199042 = 1206011120573 while

solving this equation leads to nonsparse solution

(iii) For 1199043 120573opt13 = argmin1205731205730 subject to 1199043 = 1206011120573 while

solving this equation also leads to nonsparse solution

Case 2 An overcomplete dictionary 1206012 is representing thecomponent 1199042 1206012 isin 119872119873times1198712 where119873 ≫ 1198712

(i) For 1199042 120573opt2 = argmin1205731205730 subject to 1199042 = 1206012120573

while solving this equation leads to the sparse solution(120573opt2 0 lt 120573opt

23 0 120573opt21 0)

(ii) For 1199043 120573opt23 = argmin1205731205730 subject to 1199043 = 1206012120573 while

this equation also has nonsparse solution(iii) For 1199041 120573opt

21 = argmin1205731205730 subject to 1199041 = 1206012120573 whilethis equation also has nonsparse solution

Case 3 An overcomplete dictionary 1206013 is representing thecomponent 1199043 1206013 isin 119872119873times1198713 where119873 ≫ 1198713

(i) For 1199043 120573opt3 = argmin1205731205730 subject to 1199043 = 1206013120573

while solving this equation leads to the sparse solution(120573opt3 0 lt 120573opt

32 0 120573opt31 0)

(ii) For 1199042 120573opt32 = argmin1205731205730 subject to 1199042 = 1206013120573 while

solving this equation leads to nonsparse solution

(iii) For 1199041 120573opt31 = argmin1205731205730 subject to 1199041 = 1206013120573 while

solving this equation leads to nonsparse solution

Computational and Mathematical Methods in Medicine 5

Theoretically speaking by using three dictionaries MCAcan divide the signal into components depending on eachdictionary of 1206011 1206012 and 1206013 as the sparest representation of allsignalsThe sparse components are describedmathematicallyas

120573opt1 120573opt2 120573opt3 = argmin

120573112057321205733

1003817100381710038171003817120573110038171003817100381710038170 +

1003817100381710038171003817120573210038171003817100381710038170 +

1003817100381710038171003817120573310038171003817100381710038170

subject to 119878 = 12057311206011 + 12057321206012 + 12057331206013(5)

This formulation states a nonconvex optimization problemto separate the components of the signal However each 120601119896needs to be efficient in a specific component while it remainsnoneffective in other signal components The nonconvexoptimization problem indicated that it is difficult to solve (5)in a simple manner and then the Basis Pursuit (BP) method[54] was proposed based on the idea that the replacementof 1198970 norm by 1198971 norm results in the error minimizationAccording to the improvement the BP [54] was successfullyformulated into an accurate method to represent the sparestof components which is described as

120573opt1 120573opt2 120573opt3 = argmin

120573112057321205733

3

sum119894=1

100381710038171003817100381712057311989410038171003817100381710038171 + 120582

1003817100381710038171003817100381710038171003817100381710038171003817119878 minus3

sum119894=1

1206011198941205731198941003817100381710038171003817100381710038171003817100381710038171003817

2

2

(6)

In this system 1198972 norm is considered to be the errornorm based on the assumption that the residual acts asa white zero-mean Gaussian noise and another importantfinding is the representation of noise models 1198971 Laplaciannoise with the consideration of 119897infin uniformly distributednoise in the form of the optimization problem 120582 representsthe stopping criterion or threshold By using the Block-Coordinate-Relaxation (BCR) method [55] the optimizationproblem can be solved in finite computation time Theprocedure is given below

(1) Initialize = 119868max number of iterations = 119871 threshold120575 = 120582 lowast 119868max

(2) Perform 119871 timesPart (1) update 1199041 assuming 1199042 and 1199043 are fixed

(a) Calculate the residual 119877 = 119878 minus 1199042 minus 1199043(b) Calculate 1205731 = 1206011198791119877(c) Threshold the coefficient of 1205731 and obtain 1205731(d) Reconstruct 1199041 by 1199041 = 12060111205731

Part (2) update 1199042 assuming 1199041 and 1199043 are fixed

(a) Calculate the residual 119877 = 119878 minus 1199041 minus 1199043(b) Calculate 1205732 = 1206011198792119877(c) Threshold the coefficient of 1205732 and obtain 1205732(d) Reconstruct 1199042 by 1199042 = 12060121205732

Part (3) update 1199043 assuming 1199041 and 1199042 are fixed

(a) Calculate the residual 119877 = 119878 minus 1199041 minus 1199042(b) Calculate 1205733 = 1206011198793119877

(c) Threshold the coefficient of 1205733 and obtain 1205733(d) Reconstruct 1199043 by 1199043 = 12060131205733

(3) Update the threshold by 120575 = 120575 minus 120582(4) If 120575 gt 120582 return to Step (2) else finish

3 Hypothesis

In the present study we hypothesized that appropriate threedictionaries of MCA specifically for EEG recording datawere undecimated wavelet transform (UDWT) discrete sinetransform (DST) andDIRAC (aka standard unit vector basisor Kronecker basis) Fadili et al [17] UDWT contributes toseparating slow and bump morphologies for EOG and EEGtransient slow changes DST is for monomorphic and poly-morphic EEG components (major EEG parts) and DIRAC isfor spike type activities in transient EEGs In comparison inthe simulated experiment we used the discrete cosine trans-form (DCT) discrete sine transform (DST) [56 57] and localdiscrete cosine transform (LDCT) dictionaries formajor EEGparts For the verification of the hypothesis the intracranialEEG (iEEG) data was assumed to be ldquotrue EEGrdquo signal whichwas recorded from the real brain activity and artificial EOGsincluding bump and slow changes were introduced and theperformance of the accurate reconstruction of the true EEGswas examined In iEEG there are two types of the data underthe conditions of eye-closing and eye-opening 42 Accordingto the neuroscientific evidence EEGs have a clear peakin the low-frequency range around 10Hz in the frequencyspectrum under the eye-closing condition 42 In the Resultscorrelation coefficient (cc) was used for the validation ofaccuracy in reconstruction and the frequency spectrum wasfor the validation of the nature of the information containedin EEGs

4 Results

For verification of our hypothesis in the computer experi-ments three types of the data were used (1) all simulateddata (2) a combination of real iEEG and simulated EOGand (3) recording of real EEG-EOG data and our proposedmethod was validated

41 Simulated Data In the first place two simulated signalsources were prepared for the simple test of the proposedmethod Initially Yong et al [36] proposed a combinationof the wavelet DCT and DIRAC for EEG artifact removalswhile their results could not tell how effective the methodwas in a qualitative manner In our experiment the firstsource signal consisted of a cosine wave which was assumedto be a monomorphic EEG signal and the second sourceconsisted of blinks component with three bumps designedas usual EOG signals The simulated signal as a mixture ofthe two sources and white noise (120578 = 20) was shownin Figure 3(a) where 120578 was defined as the percentage ofthe maximum amplitude of the input signal Our proposedMCA method was applied to separate the components fromthe simulated signal with the explicit dictionaries UDWT

6 Computational and Mathematical Methods in Medicine

02

0

1

2

024

1000 20000

minus2

minus2

Samples

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)1st signal source

2nd signal source

Combined signal (source)

(a)

0

15

0

2

0

1

1000 20000

minus2

Samples

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

1st separated component (UDWT)

2nd separated component (DCT)

3rd separated component (DIRAC)

(b)

0

2

4

1000 20000

minus2

Samples

Pote

ntia

l (V

)

Combined signal (source)Combination of separated component (reconstructed)

(c)

Figure 3 An example of simulated signal for decomposition and (a) the cosine with bump and spikes signals and combined signal withwhite noise (120578 = 20) (b) separated components with explicit dictionaries UDWT-DCT-DIRAC and (c) comparison between combinedsignal and sum of separated components (cc = 099)

DCT and DIRAC as shown in Figure 3(b) as a replicationtest The correlation coefficient between the simulated signaland the sum of all components was higher than 099 andthe simulated result proved the accuracy of decomposedcomponents byMCAwithUDWTDCT andDIRAC explicitdictionaries (Figure 3(c))

42 Simulated EOGContaminated iEEG Signal Theprevioussection was a simple example of the simulated data In thissection we introduced a new validation way to test theproposed method in a qualitative manner The real iEEGsignals were obtained under the closing eye condition Thelinear combination of simulated EOG and real iEEG signalswas used for the test In this case we assumed that iEEGhad already included a usual level of the white noise andthen did not add further noise additionallyThe iEEG datasetwas given by Andrzejak et al [58] with 100 trials andthe sampling rate was at 17361Hz (000576 ssample) and210(=1024) samples took about 6 s (589824 s) The linearcombination of simulated EOG and iEEG signals was appliedfor the validation

There were different combinations for simulated EOG asassumed artificial eye movement which was considered asthe step function and eye blinks by bump signalThe flatnesssignals with elevations with slow time scales compared with

the EEG time scale represent the gaze-type eyeball rotationsThe signals can be reconstructed by a mathematical methoddefined by the rate of change ()1015840 of which satisfies that119905 | ()1015840 gt 0 should be 0 Thus the definition of the EOGsmoothness is described as

()1015840119868 =

()1015840 (119905) ()1015840 (119905) = 00 ()1015840 (119905) gt 0

(7)

where 119868 = 119905 | ()1015840 = 0 leads to ()1015840119868 equiv 0 according toits definition as shown in Figure 4(b) In addition the bumpssignal was considered as the blink type EOG signal shownin Figure 4(c) Figure 4(d) showed the schematic examplefor the semisimulated signal In the same way 100 datasetsof semisimulated signals with a random combination ofcomponents in time series were used for the validation

Figures 5(a) 5(b) and 5(c) demonstrated a set of resultsfor the decomposition of the semisimulated signal by explicitdictionaries depending on the combination of dictionariesAsmentioned in Section 23 the stopping criterion dependedon 120582 lowast threshold and the parameters in this comparativestudy used a different combination of explicit dictionaries(UDWT-DCT-DIRAC UDWT-DST-DIRAC and UDWT-LDCT-DIRAC) and different type of thresholds either hardand soft and 120582 value varied from 3 to 5

Computational and Mathematical Methods in Medicine 7

200

0

minus200Pote

ntia

l (V

)

Samples40003000200010000

Intracranial real EEG signal

(a)

500

0

minus500Pote

ntia

l (V

)

Samples40003000200010000

Artificial eye movement-related EOG signal

(b)

500

0

minus500Pote

ntia

l (V

)

Samples40003000200010000

Artificial blink EOG signal

(c)

Samples

1000

0

minus1000Pote

ntia

l (V

)

40003000200010000

Combined signal (EEG + EOG)

(d)

Figure 4 A systemic representation of differentmorphological signals (a) intracranial EEG signal (b) artificial block EOG signal (c) artificialblink EOG signal and (d) combined signal

Figures 6(a) and 6(b) showed the averaged cc of decom-posed component by a respective combination of explicitdictionaries with hard and soft thresholds For EEG signaldecomposition performance cc between iEEG and eitherDST DCT or LDCT component was evaluated dependingon the three combination types (Figure 6(a)) For EOGsignal decomposition performance cc between EOG andUDWT component was evaluated (Figure 6(b)) In compari-son between hard and soft thresholds the average value of thehard threshold is around 06 which is larger than that in thesoft threshold while the average value of the soft threshold isaround 095 demonstrating fewer variances than those in thehard thresholdThismethod indicates thatUDWTdictionarywith a soft threshold is the stable performance according tothe fitness of the morphological property in this case

There were similar variances and average values in theevaluation of EEG signal decomposition using the timedomain and then we introduced a measure in the frequencydomain As mentioned in Section 22 EEG signals carryinformation to represent the current brain stage in thespecific tendency in the frequency domain such as having asynchronized neural activities by showing the existence of apeak in the frequency spectrum The EEG data used in theevaluation showed a peak around 10Hz under the closingeye condition and a peak around 50Hz under the openingeye condition Therefore in the frequency analysis a 10Hzpeak will be an index to tell how much the reconstructedsignal preserves the original information contained in theoriginal iEEG data under closing eye condition Figure 7showed the averaged normalized FFT as the comparisonbetween three combinations of the dictionaries InterestinglyalthoughDSTDCT and LDCT single components seemed toreconstruct the EEGs because of a high cc value in the timedomain the frequency spectrum analysis clarified the factthat the single component cannot reproduce the necessarytendency of EEG signals peak Meanwhile the combination

of 2nd and 3rd components which means oscillatory andspike components successfully reproduced the EEG signaltendency suggesting the importance of the spike informa-tion that presumably synchronizes background oscillatorybehaviors The 10Hz peak can be reproduced according toparameter conditions easily However 50Hz peak is difficultto be reproduced especially for LDCT-DIRAC componentin every case In the viewpoint of the tolerance in thechange of the threshold value the soft threshold methodshowed the robust performance of the signal informationpreservation which is consistent with the result of EOGsshown in Figure 6 As shown in Figure 8 the reconstructionaccuracy of the frequency profile by two dictionaries wasproved by a significant difference between the results of twomorphological and single morphological components (119905-test119901 lt 001 in both hard and soft thresholds) This evidencesuggests the importance of the DIRAC component for EEGsignals which was not equivalent to the noise or rathercarrying some information

43 Decomposition of EOG from Real EEG Data

431 EEG Data The real scalp EEG and EOG data wereobtained from the data demonstrated in the paper writtenby Ai et al (2016) [50] These data were recorded from23 EEG channels (FP1 FP2 F7 F3 Fz F4 F8 FC5 FC1FC2 FC4 T7 C3 Cz C4 T8 CP1 CP2 P3 Pz P4 O1and O2) and 7 EOG channels (V1u V1d V2u and V2dvertical EOG ⟨VEOG⟩ electrodeswere placed on supraorbitaland infraorbital rims of each eye HL and HR horizontalEOG ⟨HEOG⟩ electrodes were on the left and right outercanthi Vz was on the forehead approximately 25mm abovethe nasion) respectively according to 10ndash20 InternationalSystem (BrainAmp amplifier Brain Products GmbH) fromthe 8 participants seated in a comfortable armchair withthe base adjusted according to a participant height Theeyes of the participants were fixed straightly to the fixation

8 Computational and Mathematical Methods in Medicine

UDWT DST DIRAC400

0

minus400

Pote

ntia

l (V

)

200

0

minus200

0

100

minus100

Samples400020000

Samples400020000

Samples400020000

(a)

DCTUDWT DIRAC

400

0

minus400

Pote

ntia

l (V

)

200

0

minus200

0

100

minus100

Samples400020000

Samples400020000

Samples400020000

(b)

UDWT LDCT DIRAC400

0

minus400

Pote

ntia

l (V

)

200

0

200

0

minus200

Samples400020000

Samples400020000

Samples400020000

(c)

Figure 5 Components separation byMCA (a) explicit dictionaries are UDWT DST andDIRAC (b) UDWT DCT andDIRAC (c) UDWTLDCT and DIRAC respectively at 120582 = 4 The original signal for decomposition was shown in Figure 4(d) as combined signal

cross in the center of the monitor screen The stimulus wasdisplayed by a CRT monitor A chin support frame wasused to keep the participantrsquos head position fixed and fixtheir head to the supporting frame without laying their chinson the supporting bar to avoid the jaw clenching artifactThe distance between eyes and monitor was set to 70 cmThe sampling rate was 500Hz The whole details of theexperiment protocols were given in Ai et al (2016) [50]

432 Results with Real EEG-EOG According toAi et al [50]the real EEG-EOG data were divided into 4 sessions Eachsession had 12 tasks of eye movement The two EOG signalswere collected from ldquoV1d-V1urdquo and ldquoV2d-V2urdquo at right andleft sides of the eye as shown in Figure 9 and both signalsshowed the same kind of tendency because vertical EOG

propagated symmetrically in an anterior-posterior directionFigure 10 showed the real EEG signals were taken from someelectrodes for example Fp1 Fp2 Cz O1 and O2 whichrepresent EOG influence depending on the frontal centraland occipital parts of the brain

The selected explicit dictionaries were used to representthe targeted component for the EEG and EOG signal EEGand EOG were distinguished based on the morphologythat was observed in the EEG and EOG The lateral eyemovements mostly affect frontal electrodes [45] ThereforeFp1 electrode was used to decompose and demonstratethe effectiveness of our proposed method with MCA asshowed in Figure 11 and the same method was applied toall the 23 electrodes All EEG signals were morphologicallydecomposed with redundant transform

Computational and Mathematical Methods in Medicine 9

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

Aver

aged

corr

elat

ion

coeffi

cien

t

06

04

08

1

(a) cc between iEEG and 2nd comp (hard)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5Av

erag

ed co

rrel

atio

n co

effici

ent

06

04

08

1

(b) cc between iEEG and 2nd comp (soft)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

06

04

08

1

Aver

aged

corr

elat

ion

coeffi

cien

t

(c) cc between EOG and UDWT (hard)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

Aver

aged

corr

elat

ion

coeffi

cien

t

06

04

08

1

(d) cc between EOG and UDWT (soft)

Figure 6 A comparison between cc of decomposed morphological component with iEEG signal and artificial EOG with hard and softthresholds The mean value and standard deviation were calculated from all 100 decomposed datasets by explicit dictionaries (a) Secondmorphological component was decomposed by DST DCT and LDCT with hard and (b) soft threshold respectively (c) First morphologicalcomponent was decomposed by UDWT with a hard threshold and (d) soft threshold respectively 100 trials of iEEG and artificial EOG wereused

10 Computational and Mathematical Methods in Medicine

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

0 20 40 60 80

0

2

4

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(a) Hard (120582 = 3)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(b) Hard (120582 = 4)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(c) Hard (120582 = 5)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(d) Soft (120582 = 3)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(e) Soft (120582 = 4)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Nor

mal

ized

pow

er (d

B)

Frequency (Hz)

minus2

(f) Soft (120582 = 5)

Figure 7 An averaged normalized FFT obtained from 100 of iEEG and combination of two morphological components and singlemorphological component at 120582 varies from 3 to 5 with hard and soft thresholds

Figure 11(a) demonstrated the decomposition of compo-nents by the first explicit dictionary it was divided into threedifferent morphologies of the EEG signal Figures 11(b) and11(c) showed the second and the third explicit dictionary ofredundant transform respectively The overcomplete dictio-nary was a combination of redundant transforms that char-acterized the component in a different morphology Accord-ingly one of redundant transforms can be differentiated intodecomposed components by overcomplete dictionaries Thefirst component was decomposed by ldquoUDWTrdquo of each over-complete dictionary and was analyzed via the slow and blinktype morphology The second component was decomposedby ldquoDCTrdquo ldquoDSTrdquo and ldquoLDCTrdquo and was analyzed via thebackground of the signal which was similar to the EEG signal

and the third component was decomposed by ldquoDIRACrdquo andwas analyzed via the unexpected spikeThe first overcompletedictionary decomposed the EEG signal without changingthe monomorphic polymorphic and transient propertiesThe cc between the original signal and the summation of alldecomposed components was close to one Figure 12 showedthe raw EOG signal taken from the vertical and horizontalchannel and first decomposed component taken from Fp1Fp2 Cz O1 and O2 respectively

Table 1 showed individual cc of original EEG signals andrecomposed EEG signals from the combination of compo-nents with respect to different channels and combinationsof dictionaries Table 2 showed the cc between filter rawEOG signal taken from vertical and horizontal channels and

Computational and Mathematical Methods in Medicine 11

3 4 5

02

03

04

05

06

07

08

09

Aver

aged

FFT

corr

elat

ion

coeffi

cien

t

01

1

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

lowast lowast lowast

(a) Hard threshold

3 4 5

Aver

aged

FFT

corr

elat

ion

coeffi

cien

t02

03

04

05

06

07

08

09

01

1

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

lowast lowast lowast

(b) Soft threshold

Figure 8 A comparison of FFT correlation coefficients between iEEG data and morphological component decomposed by explicitdictionaries lowastSignificant differences (119901 lt 005) (a) Combined two morphological components and (b) single morphological componentMean value and standard deviation calculated from all 100 decomposed datasets by explicit dictionaries with hard and soft thresholds

400

Pote

ntia

l (V

)

200

0

minus200

400

Pote

ntia

l (V

)

200

0

minus200

Samples20000 1000

EOG (V1u-V1d)

EOG (V2u-V2d)

Figure 9 An example of EOG signal taken from right and left sideof eyes

decomposed first component from Fp1 Fp2 Cz O1 and O2respectively

5 Discussion

Artifact contamination in EEG signal has been a com-mon important issue in neurobiological event diagnosis and

Table 1 cc of original signal and sum of the decomposed compo-nents

EEG channelCorrelation coefficient

UDWT-DST-DIRAC

UDWT-DCT-DIRAC

UDWT-LDCT-DIRAC

Fp1 09921 plusmn 0014 09921 plusmn 0014 09932 plusmn 0013Fp2 0992 plusmn 017 09919 plusmn 018 09932 plusmn 014Cz 09898 plusmn 01 09899 plusmn 01 09908 plusmn 009O1 09836 plusmn 015 09836 plusmn 016 09869 plusmn 012O2 09855 plusmn 013 09856 plusmn 013 09849 plusmn 015

neuroscientific researchThevariousmethodswere applied toremove the artifacts from EEG [2 11ndash13 21 23 24 26ndash28 52]The decomposition based analysis was used in removal ofEOG artifacts in EEG [22 27 28 30 40 42] Howeverthose methods lack the elucidation of what the nature ofEEG signals is in the viewpoint of the signal analysis and asystematic approach was required by treating the sparsity andnonlinearity of the signal in the time domain

12 Computational and Mathematical Methods in Medicine

0

0

50

Fp1

Fp2

Cz

O1

O2

100

0

minus100

minus50

minus40

Pote

ntia

l (V

)

0

50

minus50

Pote

ntia

l (V

)

050

minus50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

Figure 10 An example of real EEG signal taken from Fp1 Fp2 Cz O1 and O2 electrode channels

Table 2 cc between filtered EOG and UDWT component decomposed by UDWT dictionary

EOG channels EEG channelsFp1 Fp2 Cz O1 O2

Correlation coefficientUDWT-DST-DIRACV1d 06777 0657 07267 09223 06445V1u 06814 0646 06606 09419 06354V2d 0916 0906 09402 0882 05402V2u 02332 02268 02353 06388 08494H1 08582 0847 08444 06902 05839H2 09419 09468 09559 07476 04752

UDWT-DCT-DIRACV1d 06792 06595 068 09213 06352V1u 06835 06396 06424 09581 06585V2d 09193 0902 09362 08764 05145V2u 02331 02183 02316 06639 08919H1 08593 08507 08626 06759 05376H2 09442 09465 09662 07266 04346

UDWT-LDCT-DIRACV1d 06794 06403 07219 08892 065V1u 06443 06279 06459 08196 05381V2d 09142 09072 09395 09592 06506V2u 02351 02235 02383 03747 06804H1 08637 08449 08471 07638 05734H2 09586 09558 09577 08826 05598

Computational and Mathematical Methods in Medicine 13

0

50

0

20

UDWT

DCT

DIRAC

0

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus30

(a)

UDWT

DST

DIRAC

0

0

20

0

50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus20

minus20

(b)

0

0

50

100

0

UDWT

LDCT

DIRAC

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus20

minus40

minus80

(c)

Figure 11 Component separated fromEEG (Fp1 electrode) signal by explicit dictionaries (a)UDWT-DCT-DIRAC (b)UDWT-DST-DIRACand (c) UDWT-LDCT-DIRAC respectively

This study revealed the nature of EEG signals in the senseof morphologies contained in the original signal by usingMCA The UDWT was used to decompose the slow andbump morphology The DCT DST and LDCT transformwere used to decompose the EEG signal Spike typemorphol-ogy was decomposed by DIRAC Redundant transforms ofDCT and DST have a similar capability in representing themorphology of oscillatory activities Therefore we used theDCT LDCT and DST dictionaries for validations of EEGsignal The detailed significant differences in morphology ofDCT and DST were given in past studies [56 57] while inour analysis there were no significant differences The rightcombination of redundant transforms to form overcompletedictionary revealed the desired decomposition in principle

In Section 42 ldquoBlocksrdquo ldquoBumpsrdquo similar to simulatedEOG signal defined in past studies [59ndash61] as shown in

Figure 4 and EEG data [58] were used to validate ourpurposed method The ldquoBlocksrdquo with abrupt changes weresimilar to the horizontal and vertical eye movements sim-ply as described by past studies [25 51] For the sake ofsimplicity in the present study ldquoBumpsrdquo were used as arepresentative signal form as eye blinks that happens inunexpected timings as illustrated in Figure 5 The separationof components by given dictionary works well in this evalu-ation but the further analysis is necessary for the evaluationof the signal decomposition with complex eye movementswhich requires presumably various redundant dictionariesIn the verification of the component discrimination as shownin Figures 6 and 7 the accuracy of the averaged EOGcomponent decomposition was above 90 which suggests aplausible performance even in the complex eye movementsThe combined DST and DIRAC dictionaries had better

14 Computational and Mathematical Methods in Medicine

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

Samples20000 1000

V1u

H1

(a) UDWT components separated by UDWT-DST-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(b) UDWT components separated by UDWT-DCT-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(c) UDWT components separated by UDWT-LDCT-DIRAC

Figure 12 UDWT component taken from Fp1 Fp2 Cz O1 and O2 separated by UDWT-DCT-DIRAC UDWT-DST-DIRAC and UDWT-LDCT-DIRAC respectively

decomposition performance than others while DST andDCT theoretically have no meaningful difference The usageof iEEG as the true EEG signal had a large benefit whichcan be used for the performance test for past proposedmethods like ICA and PCA consistently Our proposedmethod successfully demonstrated the performance in cc andthe frequency profile especially in Section 42 while in theserious discussion of the real EEG and EOG signals the DSTor DCT component exhibited a baseline fluctuation of thesignal which denotes the persistence of the EOG componentor other slow frequency artifacts noises and the factor willbe improved by the fine-tuned design of the DST or DCTdictionary with a band pass filter function In addition thethreshold problem exits in the optimization algorithm andnumber of iterations [37]

The EEG decomposition had not mark with a combi-nation of a second and a third component of EEG signal

decomposed by ldquoDST DCT and LDCTrdquo andDIRAC respec-tively based on the morphology Therefore the accuratecombination in the further perspective will be considerableEven the combination of all components and the mixedsignal or real EEG signal had cc above 97 for all redundanttransforms as is analyzed in the frequency spectrum thesignal morphology has further meaning in the viewpointof the signal transmission The MCA method has such anextended and flexible availability for signal analyses

6 Conclusion

Morphological Component Analysis methodology wasapplied to the simulated semisimulated and real EOGand EEG signal The successful decomposition of the EOGand EEG signal into their morphological component wasdemonstrated It seems to be that the EEG signals and

Computational and Mathematical Methods in Medicine 15

artifacts in EEG have been represented by different explicitdictionaries We analyzed the EEG signals involved with theEOG artifacts which were influenced by task conditionsTheDIRAC explicit dictionary decomposed the EEG signal intospike-like activities which may be related to the transientproperty of EEG UDWT explicit dictionary representsslow movement or bumps DCT DST and LDCT explicitdictionaries represent dominant signal that represents EEGsor pure tones signals as monomorphic and polymorphicactivities These results suggested that the effectivenessof MCA in ocular artifacts removal from the EEG rawsignal was derived from signal morphology characterizedas slow and smooth change of EOG time series In thefurther analysis the MCA is required to compare withother competing methods for the EEG and EOG signaldecomposition

Competing Interests

The authors have declared that no competing interests exist

Acknowledgments

This work was partly supported by JSPS KAKENHI 16H01616and 26240032 and theNewEnergy and Industrial TechnologyDevelopment Organization (NEDO) ldquoNext-Generation Arti-ficial Intelligence (3) Base Technology for Next-GenerationAIrdquo (Automated Driving Task) and the collaborative researchproject with Fujitsu Ten Limited

References

[1] J P Donoghue J N Sanes N G Hatsopoulos and G GaalldquoNeural discharge and local field potential oscillations in pri-mate motor cortex during voluntary movementsrdquo Journal ofNeurophysiology vol 79 no 1 pp 159ndash173 1998

[2] J A Uriguen and B Garcia-Zapirain ldquoEEG artifact removalmdashstate-of-the-art and guidelinesrdquo Journal of Neural Engineeringvol 12 no 3 Article ID 031001 2015

[3] C Kamarajan and B Porjesz ldquoAdvances in electrophysiologicalresearchrdquoAlcohol Research Current Reviews vol 37 no 1 article53 2015

[4] L F Nicolas-Alonso and J Gomez-Gil ldquoBrain computer inter-faces a reviewrdquo Sensors vol 12 no 2 pp 1211ndash1279 2012

[5] L Mayaud M Congedo A Van Laghenhove et al ldquoA compar-ison of recording modalities of P300 event-related potentials(ERP) for brain-computer interface (BCI) paradigmrdquo Neuro-physiologie CliniqueClinical Neurophysiology vol 43 no 4 pp217ndash227 2013

[6] X-Y Wang J Jin Y Zhang and B Wang ldquoBrain controlhuman-computer integration control based on brain-computerinterfacerdquo Acta Automatica Sinica vol 39 no 3 pp 208ndash2212013

[7] G Al-Hudhud ldquoAffective command-based control system inte-grating brain signals in commands control systemsrdquo Computersin Human Behavior vol 30 pp 535ndash541 2014

[8] J L Sirvent Blasco E Ianez A Ubeda and JM Azorın ldquoVisualevoked potential-based brain-machine interface applications toassist disabled peoplerdquo Expert Systems with Applications vol 39no 9 pp 7908ndash7918 2012

[9] H Cecotti ldquoSpelling with non-invasive Brain-Computer Inter-facesmdashcurrent and future trendsrdquo Journal of Physiology Parisvol 105 no 1ndash3 pp 106ndash114 2011

[10] I S Kotchetkov B Y Hwang G Appelboom C P Kellnerand E S Connolly Jr ldquoBrain-computer interfaces militaryneurosurgical and ethical perspectiverdquo Neurosurgical Focusvol 28 no 5 article no E25 2010

[11] R N Vigario ldquoExtraction of ocular artefacts from EEG usingindependent component analysisrdquo Electroencephalography andClinical Neurophysiology vol 103 no 3 pp 395ndash404 1997

[12] W Zhou and J Gotman ldquoAutomatic removal of eye movementartifacts from the EEG using ICA and the dipole modelrdquoProgress in Natural Science vol 19 no 9 pp 1165ndash1170 2009

[13] R Sameni andCGouy-Pailler ldquoAn iterative subspace denoisingalgorithm for removing electroencephalogram ocular artifactsrdquoJournal of Neuroscience Methods vol 225 pp 97ndash105 2014

[14] M Breakspear and J R Terry ldquoDetection and description ofnon-linear interdependence in normal multichannel humanEEG datardquo Clinical Neurophysiology vol 113 no 5 pp 735ndash7532002

[15] U R Acharya O Faust N Kannathal T Chua and S Laxmin-arayan ldquoNon-linear analysis of EEG signals at various sleepstagesrdquo Computer Methods and Programs in Biomedicine vol80 no 1 pp 37ndash45 2005

[16] L I Aftanas and S A Golocheikine ldquoNon-linear dynamiccomplexity of the human EEGduringmeditationrdquoNeuroscienceLetters vol 330 no 2 pp 143ndash146 2002

[17] M J Fadili J-L Starck J Bobin and Y Moudden ldquoImagedecomposition and separation using sparse representations anoverviewrdquo Proceedings of the IEEE vol 98 no 6 pp 983ndash9942010

[18] K J Blinowska and P J Durka ldquoUnbiased high resolutionmethod of EEG analysis in time-frequency spacerdquo Acta Neuro-biologiae Experimentalis vol 61 no 3 pp 157ndash174 2001

[19] E Imani H-R Pourreza and T Banaee ldquoFully automateddiabetic retinopathy screening usingmorphological componentanalysisrdquo Computerized Medical Imaging and Graphics vol 43pp 78ndash88 2015

[20] E Imani M Javidi and H-R Pourreza ldquoImprovement ofretinal blood vessel detection using morphological componentanalysisrdquo Computer Methods and Programs in Biomedicine vol118 no 3 pp 263ndash279 2016

[21] A S Al-Fahoum and A A Al-Fraihat ldquoMethods of EEG signalfeatures extraction using linear analysis in frequency and time-frequency domainsrdquo ISRN Neuroscience vol 2014 Article ID730218 7 pages 2014

[22] M Zibulevsky and B A Pearlmutter ldquoBlind source separationby sparse decomposition in a signal dictionaryrdquoNeural Compu-tation vol 13 no 4 pp 863ndash882 2001

[23] N P Castellanos andVAMakarov ldquoRecovering EEGbrain sig-nals artifact suppression with wavelet enhanced independentcomponent analysisrdquo Journal of Neuroscience Methods vol 158no 2 pp 300ndash312 2006

[24] J Hou K Morgan D M Tucker et al ldquoAn improved artifactsremoval method for high dimensional EEGrdquo Journal of Neuro-science Methods vol 268 pp 31ndash42 2016

[25] P Berg and M Scherg ldquoA multiple source approach to thecorrection of eye artifactsrdquo Electroencephalography and ClinicalNeurophysiology vol 90 no 3 pp 229ndash241 1994

[26] P K Sadasivan and D Narayana Dutt ldquoSVD based techniquefor noise reduction in electroencephalographic signalsrdquo SignalProcessing vol 55 no 2 pp 179ndash189 1996

16 Computational and Mathematical Methods in Medicine

[27] C A Joyce I F Gorodnitsky andMKutas ldquoAutomatic removalof eye movement and blink artifacts from EEG data using blindcomponent separationrdquo Psychophysiology vol 41 no 2 pp 313ndash325 2004

[28] G L Wallstrom R E Kass A Miller J F Cohn and N A FoxldquoAutomatic correction of ocular artifacts in the EEG a com-parison of regression-based and component-based methodsrdquoInternational Journal of Psychophysiology vol 53 no 2 pp 105ndash119 2004

[29] S M Gordon V Lawhern A D Passaro and K McDowellldquoInformed decomposition of electroencephalographic datardquoJournal of Neuroscience Methods vol 256 pp 41ndash55 2015

[30] D StuderUHoffmann andTKoenig ldquoFromEEGdependencymultichannel matching pursuit to sparse topographic EEGdecompositionrdquo Journal of Neuroscience Methods vol 153 no2 pp 261ndash275 2006

[31] J-L Starck M Elad and D Donoho ldquoRedundant multiscaletransforms and their application for morphological componentseparationrdquo Advances in Imaging and Electron Physics vol 132pp 287ndash348 2004

[32] P J Franaszczuk G K Bergey P J Durka andHM EisenbergldquoTime-frequency analysis using thematching pursuit algorithmapplied to seizures originating from the mesial temporal loberdquoElectroencephalography and Clinical Neurophysiology vol 106no 6 pp 513ndash521 1998

[33] P J Durka A Matysiak E M Montes P V Sosa and K JBlinowska ldquoMultichannel matching pursuit and EEG inversesolutionsrdquo Journal of Neuroscience Methods vol 148 no 1 pp49ndash59 2005

[34] J Bobin J-L Starck J Fadili and Y Moudden ldquoSparsityand morphological diversity in blind source separationrdquo IEEETransactions on Image Processing vol 16 no 11 pp 2662ndash26742007

[35] P J Durka D Ircha and K J Blinowska ldquoStochastic time-frequency dictionaries formatching pursuitrdquo IEEE Transactionson Signal Processing vol 49 no 3 pp 507ndash510 2001

[36] X Yong R K Ward and G E Birch ldquoGeneralized morpholog-ical component analysis for EEG source separation and artifactremovalrdquo in Proceedings of the 4th International IEEEEMBSConference on Neural Engineering (NER rsquo09) pp 343ndash346Antalya Turkey May 2009

[37] B Singh G Ai and H Wagatsuma ldquoAn electrooculographyanalysis in the time-frequency domain using morphologicalcomponent analysis toward the development of mobile BCIsystemsrdquo in Universal Access in Human-Computer InteractionAccess to Interaction 9th International Conference UAHCI 2015Held as Part of HCI International 2015 Los Angeles CA USAAugust 2ndash7 2015 Proceedings Part II vol 9176 of Lecture Notesin Computer Science pp 528ndash537 Springer Berlin Germany2015

[38] S S Chen D L Donoho and M A Saunders ldquoAtomicdecomposition by basis pursuitrdquo SIAM Review vol 43 no 1pp 129ndash159 2001

[39] D L Donoho and X Huo ldquoUncertainty principles and idealatomic decompositionrdquo IEEE Transactions on InformationThe-ory vol 47 no 7 pp 2845ndash2862 2001

[40] F Miwakeichi E Martınez-Montes P A Valdes-Sosa NNishiyama H Mizuhara and Y Yamaguchi ldquoDecomposingEEG data into spacendashtimendashfrequency components using par-allel factor analysisrdquo NeuroImage vol 22 no 3 pp 1035ndash10452004

[41] K J Friston C D Frith P F Liddle and R S J FrackowiakldquoFunctional connectivity the principal-component analysis oflarge (PET) data setsrdquo Journal of Cerebral Blood Flow andMetabolism vol 13 no 1 pp 5ndash14 1993

[42] S Makeig T-P Jung A J Bell D Ghahremani and T JSejnowski ldquoBlind separation of auditory event-related brainresponses into independent componentsrdquo Proceedings of theNational Academy of Sciences of the United States of Americavol 94 no 20 pp 10979ndash10984 1997

[43] Biomedical Signal httpwwwmedicinemcgillcaphysiovlabbiomed signalseeg nhtm

[44] S E G Nilsson and B E Andersson ldquoCorneal DC recordingsof slow ocular potential changes such as the ERG c-wave and thelight peak in clinical workmdashequipment and examples of resultsrdquoDocumenta Ophthalmologica vol 68 no 3-4 pp 313ndash325 1988

[45] OG Lins TW Picton P Berg andM Scherg ldquoOcular artifactsin EEG and event-related potentials I scalp topographyrdquo BrainTopography vol 6 no 1 pp 51ndash63 1993

[46] T W Picton P Van Roon M L Armilio P Berg N Ille andM Scherg ldquoThe correction of ocular artifacts a topographicperspectiverdquo Clinical Neurophysiology vol 111 no 1 pp 53ndash652000

[47] A S Keren S Yuval-Greenberg and L Y Deouell ldquoSaccadicspike potentials in gamma-band EEG characterization detec-tion and suppressionrdquo NeuroImage vol 49 no 3 pp 2248ndash2263 2010

[48] M Plochl J P Ossandon and P Konig ldquoCombining EEG andeye tracking identification characterization and correctionof eye movement artifacts in electroencephalographic datardquoFrontiers in Human Neuroscience vol 6 article 278 2012

[49] S Dandekar C Privitera T Carney and S A Klein ldquoNeuralsaccadic response estimation during natural viewingrdquo Journalof Neurophysiology vol 107 no 6 pp 1776ndash1790 2012

[50] G Ai N Sato B Singh and H Wagatsuma ldquoDirection andviewing area-sensitive influence of EOGartifacts revealed in theEEG topographic pattern analysisrdquo Cognitive Neurodynamicsvol 10 no 4 pp 301ndash314 2016

[51] P Berg and M Scherg ldquoDipole models of eye movements andblinksrdquo Electroencephalography and Clinical Neurophysiologyvol 79 no 1 pp 36ndash44 1991

[52] R J Croft and R J Barry ldquoRemoval of ocular artifact from theEEG a reviewrdquo Neurophysiologie Clinique vol 30 no 1 pp 5ndash19 2000

[53] I J Rampil ldquoA primer for EEG signal processing in anesthesiardquoAnesthesiology vol 89 no 4 pp 980ndash1002 1998

[54] J L Starck Y Moudden J Bobin M Elad and D DonoholdquoMorphological component analysisrdquo in Optics amp Photonics2005 p 59140Q International Society forOptics and Photonics2005

[55] S Sardy A Bruce and P Tseng ldquoBlock coordinate relaxationmethods for nonparametric signal denoising with waveletdictionariesrdquo Journal of Computational and Graphical Statisticsvol 9 pp 361ndash379 2000

[56] M Puschel and J M F Moura ldquoThe algebraic approach to thediscrete cosine and sine transforms and their fast algorithmsrdquoSIAM Journal on Computing vol 32 no 5 pp 1280ndash1316 2003

[57] X Shao and S G Johnson ldquoType-IV DCT DST and MDCTalgorithms with reduced numbers of arithmetic operationsrdquoSignal Processing vol 88 no 6 pp 1313ndash1326 2008

[58] R G Andrzejak K Lehnertz F Mormann C Rieke P Davidand C E Elger ldquoIndications of nonlinear deterministic and

Computational and Mathematical Methods in Medicine 5

Theoretically speaking by using three dictionaries MCAcan divide the signal into components depending on eachdictionary of 1206011 1206012 and 1206013 as the sparest representation of allsignalsThe sparse components are describedmathematicallyas

120573opt1 120573opt2 120573opt3 = argmin

120573112057321205733

1003817100381710038171003817120573110038171003817100381710038170 +

1003817100381710038171003817120573210038171003817100381710038170 +

1003817100381710038171003817120573310038171003817100381710038170

subject to 119878 = 12057311206011 + 12057321206012 + 12057331206013(5)

This formulation states a nonconvex optimization problemto separate the components of the signal However each 120601119896needs to be efficient in a specific component while it remainsnoneffective in other signal components The nonconvexoptimization problem indicated that it is difficult to solve (5)in a simple manner and then the Basis Pursuit (BP) method[54] was proposed based on the idea that the replacementof 1198970 norm by 1198971 norm results in the error minimizationAccording to the improvement the BP [54] was successfullyformulated into an accurate method to represent the sparestof components which is described as

120573opt1 120573opt2 120573opt3 = argmin

120573112057321205733

3

sum119894=1

100381710038171003817100381712057311989410038171003817100381710038171 + 120582

1003817100381710038171003817100381710038171003817100381710038171003817119878 minus3

sum119894=1

1206011198941205731198941003817100381710038171003817100381710038171003817100381710038171003817

2

2

(6)

In this system 1198972 norm is considered to be the errornorm based on the assumption that the residual acts asa white zero-mean Gaussian noise and another importantfinding is the representation of noise models 1198971 Laplaciannoise with the consideration of 119897infin uniformly distributednoise in the form of the optimization problem 120582 representsthe stopping criterion or threshold By using the Block-Coordinate-Relaxation (BCR) method [55] the optimizationproblem can be solved in finite computation time Theprocedure is given below

(1) Initialize = 119868max number of iterations = 119871 threshold120575 = 120582 lowast 119868max

(2) Perform 119871 timesPart (1) update 1199041 assuming 1199042 and 1199043 are fixed

(a) Calculate the residual 119877 = 119878 minus 1199042 minus 1199043(b) Calculate 1205731 = 1206011198791119877(c) Threshold the coefficient of 1205731 and obtain 1205731(d) Reconstruct 1199041 by 1199041 = 12060111205731

Part (2) update 1199042 assuming 1199041 and 1199043 are fixed

(a) Calculate the residual 119877 = 119878 minus 1199041 minus 1199043(b) Calculate 1205732 = 1206011198792119877(c) Threshold the coefficient of 1205732 and obtain 1205732(d) Reconstruct 1199042 by 1199042 = 12060121205732

Part (3) update 1199043 assuming 1199041 and 1199042 are fixed

(a) Calculate the residual 119877 = 119878 minus 1199041 minus 1199042(b) Calculate 1205733 = 1206011198793119877

(c) Threshold the coefficient of 1205733 and obtain 1205733(d) Reconstruct 1199043 by 1199043 = 12060131205733

(3) Update the threshold by 120575 = 120575 minus 120582(4) If 120575 gt 120582 return to Step (2) else finish

3 Hypothesis

In the present study we hypothesized that appropriate threedictionaries of MCA specifically for EEG recording datawere undecimated wavelet transform (UDWT) discrete sinetransform (DST) andDIRAC (aka standard unit vector basisor Kronecker basis) Fadili et al [17] UDWT contributes toseparating slow and bump morphologies for EOG and EEGtransient slow changes DST is for monomorphic and poly-morphic EEG components (major EEG parts) and DIRAC isfor spike type activities in transient EEGs In comparison inthe simulated experiment we used the discrete cosine trans-form (DCT) discrete sine transform (DST) [56 57] and localdiscrete cosine transform (LDCT) dictionaries formajor EEGparts For the verification of the hypothesis the intracranialEEG (iEEG) data was assumed to be ldquotrue EEGrdquo signal whichwas recorded from the real brain activity and artificial EOGsincluding bump and slow changes were introduced and theperformance of the accurate reconstruction of the true EEGswas examined In iEEG there are two types of the data underthe conditions of eye-closing and eye-opening 42 Accordingto the neuroscientific evidence EEGs have a clear peakin the low-frequency range around 10Hz in the frequencyspectrum under the eye-closing condition 42 In the Resultscorrelation coefficient (cc) was used for the validation ofaccuracy in reconstruction and the frequency spectrum wasfor the validation of the nature of the information containedin EEGs

4 Results

For verification of our hypothesis in the computer experi-ments three types of the data were used (1) all simulateddata (2) a combination of real iEEG and simulated EOGand (3) recording of real EEG-EOG data and our proposedmethod was validated

41 Simulated Data In the first place two simulated signalsources were prepared for the simple test of the proposedmethod Initially Yong et al [36] proposed a combinationof the wavelet DCT and DIRAC for EEG artifact removalswhile their results could not tell how effective the methodwas in a qualitative manner In our experiment the firstsource signal consisted of a cosine wave which was assumedto be a monomorphic EEG signal and the second sourceconsisted of blinks component with three bumps designedas usual EOG signals The simulated signal as a mixture ofthe two sources and white noise (120578 = 20) was shownin Figure 3(a) where 120578 was defined as the percentage ofthe maximum amplitude of the input signal Our proposedMCA method was applied to separate the components fromthe simulated signal with the explicit dictionaries UDWT

6 Computational and Mathematical Methods in Medicine

02

0

1

2

024

1000 20000

minus2

minus2

Samples

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)1st signal source

2nd signal source

Combined signal (source)

(a)

0

15

0

2

0

1

1000 20000

minus2

Samples

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

1st separated component (UDWT)

2nd separated component (DCT)

3rd separated component (DIRAC)

(b)

0

2

4

1000 20000

minus2

Samples

Pote

ntia

l (V

)

Combined signal (source)Combination of separated component (reconstructed)

(c)

Figure 3 An example of simulated signal for decomposition and (a) the cosine with bump and spikes signals and combined signal withwhite noise (120578 = 20) (b) separated components with explicit dictionaries UDWT-DCT-DIRAC and (c) comparison between combinedsignal and sum of separated components (cc = 099)

DCT and DIRAC as shown in Figure 3(b) as a replicationtest The correlation coefficient between the simulated signaland the sum of all components was higher than 099 andthe simulated result proved the accuracy of decomposedcomponents byMCAwithUDWTDCT andDIRAC explicitdictionaries (Figure 3(c))

42 Simulated EOGContaminated iEEG Signal Theprevioussection was a simple example of the simulated data In thissection we introduced a new validation way to test theproposed method in a qualitative manner The real iEEGsignals were obtained under the closing eye condition Thelinear combination of simulated EOG and real iEEG signalswas used for the test In this case we assumed that iEEGhad already included a usual level of the white noise andthen did not add further noise additionallyThe iEEG datasetwas given by Andrzejak et al [58] with 100 trials andthe sampling rate was at 17361Hz (000576 ssample) and210(=1024) samples took about 6 s (589824 s) The linearcombination of simulated EOG and iEEG signals was appliedfor the validation

There were different combinations for simulated EOG asassumed artificial eye movement which was considered asthe step function and eye blinks by bump signalThe flatnesssignals with elevations with slow time scales compared with

the EEG time scale represent the gaze-type eyeball rotationsThe signals can be reconstructed by a mathematical methoddefined by the rate of change ()1015840 of which satisfies that119905 | ()1015840 gt 0 should be 0 Thus the definition of the EOGsmoothness is described as

()1015840119868 =

()1015840 (119905) ()1015840 (119905) = 00 ()1015840 (119905) gt 0

(7)

where 119868 = 119905 | ()1015840 = 0 leads to ()1015840119868 equiv 0 according toits definition as shown in Figure 4(b) In addition the bumpssignal was considered as the blink type EOG signal shownin Figure 4(c) Figure 4(d) showed the schematic examplefor the semisimulated signal In the same way 100 datasetsof semisimulated signals with a random combination ofcomponents in time series were used for the validation

Figures 5(a) 5(b) and 5(c) demonstrated a set of resultsfor the decomposition of the semisimulated signal by explicitdictionaries depending on the combination of dictionariesAsmentioned in Section 23 the stopping criterion dependedon 120582 lowast threshold and the parameters in this comparativestudy used a different combination of explicit dictionaries(UDWT-DCT-DIRAC UDWT-DST-DIRAC and UDWT-LDCT-DIRAC) and different type of thresholds either hardand soft and 120582 value varied from 3 to 5

Computational and Mathematical Methods in Medicine 7

200

0

minus200Pote

ntia

l (V

)

Samples40003000200010000

Intracranial real EEG signal

(a)

500

0

minus500Pote

ntia

l (V

)

Samples40003000200010000

Artificial eye movement-related EOG signal

(b)

500

0

minus500Pote

ntia

l (V

)

Samples40003000200010000

Artificial blink EOG signal

(c)

Samples

1000

0

minus1000Pote

ntia

l (V

)

40003000200010000

Combined signal (EEG + EOG)

(d)

Figure 4 A systemic representation of differentmorphological signals (a) intracranial EEG signal (b) artificial block EOG signal (c) artificialblink EOG signal and (d) combined signal

Figures 6(a) and 6(b) showed the averaged cc of decom-posed component by a respective combination of explicitdictionaries with hard and soft thresholds For EEG signaldecomposition performance cc between iEEG and eitherDST DCT or LDCT component was evaluated dependingon the three combination types (Figure 6(a)) For EOGsignal decomposition performance cc between EOG andUDWT component was evaluated (Figure 6(b)) In compari-son between hard and soft thresholds the average value of thehard threshold is around 06 which is larger than that in thesoft threshold while the average value of the soft threshold isaround 095 demonstrating fewer variances than those in thehard thresholdThismethod indicates thatUDWTdictionarywith a soft threshold is the stable performance according tothe fitness of the morphological property in this case

There were similar variances and average values in theevaluation of EEG signal decomposition using the timedomain and then we introduced a measure in the frequencydomain As mentioned in Section 22 EEG signals carryinformation to represent the current brain stage in thespecific tendency in the frequency domain such as having asynchronized neural activities by showing the existence of apeak in the frequency spectrum The EEG data used in theevaluation showed a peak around 10Hz under the closingeye condition and a peak around 50Hz under the openingeye condition Therefore in the frequency analysis a 10Hzpeak will be an index to tell how much the reconstructedsignal preserves the original information contained in theoriginal iEEG data under closing eye condition Figure 7showed the averaged normalized FFT as the comparisonbetween three combinations of the dictionaries InterestinglyalthoughDSTDCT and LDCT single components seemed toreconstruct the EEGs because of a high cc value in the timedomain the frequency spectrum analysis clarified the factthat the single component cannot reproduce the necessarytendency of EEG signals peak Meanwhile the combination

of 2nd and 3rd components which means oscillatory andspike components successfully reproduced the EEG signaltendency suggesting the importance of the spike informa-tion that presumably synchronizes background oscillatorybehaviors The 10Hz peak can be reproduced according toparameter conditions easily However 50Hz peak is difficultto be reproduced especially for LDCT-DIRAC componentin every case In the viewpoint of the tolerance in thechange of the threshold value the soft threshold methodshowed the robust performance of the signal informationpreservation which is consistent with the result of EOGsshown in Figure 6 As shown in Figure 8 the reconstructionaccuracy of the frequency profile by two dictionaries wasproved by a significant difference between the results of twomorphological and single morphological components (119905-test119901 lt 001 in both hard and soft thresholds) This evidencesuggests the importance of the DIRAC component for EEGsignals which was not equivalent to the noise or rathercarrying some information

43 Decomposition of EOG from Real EEG Data

431 EEG Data The real scalp EEG and EOG data wereobtained from the data demonstrated in the paper writtenby Ai et al (2016) [50] These data were recorded from23 EEG channels (FP1 FP2 F7 F3 Fz F4 F8 FC5 FC1FC2 FC4 T7 C3 Cz C4 T8 CP1 CP2 P3 Pz P4 O1and O2) and 7 EOG channels (V1u V1d V2u and V2dvertical EOG ⟨VEOG⟩ electrodeswere placed on supraorbitaland infraorbital rims of each eye HL and HR horizontalEOG ⟨HEOG⟩ electrodes were on the left and right outercanthi Vz was on the forehead approximately 25mm abovethe nasion) respectively according to 10ndash20 InternationalSystem (BrainAmp amplifier Brain Products GmbH) fromthe 8 participants seated in a comfortable armchair withthe base adjusted according to a participant height Theeyes of the participants were fixed straightly to the fixation

8 Computational and Mathematical Methods in Medicine

UDWT DST DIRAC400

0

minus400

Pote

ntia

l (V

)

200

0

minus200

0

100

minus100

Samples400020000

Samples400020000

Samples400020000

(a)

DCTUDWT DIRAC

400

0

minus400

Pote

ntia

l (V

)

200

0

minus200

0

100

minus100

Samples400020000

Samples400020000

Samples400020000

(b)

UDWT LDCT DIRAC400

0

minus400

Pote

ntia

l (V

)

200

0

200

0

minus200

Samples400020000

Samples400020000

Samples400020000

(c)

Figure 5 Components separation byMCA (a) explicit dictionaries are UDWT DST andDIRAC (b) UDWT DCT andDIRAC (c) UDWTLDCT and DIRAC respectively at 120582 = 4 The original signal for decomposition was shown in Figure 4(d) as combined signal

cross in the center of the monitor screen The stimulus wasdisplayed by a CRT monitor A chin support frame wasused to keep the participantrsquos head position fixed and fixtheir head to the supporting frame without laying their chinson the supporting bar to avoid the jaw clenching artifactThe distance between eyes and monitor was set to 70 cmThe sampling rate was 500Hz The whole details of theexperiment protocols were given in Ai et al (2016) [50]

432 Results with Real EEG-EOG According toAi et al [50]the real EEG-EOG data were divided into 4 sessions Eachsession had 12 tasks of eye movement The two EOG signalswere collected from ldquoV1d-V1urdquo and ldquoV2d-V2urdquo at right andleft sides of the eye as shown in Figure 9 and both signalsshowed the same kind of tendency because vertical EOG

propagated symmetrically in an anterior-posterior directionFigure 10 showed the real EEG signals were taken from someelectrodes for example Fp1 Fp2 Cz O1 and O2 whichrepresent EOG influence depending on the frontal centraland occipital parts of the brain

The selected explicit dictionaries were used to representthe targeted component for the EEG and EOG signal EEGand EOG were distinguished based on the morphologythat was observed in the EEG and EOG The lateral eyemovements mostly affect frontal electrodes [45] ThereforeFp1 electrode was used to decompose and demonstratethe effectiveness of our proposed method with MCA asshowed in Figure 11 and the same method was applied toall the 23 electrodes All EEG signals were morphologicallydecomposed with redundant transform

Computational and Mathematical Methods in Medicine 9

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

Aver

aged

corr

elat

ion

coeffi

cien

t

06

04

08

1

(a) cc between iEEG and 2nd comp (hard)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5Av

erag

ed co

rrel

atio

n co

effici

ent

06

04

08

1

(b) cc between iEEG and 2nd comp (soft)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

06

04

08

1

Aver

aged

corr

elat

ion

coeffi

cien

t

(c) cc between EOG and UDWT (hard)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

Aver

aged

corr

elat

ion

coeffi

cien

t

06

04

08

1

(d) cc between EOG and UDWT (soft)

Figure 6 A comparison between cc of decomposed morphological component with iEEG signal and artificial EOG with hard and softthresholds The mean value and standard deviation were calculated from all 100 decomposed datasets by explicit dictionaries (a) Secondmorphological component was decomposed by DST DCT and LDCT with hard and (b) soft threshold respectively (c) First morphologicalcomponent was decomposed by UDWT with a hard threshold and (d) soft threshold respectively 100 trials of iEEG and artificial EOG wereused

10 Computational and Mathematical Methods in Medicine

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

0 20 40 60 80

0

2

4

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(a) Hard (120582 = 3)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(b) Hard (120582 = 4)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(c) Hard (120582 = 5)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(d) Soft (120582 = 3)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(e) Soft (120582 = 4)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Nor

mal

ized

pow

er (d

B)

Frequency (Hz)

minus2

(f) Soft (120582 = 5)

Figure 7 An averaged normalized FFT obtained from 100 of iEEG and combination of two morphological components and singlemorphological component at 120582 varies from 3 to 5 with hard and soft thresholds

Figure 11(a) demonstrated the decomposition of compo-nents by the first explicit dictionary it was divided into threedifferent morphologies of the EEG signal Figures 11(b) and11(c) showed the second and the third explicit dictionary ofredundant transform respectively The overcomplete dictio-nary was a combination of redundant transforms that char-acterized the component in a different morphology Accord-ingly one of redundant transforms can be differentiated intodecomposed components by overcomplete dictionaries Thefirst component was decomposed by ldquoUDWTrdquo of each over-complete dictionary and was analyzed via the slow and blinktype morphology The second component was decomposedby ldquoDCTrdquo ldquoDSTrdquo and ldquoLDCTrdquo and was analyzed via thebackground of the signal which was similar to the EEG signal

and the third component was decomposed by ldquoDIRACrdquo andwas analyzed via the unexpected spikeThe first overcompletedictionary decomposed the EEG signal without changingthe monomorphic polymorphic and transient propertiesThe cc between the original signal and the summation of alldecomposed components was close to one Figure 12 showedthe raw EOG signal taken from the vertical and horizontalchannel and first decomposed component taken from Fp1Fp2 Cz O1 and O2 respectively

Table 1 showed individual cc of original EEG signals andrecomposed EEG signals from the combination of compo-nents with respect to different channels and combinationsof dictionaries Table 2 showed the cc between filter rawEOG signal taken from vertical and horizontal channels and

Computational and Mathematical Methods in Medicine 11

3 4 5

02

03

04

05

06

07

08

09

Aver

aged

FFT

corr

elat

ion

coeffi

cien

t

01

1

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

lowast lowast lowast

(a) Hard threshold

3 4 5

Aver

aged

FFT

corr

elat

ion

coeffi

cien

t02

03

04

05

06

07

08

09

01

1

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

lowast lowast lowast

(b) Soft threshold

Figure 8 A comparison of FFT correlation coefficients between iEEG data and morphological component decomposed by explicitdictionaries lowastSignificant differences (119901 lt 005) (a) Combined two morphological components and (b) single morphological componentMean value and standard deviation calculated from all 100 decomposed datasets by explicit dictionaries with hard and soft thresholds

400

Pote

ntia

l (V

)

200

0

minus200

400

Pote

ntia

l (V

)

200

0

minus200

Samples20000 1000

EOG (V1u-V1d)

EOG (V2u-V2d)

Figure 9 An example of EOG signal taken from right and left sideof eyes

decomposed first component from Fp1 Fp2 Cz O1 and O2respectively

5 Discussion

Artifact contamination in EEG signal has been a com-mon important issue in neurobiological event diagnosis and

Table 1 cc of original signal and sum of the decomposed compo-nents

EEG channelCorrelation coefficient

UDWT-DST-DIRAC

UDWT-DCT-DIRAC

UDWT-LDCT-DIRAC

Fp1 09921 plusmn 0014 09921 plusmn 0014 09932 plusmn 0013Fp2 0992 plusmn 017 09919 plusmn 018 09932 plusmn 014Cz 09898 plusmn 01 09899 plusmn 01 09908 plusmn 009O1 09836 plusmn 015 09836 plusmn 016 09869 plusmn 012O2 09855 plusmn 013 09856 plusmn 013 09849 plusmn 015

neuroscientific researchThevariousmethodswere applied toremove the artifacts from EEG [2 11ndash13 21 23 24 26ndash28 52]The decomposition based analysis was used in removal ofEOG artifacts in EEG [22 27 28 30 40 42] Howeverthose methods lack the elucidation of what the nature ofEEG signals is in the viewpoint of the signal analysis and asystematic approach was required by treating the sparsity andnonlinearity of the signal in the time domain

12 Computational and Mathematical Methods in Medicine

0

0

50

Fp1

Fp2

Cz

O1

O2

100

0

minus100

minus50

minus40

Pote

ntia

l (V

)

0

50

minus50

Pote

ntia

l (V

)

050

minus50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

Figure 10 An example of real EEG signal taken from Fp1 Fp2 Cz O1 and O2 electrode channels

Table 2 cc between filtered EOG and UDWT component decomposed by UDWT dictionary

EOG channels EEG channelsFp1 Fp2 Cz O1 O2

Correlation coefficientUDWT-DST-DIRACV1d 06777 0657 07267 09223 06445V1u 06814 0646 06606 09419 06354V2d 0916 0906 09402 0882 05402V2u 02332 02268 02353 06388 08494H1 08582 0847 08444 06902 05839H2 09419 09468 09559 07476 04752

UDWT-DCT-DIRACV1d 06792 06595 068 09213 06352V1u 06835 06396 06424 09581 06585V2d 09193 0902 09362 08764 05145V2u 02331 02183 02316 06639 08919H1 08593 08507 08626 06759 05376H2 09442 09465 09662 07266 04346

UDWT-LDCT-DIRACV1d 06794 06403 07219 08892 065V1u 06443 06279 06459 08196 05381V2d 09142 09072 09395 09592 06506V2u 02351 02235 02383 03747 06804H1 08637 08449 08471 07638 05734H2 09586 09558 09577 08826 05598

Computational and Mathematical Methods in Medicine 13

0

50

0

20

UDWT

DCT

DIRAC

0

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus30

(a)

UDWT

DST

DIRAC

0

0

20

0

50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus20

minus20

(b)

0

0

50

100

0

UDWT

LDCT

DIRAC

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus20

minus40

minus80

(c)

Figure 11 Component separated fromEEG (Fp1 electrode) signal by explicit dictionaries (a)UDWT-DCT-DIRAC (b)UDWT-DST-DIRACand (c) UDWT-LDCT-DIRAC respectively

This study revealed the nature of EEG signals in the senseof morphologies contained in the original signal by usingMCA The UDWT was used to decompose the slow andbump morphology The DCT DST and LDCT transformwere used to decompose the EEG signal Spike typemorphol-ogy was decomposed by DIRAC Redundant transforms ofDCT and DST have a similar capability in representing themorphology of oscillatory activities Therefore we used theDCT LDCT and DST dictionaries for validations of EEGsignal The detailed significant differences in morphology ofDCT and DST were given in past studies [56 57] while inour analysis there were no significant differences The rightcombination of redundant transforms to form overcompletedictionary revealed the desired decomposition in principle

In Section 42 ldquoBlocksrdquo ldquoBumpsrdquo similar to simulatedEOG signal defined in past studies [59ndash61] as shown in

Figure 4 and EEG data [58] were used to validate ourpurposed method The ldquoBlocksrdquo with abrupt changes weresimilar to the horizontal and vertical eye movements sim-ply as described by past studies [25 51] For the sake ofsimplicity in the present study ldquoBumpsrdquo were used as arepresentative signal form as eye blinks that happens inunexpected timings as illustrated in Figure 5 The separationof components by given dictionary works well in this evalu-ation but the further analysis is necessary for the evaluationof the signal decomposition with complex eye movementswhich requires presumably various redundant dictionariesIn the verification of the component discrimination as shownin Figures 6 and 7 the accuracy of the averaged EOGcomponent decomposition was above 90 which suggests aplausible performance even in the complex eye movementsThe combined DST and DIRAC dictionaries had better

14 Computational and Mathematical Methods in Medicine

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

Samples20000 1000

V1u

H1

(a) UDWT components separated by UDWT-DST-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(b) UDWT components separated by UDWT-DCT-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(c) UDWT components separated by UDWT-LDCT-DIRAC

Figure 12 UDWT component taken from Fp1 Fp2 Cz O1 and O2 separated by UDWT-DCT-DIRAC UDWT-DST-DIRAC and UDWT-LDCT-DIRAC respectively

decomposition performance than others while DST andDCT theoretically have no meaningful difference The usageof iEEG as the true EEG signal had a large benefit whichcan be used for the performance test for past proposedmethods like ICA and PCA consistently Our proposedmethod successfully demonstrated the performance in cc andthe frequency profile especially in Section 42 while in theserious discussion of the real EEG and EOG signals the DSTor DCT component exhibited a baseline fluctuation of thesignal which denotes the persistence of the EOG componentor other slow frequency artifacts noises and the factor willbe improved by the fine-tuned design of the DST or DCTdictionary with a band pass filter function In addition thethreshold problem exits in the optimization algorithm andnumber of iterations [37]

The EEG decomposition had not mark with a combi-nation of a second and a third component of EEG signal

decomposed by ldquoDST DCT and LDCTrdquo andDIRAC respec-tively based on the morphology Therefore the accuratecombination in the further perspective will be considerableEven the combination of all components and the mixedsignal or real EEG signal had cc above 97 for all redundanttransforms as is analyzed in the frequency spectrum thesignal morphology has further meaning in the viewpointof the signal transmission The MCA method has such anextended and flexible availability for signal analyses

6 Conclusion

Morphological Component Analysis methodology wasapplied to the simulated semisimulated and real EOGand EEG signal The successful decomposition of the EOGand EEG signal into their morphological component wasdemonstrated It seems to be that the EEG signals and

Computational and Mathematical Methods in Medicine 15

artifacts in EEG have been represented by different explicitdictionaries We analyzed the EEG signals involved with theEOG artifacts which were influenced by task conditionsTheDIRAC explicit dictionary decomposed the EEG signal intospike-like activities which may be related to the transientproperty of EEG UDWT explicit dictionary representsslow movement or bumps DCT DST and LDCT explicitdictionaries represent dominant signal that represents EEGsor pure tones signals as monomorphic and polymorphicactivities These results suggested that the effectivenessof MCA in ocular artifacts removal from the EEG rawsignal was derived from signal morphology characterizedas slow and smooth change of EOG time series In thefurther analysis the MCA is required to compare withother competing methods for the EEG and EOG signaldecomposition

Competing Interests

The authors have declared that no competing interests exist

Acknowledgments

This work was partly supported by JSPS KAKENHI 16H01616and 26240032 and theNewEnergy and Industrial TechnologyDevelopment Organization (NEDO) ldquoNext-Generation Arti-ficial Intelligence (3) Base Technology for Next-GenerationAIrdquo (Automated Driving Task) and the collaborative researchproject with Fujitsu Ten Limited

References

[1] J P Donoghue J N Sanes N G Hatsopoulos and G GaalldquoNeural discharge and local field potential oscillations in pri-mate motor cortex during voluntary movementsrdquo Journal ofNeurophysiology vol 79 no 1 pp 159ndash173 1998

[2] J A Uriguen and B Garcia-Zapirain ldquoEEG artifact removalmdashstate-of-the-art and guidelinesrdquo Journal of Neural Engineeringvol 12 no 3 Article ID 031001 2015

[3] C Kamarajan and B Porjesz ldquoAdvances in electrophysiologicalresearchrdquoAlcohol Research Current Reviews vol 37 no 1 article53 2015

[4] L F Nicolas-Alonso and J Gomez-Gil ldquoBrain computer inter-faces a reviewrdquo Sensors vol 12 no 2 pp 1211ndash1279 2012

[5] L Mayaud M Congedo A Van Laghenhove et al ldquoA compar-ison of recording modalities of P300 event-related potentials(ERP) for brain-computer interface (BCI) paradigmrdquo Neuro-physiologie CliniqueClinical Neurophysiology vol 43 no 4 pp217ndash227 2013

[6] X-Y Wang J Jin Y Zhang and B Wang ldquoBrain controlhuman-computer integration control based on brain-computerinterfacerdquo Acta Automatica Sinica vol 39 no 3 pp 208ndash2212013

[7] G Al-Hudhud ldquoAffective command-based control system inte-grating brain signals in commands control systemsrdquo Computersin Human Behavior vol 30 pp 535ndash541 2014

[8] J L Sirvent Blasco E Ianez A Ubeda and JM Azorın ldquoVisualevoked potential-based brain-machine interface applications toassist disabled peoplerdquo Expert Systems with Applications vol 39no 9 pp 7908ndash7918 2012

[9] H Cecotti ldquoSpelling with non-invasive Brain-Computer Inter-facesmdashcurrent and future trendsrdquo Journal of Physiology Parisvol 105 no 1ndash3 pp 106ndash114 2011

[10] I S Kotchetkov B Y Hwang G Appelboom C P Kellnerand E S Connolly Jr ldquoBrain-computer interfaces militaryneurosurgical and ethical perspectiverdquo Neurosurgical Focusvol 28 no 5 article no E25 2010

[11] R N Vigario ldquoExtraction of ocular artefacts from EEG usingindependent component analysisrdquo Electroencephalography andClinical Neurophysiology vol 103 no 3 pp 395ndash404 1997

[12] W Zhou and J Gotman ldquoAutomatic removal of eye movementartifacts from the EEG using ICA and the dipole modelrdquoProgress in Natural Science vol 19 no 9 pp 1165ndash1170 2009

[13] R Sameni andCGouy-Pailler ldquoAn iterative subspace denoisingalgorithm for removing electroencephalogram ocular artifactsrdquoJournal of Neuroscience Methods vol 225 pp 97ndash105 2014

[14] M Breakspear and J R Terry ldquoDetection and description ofnon-linear interdependence in normal multichannel humanEEG datardquo Clinical Neurophysiology vol 113 no 5 pp 735ndash7532002

[15] U R Acharya O Faust N Kannathal T Chua and S Laxmin-arayan ldquoNon-linear analysis of EEG signals at various sleepstagesrdquo Computer Methods and Programs in Biomedicine vol80 no 1 pp 37ndash45 2005

[16] L I Aftanas and S A Golocheikine ldquoNon-linear dynamiccomplexity of the human EEGduringmeditationrdquoNeuroscienceLetters vol 330 no 2 pp 143ndash146 2002

[17] M J Fadili J-L Starck J Bobin and Y Moudden ldquoImagedecomposition and separation using sparse representations anoverviewrdquo Proceedings of the IEEE vol 98 no 6 pp 983ndash9942010

[18] K J Blinowska and P J Durka ldquoUnbiased high resolutionmethod of EEG analysis in time-frequency spacerdquo Acta Neuro-biologiae Experimentalis vol 61 no 3 pp 157ndash174 2001

[19] E Imani H-R Pourreza and T Banaee ldquoFully automateddiabetic retinopathy screening usingmorphological componentanalysisrdquo Computerized Medical Imaging and Graphics vol 43pp 78ndash88 2015

[20] E Imani M Javidi and H-R Pourreza ldquoImprovement ofretinal blood vessel detection using morphological componentanalysisrdquo Computer Methods and Programs in Biomedicine vol118 no 3 pp 263ndash279 2016

[21] A S Al-Fahoum and A A Al-Fraihat ldquoMethods of EEG signalfeatures extraction using linear analysis in frequency and time-frequency domainsrdquo ISRN Neuroscience vol 2014 Article ID730218 7 pages 2014

[22] M Zibulevsky and B A Pearlmutter ldquoBlind source separationby sparse decomposition in a signal dictionaryrdquoNeural Compu-tation vol 13 no 4 pp 863ndash882 2001

[23] N P Castellanos andVAMakarov ldquoRecovering EEGbrain sig-nals artifact suppression with wavelet enhanced independentcomponent analysisrdquo Journal of Neuroscience Methods vol 158no 2 pp 300ndash312 2006

[24] J Hou K Morgan D M Tucker et al ldquoAn improved artifactsremoval method for high dimensional EEGrdquo Journal of Neuro-science Methods vol 268 pp 31ndash42 2016

[25] P Berg and M Scherg ldquoA multiple source approach to thecorrection of eye artifactsrdquo Electroencephalography and ClinicalNeurophysiology vol 90 no 3 pp 229ndash241 1994

[26] P K Sadasivan and D Narayana Dutt ldquoSVD based techniquefor noise reduction in electroencephalographic signalsrdquo SignalProcessing vol 55 no 2 pp 179ndash189 1996

16 Computational and Mathematical Methods in Medicine

[27] C A Joyce I F Gorodnitsky andMKutas ldquoAutomatic removalof eye movement and blink artifacts from EEG data using blindcomponent separationrdquo Psychophysiology vol 41 no 2 pp 313ndash325 2004

[28] G L Wallstrom R E Kass A Miller J F Cohn and N A FoxldquoAutomatic correction of ocular artifacts in the EEG a com-parison of regression-based and component-based methodsrdquoInternational Journal of Psychophysiology vol 53 no 2 pp 105ndash119 2004

[29] S M Gordon V Lawhern A D Passaro and K McDowellldquoInformed decomposition of electroencephalographic datardquoJournal of Neuroscience Methods vol 256 pp 41ndash55 2015

[30] D StuderUHoffmann andTKoenig ldquoFromEEGdependencymultichannel matching pursuit to sparse topographic EEGdecompositionrdquo Journal of Neuroscience Methods vol 153 no2 pp 261ndash275 2006

[31] J-L Starck M Elad and D Donoho ldquoRedundant multiscaletransforms and their application for morphological componentseparationrdquo Advances in Imaging and Electron Physics vol 132pp 287ndash348 2004

[32] P J Franaszczuk G K Bergey P J Durka andHM EisenbergldquoTime-frequency analysis using thematching pursuit algorithmapplied to seizures originating from the mesial temporal loberdquoElectroencephalography and Clinical Neurophysiology vol 106no 6 pp 513ndash521 1998

[33] P J Durka A Matysiak E M Montes P V Sosa and K JBlinowska ldquoMultichannel matching pursuit and EEG inversesolutionsrdquo Journal of Neuroscience Methods vol 148 no 1 pp49ndash59 2005

[34] J Bobin J-L Starck J Fadili and Y Moudden ldquoSparsityand morphological diversity in blind source separationrdquo IEEETransactions on Image Processing vol 16 no 11 pp 2662ndash26742007

[35] P J Durka D Ircha and K J Blinowska ldquoStochastic time-frequency dictionaries formatching pursuitrdquo IEEE Transactionson Signal Processing vol 49 no 3 pp 507ndash510 2001

[36] X Yong R K Ward and G E Birch ldquoGeneralized morpholog-ical component analysis for EEG source separation and artifactremovalrdquo in Proceedings of the 4th International IEEEEMBSConference on Neural Engineering (NER rsquo09) pp 343ndash346Antalya Turkey May 2009

[37] B Singh G Ai and H Wagatsuma ldquoAn electrooculographyanalysis in the time-frequency domain using morphologicalcomponent analysis toward the development of mobile BCIsystemsrdquo in Universal Access in Human-Computer InteractionAccess to Interaction 9th International Conference UAHCI 2015Held as Part of HCI International 2015 Los Angeles CA USAAugust 2ndash7 2015 Proceedings Part II vol 9176 of Lecture Notesin Computer Science pp 528ndash537 Springer Berlin Germany2015

[38] S S Chen D L Donoho and M A Saunders ldquoAtomicdecomposition by basis pursuitrdquo SIAM Review vol 43 no 1pp 129ndash159 2001

[39] D L Donoho and X Huo ldquoUncertainty principles and idealatomic decompositionrdquo IEEE Transactions on InformationThe-ory vol 47 no 7 pp 2845ndash2862 2001

[40] F Miwakeichi E Martınez-Montes P A Valdes-Sosa NNishiyama H Mizuhara and Y Yamaguchi ldquoDecomposingEEG data into spacendashtimendashfrequency components using par-allel factor analysisrdquo NeuroImage vol 22 no 3 pp 1035ndash10452004

[41] K J Friston C D Frith P F Liddle and R S J FrackowiakldquoFunctional connectivity the principal-component analysis oflarge (PET) data setsrdquo Journal of Cerebral Blood Flow andMetabolism vol 13 no 1 pp 5ndash14 1993

[42] S Makeig T-P Jung A J Bell D Ghahremani and T JSejnowski ldquoBlind separation of auditory event-related brainresponses into independent componentsrdquo Proceedings of theNational Academy of Sciences of the United States of Americavol 94 no 20 pp 10979ndash10984 1997

[43] Biomedical Signal httpwwwmedicinemcgillcaphysiovlabbiomed signalseeg nhtm

[44] S E G Nilsson and B E Andersson ldquoCorneal DC recordingsof slow ocular potential changes such as the ERG c-wave and thelight peak in clinical workmdashequipment and examples of resultsrdquoDocumenta Ophthalmologica vol 68 no 3-4 pp 313ndash325 1988

[45] OG Lins TW Picton P Berg andM Scherg ldquoOcular artifactsin EEG and event-related potentials I scalp topographyrdquo BrainTopography vol 6 no 1 pp 51ndash63 1993

[46] T W Picton P Van Roon M L Armilio P Berg N Ille andM Scherg ldquoThe correction of ocular artifacts a topographicperspectiverdquo Clinical Neurophysiology vol 111 no 1 pp 53ndash652000

[47] A S Keren S Yuval-Greenberg and L Y Deouell ldquoSaccadicspike potentials in gamma-band EEG characterization detec-tion and suppressionrdquo NeuroImage vol 49 no 3 pp 2248ndash2263 2010

[48] M Plochl J P Ossandon and P Konig ldquoCombining EEG andeye tracking identification characterization and correctionof eye movement artifacts in electroencephalographic datardquoFrontiers in Human Neuroscience vol 6 article 278 2012

[49] S Dandekar C Privitera T Carney and S A Klein ldquoNeuralsaccadic response estimation during natural viewingrdquo Journalof Neurophysiology vol 107 no 6 pp 1776ndash1790 2012

[50] G Ai N Sato B Singh and H Wagatsuma ldquoDirection andviewing area-sensitive influence of EOGartifacts revealed in theEEG topographic pattern analysisrdquo Cognitive Neurodynamicsvol 10 no 4 pp 301ndash314 2016

[51] P Berg and M Scherg ldquoDipole models of eye movements andblinksrdquo Electroencephalography and Clinical Neurophysiologyvol 79 no 1 pp 36ndash44 1991

[52] R J Croft and R J Barry ldquoRemoval of ocular artifact from theEEG a reviewrdquo Neurophysiologie Clinique vol 30 no 1 pp 5ndash19 2000

[53] I J Rampil ldquoA primer for EEG signal processing in anesthesiardquoAnesthesiology vol 89 no 4 pp 980ndash1002 1998

[54] J L Starck Y Moudden J Bobin M Elad and D DonoholdquoMorphological component analysisrdquo in Optics amp Photonics2005 p 59140Q International Society forOptics and Photonics2005

[55] S Sardy A Bruce and P Tseng ldquoBlock coordinate relaxationmethods for nonparametric signal denoising with waveletdictionariesrdquo Journal of Computational and Graphical Statisticsvol 9 pp 361ndash379 2000

[56] M Puschel and J M F Moura ldquoThe algebraic approach to thediscrete cosine and sine transforms and their fast algorithmsrdquoSIAM Journal on Computing vol 32 no 5 pp 1280ndash1316 2003

[57] X Shao and S G Johnson ldquoType-IV DCT DST and MDCTalgorithms with reduced numbers of arithmetic operationsrdquoSignal Processing vol 88 no 6 pp 1313ndash1326 2008

[58] R G Andrzejak K Lehnertz F Mormann C Rieke P Davidand C E Elger ldquoIndications of nonlinear deterministic and

6 Computational and Mathematical Methods in Medicine

02

0

1

2

024

1000 20000

minus2

minus2

Samples

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)1st signal source

2nd signal source

Combined signal (source)

(a)

0

15

0

2

0

1

1000 20000

minus2

Samples

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

1st separated component (UDWT)

2nd separated component (DCT)

3rd separated component (DIRAC)

(b)

0

2

4

1000 20000

minus2

Samples

Pote

ntia

l (V

)

Combined signal (source)Combination of separated component (reconstructed)

(c)

Figure 3 An example of simulated signal for decomposition and (a) the cosine with bump and spikes signals and combined signal withwhite noise (120578 = 20) (b) separated components with explicit dictionaries UDWT-DCT-DIRAC and (c) comparison between combinedsignal and sum of separated components (cc = 099)

DCT and DIRAC as shown in Figure 3(b) as a replicationtest The correlation coefficient between the simulated signaland the sum of all components was higher than 099 andthe simulated result proved the accuracy of decomposedcomponents byMCAwithUDWTDCT andDIRAC explicitdictionaries (Figure 3(c))

42 Simulated EOGContaminated iEEG Signal Theprevioussection was a simple example of the simulated data In thissection we introduced a new validation way to test theproposed method in a qualitative manner The real iEEGsignals were obtained under the closing eye condition Thelinear combination of simulated EOG and real iEEG signalswas used for the test In this case we assumed that iEEGhad already included a usual level of the white noise andthen did not add further noise additionallyThe iEEG datasetwas given by Andrzejak et al [58] with 100 trials andthe sampling rate was at 17361Hz (000576 ssample) and210(=1024) samples took about 6 s (589824 s) The linearcombination of simulated EOG and iEEG signals was appliedfor the validation

There were different combinations for simulated EOG asassumed artificial eye movement which was considered asthe step function and eye blinks by bump signalThe flatnesssignals with elevations with slow time scales compared with

the EEG time scale represent the gaze-type eyeball rotationsThe signals can be reconstructed by a mathematical methoddefined by the rate of change ()1015840 of which satisfies that119905 | ()1015840 gt 0 should be 0 Thus the definition of the EOGsmoothness is described as

()1015840119868 =

()1015840 (119905) ()1015840 (119905) = 00 ()1015840 (119905) gt 0

(7)

where 119868 = 119905 | ()1015840 = 0 leads to ()1015840119868 equiv 0 according toits definition as shown in Figure 4(b) In addition the bumpssignal was considered as the blink type EOG signal shownin Figure 4(c) Figure 4(d) showed the schematic examplefor the semisimulated signal In the same way 100 datasetsof semisimulated signals with a random combination ofcomponents in time series were used for the validation

Figures 5(a) 5(b) and 5(c) demonstrated a set of resultsfor the decomposition of the semisimulated signal by explicitdictionaries depending on the combination of dictionariesAsmentioned in Section 23 the stopping criterion dependedon 120582 lowast threshold and the parameters in this comparativestudy used a different combination of explicit dictionaries(UDWT-DCT-DIRAC UDWT-DST-DIRAC and UDWT-LDCT-DIRAC) and different type of thresholds either hardand soft and 120582 value varied from 3 to 5

Computational and Mathematical Methods in Medicine 7

200

0

minus200Pote

ntia

l (V

)

Samples40003000200010000

Intracranial real EEG signal

(a)

500

0

minus500Pote

ntia

l (V

)

Samples40003000200010000

Artificial eye movement-related EOG signal

(b)

500

0

minus500Pote

ntia

l (V

)

Samples40003000200010000

Artificial blink EOG signal

(c)

Samples

1000

0

minus1000Pote

ntia

l (V

)

40003000200010000

Combined signal (EEG + EOG)

(d)

Figure 4 A systemic representation of differentmorphological signals (a) intracranial EEG signal (b) artificial block EOG signal (c) artificialblink EOG signal and (d) combined signal

Figures 6(a) and 6(b) showed the averaged cc of decom-posed component by a respective combination of explicitdictionaries with hard and soft thresholds For EEG signaldecomposition performance cc between iEEG and eitherDST DCT or LDCT component was evaluated dependingon the three combination types (Figure 6(a)) For EOGsignal decomposition performance cc between EOG andUDWT component was evaluated (Figure 6(b)) In compari-son between hard and soft thresholds the average value of thehard threshold is around 06 which is larger than that in thesoft threshold while the average value of the soft threshold isaround 095 demonstrating fewer variances than those in thehard thresholdThismethod indicates thatUDWTdictionarywith a soft threshold is the stable performance according tothe fitness of the morphological property in this case

There were similar variances and average values in theevaluation of EEG signal decomposition using the timedomain and then we introduced a measure in the frequencydomain As mentioned in Section 22 EEG signals carryinformation to represent the current brain stage in thespecific tendency in the frequency domain such as having asynchronized neural activities by showing the existence of apeak in the frequency spectrum The EEG data used in theevaluation showed a peak around 10Hz under the closingeye condition and a peak around 50Hz under the openingeye condition Therefore in the frequency analysis a 10Hzpeak will be an index to tell how much the reconstructedsignal preserves the original information contained in theoriginal iEEG data under closing eye condition Figure 7showed the averaged normalized FFT as the comparisonbetween three combinations of the dictionaries InterestinglyalthoughDSTDCT and LDCT single components seemed toreconstruct the EEGs because of a high cc value in the timedomain the frequency spectrum analysis clarified the factthat the single component cannot reproduce the necessarytendency of EEG signals peak Meanwhile the combination

of 2nd and 3rd components which means oscillatory andspike components successfully reproduced the EEG signaltendency suggesting the importance of the spike informa-tion that presumably synchronizes background oscillatorybehaviors The 10Hz peak can be reproduced according toparameter conditions easily However 50Hz peak is difficultto be reproduced especially for LDCT-DIRAC componentin every case In the viewpoint of the tolerance in thechange of the threshold value the soft threshold methodshowed the robust performance of the signal informationpreservation which is consistent with the result of EOGsshown in Figure 6 As shown in Figure 8 the reconstructionaccuracy of the frequency profile by two dictionaries wasproved by a significant difference between the results of twomorphological and single morphological components (119905-test119901 lt 001 in both hard and soft thresholds) This evidencesuggests the importance of the DIRAC component for EEGsignals which was not equivalent to the noise or rathercarrying some information

43 Decomposition of EOG from Real EEG Data

431 EEG Data The real scalp EEG and EOG data wereobtained from the data demonstrated in the paper writtenby Ai et al (2016) [50] These data were recorded from23 EEG channels (FP1 FP2 F7 F3 Fz F4 F8 FC5 FC1FC2 FC4 T7 C3 Cz C4 T8 CP1 CP2 P3 Pz P4 O1and O2) and 7 EOG channels (V1u V1d V2u and V2dvertical EOG ⟨VEOG⟩ electrodeswere placed on supraorbitaland infraorbital rims of each eye HL and HR horizontalEOG ⟨HEOG⟩ electrodes were on the left and right outercanthi Vz was on the forehead approximately 25mm abovethe nasion) respectively according to 10ndash20 InternationalSystem (BrainAmp amplifier Brain Products GmbH) fromthe 8 participants seated in a comfortable armchair withthe base adjusted according to a participant height Theeyes of the participants were fixed straightly to the fixation

8 Computational and Mathematical Methods in Medicine

UDWT DST DIRAC400

0

minus400

Pote

ntia

l (V

)

200

0

minus200

0

100

minus100

Samples400020000

Samples400020000

Samples400020000

(a)

DCTUDWT DIRAC

400

0

minus400

Pote

ntia

l (V

)

200

0

minus200

0

100

minus100

Samples400020000

Samples400020000

Samples400020000

(b)

UDWT LDCT DIRAC400

0

minus400

Pote

ntia

l (V

)

200

0

200

0

minus200

Samples400020000

Samples400020000

Samples400020000

(c)

Figure 5 Components separation byMCA (a) explicit dictionaries are UDWT DST andDIRAC (b) UDWT DCT andDIRAC (c) UDWTLDCT and DIRAC respectively at 120582 = 4 The original signal for decomposition was shown in Figure 4(d) as combined signal

cross in the center of the monitor screen The stimulus wasdisplayed by a CRT monitor A chin support frame wasused to keep the participantrsquos head position fixed and fixtheir head to the supporting frame without laying their chinson the supporting bar to avoid the jaw clenching artifactThe distance between eyes and monitor was set to 70 cmThe sampling rate was 500Hz The whole details of theexperiment protocols were given in Ai et al (2016) [50]

432 Results with Real EEG-EOG According toAi et al [50]the real EEG-EOG data were divided into 4 sessions Eachsession had 12 tasks of eye movement The two EOG signalswere collected from ldquoV1d-V1urdquo and ldquoV2d-V2urdquo at right andleft sides of the eye as shown in Figure 9 and both signalsshowed the same kind of tendency because vertical EOG

propagated symmetrically in an anterior-posterior directionFigure 10 showed the real EEG signals were taken from someelectrodes for example Fp1 Fp2 Cz O1 and O2 whichrepresent EOG influence depending on the frontal centraland occipital parts of the brain

The selected explicit dictionaries were used to representthe targeted component for the EEG and EOG signal EEGand EOG were distinguished based on the morphologythat was observed in the EEG and EOG The lateral eyemovements mostly affect frontal electrodes [45] ThereforeFp1 electrode was used to decompose and demonstratethe effectiveness of our proposed method with MCA asshowed in Figure 11 and the same method was applied toall the 23 electrodes All EEG signals were morphologicallydecomposed with redundant transform

Computational and Mathematical Methods in Medicine 9

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

Aver

aged

corr

elat

ion

coeffi

cien

t

06

04

08

1

(a) cc between iEEG and 2nd comp (hard)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5Av

erag

ed co

rrel

atio

n co

effici

ent

06

04

08

1

(b) cc between iEEG and 2nd comp (soft)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

06

04

08

1

Aver

aged

corr

elat

ion

coeffi

cien

t

(c) cc between EOG and UDWT (hard)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

Aver

aged

corr

elat

ion

coeffi

cien

t

06

04

08

1

(d) cc between EOG and UDWT (soft)

Figure 6 A comparison between cc of decomposed morphological component with iEEG signal and artificial EOG with hard and softthresholds The mean value and standard deviation were calculated from all 100 decomposed datasets by explicit dictionaries (a) Secondmorphological component was decomposed by DST DCT and LDCT with hard and (b) soft threshold respectively (c) First morphologicalcomponent was decomposed by UDWT with a hard threshold and (d) soft threshold respectively 100 trials of iEEG and artificial EOG wereused

10 Computational and Mathematical Methods in Medicine

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

0 20 40 60 80

0

2

4

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(a) Hard (120582 = 3)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(b) Hard (120582 = 4)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(c) Hard (120582 = 5)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(d) Soft (120582 = 3)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(e) Soft (120582 = 4)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Nor

mal

ized

pow

er (d

B)

Frequency (Hz)

minus2

(f) Soft (120582 = 5)

Figure 7 An averaged normalized FFT obtained from 100 of iEEG and combination of two morphological components and singlemorphological component at 120582 varies from 3 to 5 with hard and soft thresholds

Figure 11(a) demonstrated the decomposition of compo-nents by the first explicit dictionary it was divided into threedifferent morphologies of the EEG signal Figures 11(b) and11(c) showed the second and the third explicit dictionary ofredundant transform respectively The overcomplete dictio-nary was a combination of redundant transforms that char-acterized the component in a different morphology Accord-ingly one of redundant transforms can be differentiated intodecomposed components by overcomplete dictionaries Thefirst component was decomposed by ldquoUDWTrdquo of each over-complete dictionary and was analyzed via the slow and blinktype morphology The second component was decomposedby ldquoDCTrdquo ldquoDSTrdquo and ldquoLDCTrdquo and was analyzed via thebackground of the signal which was similar to the EEG signal

and the third component was decomposed by ldquoDIRACrdquo andwas analyzed via the unexpected spikeThe first overcompletedictionary decomposed the EEG signal without changingthe monomorphic polymorphic and transient propertiesThe cc between the original signal and the summation of alldecomposed components was close to one Figure 12 showedthe raw EOG signal taken from the vertical and horizontalchannel and first decomposed component taken from Fp1Fp2 Cz O1 and O2 respectively

Table 1 showed individual cc of original EEG signals andrecomposed EEG signals from the combination of compo-nents with respect to different channels and combinationsof dictionaries Table 2 showed the cc between filter rawEOG signal taken from vertical and horizontal channels and

Computational and Mathematical Methods in Medicine 11

3 4 5

02

03

04

05

06

07

08

09

Aver

aged

FFT

corr

elat

ion

coeffi

cien

t

01

1

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

lowast lowast lowast

(a) Hard threshold

3 4 5

Aver

aged

FFT

corr

elat

ion

coeffi

cien

t02

03

04

05

06

07

08

09

01

1

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

lowast lowast lowast

(b) Soft threshold

Figure 8 A comparison of FFT correlation coefficients between iEEG data and morphological component decomposed by explicitdictionaries lowastSignificant differences (119901 lt 005) (a) Combined two morphological components and (b) single morphological componentMean value and standard deviation calculated from all 100 decomposed datasets by explicit dictionaries with hard and soft thresholds

400

Pote

ntia

l (V

)

200

0

minus200

400

Pote

ntia

l (V

)

200

0

minus200

Samples20000 1000

EOG (V1u-V1d)

EOG (V2u-V2d)

Figure 9 An example of EOG signal taken from right and left sideof eyes

decomposed first component from Fp1 Fp2 Cz O1 and O2respectively

5 Discussion

Artifact contamination in EEG signal has been a com-mon important issue in neurobiological event diagnosis and

Table 1 cc of original signal and sum of the decomposed compo-nents

EEG channelCorrelation coefficient

UDWT-DST-DIRAC

UDWT-DCT-DIRAC

UDWT-LDCT-DIRAC

Fp1 09921 plusmn 0014 09921 plusmn 0014 09932 plusmn 0013Fp2 0992 plusmn 017 09919 plusmn 018 09932 plusmn 014Cz 09898 plusmn 01 09899 plusmn 01 09908 plusmn 009O1 09836 plusmn 015 09836 plusmn 016 09869 plusmn 012O2 09855 plusmn 013 09856 plusmn 013 09849 plusmn 015

neuroscientific researchThevariousmethodswere applied toremove the artifacts from EEG [2 11ndash13 21 23 24 26ndash28 52]The decomposition based analysis was used in removal ofEOG artifacts in EEG [22 27 28 30 40 42] Howeverthose methods lack the elucidation of what the nature ofEEG signals is in the viewpoint of the signal analysis and asystematic approach was required by treating the sparsity andnonlinearity of the signal in the time domain

12 Computational and Mathematical Methods in Medicine

0

0

50

Fp1

Fp2

Cz

O1

O2

100

0

minus100

minus50

minus40

Pote

ntia

l (V

)

0

50

minus50

Pote

ntia

l (V

)

050

minus50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

Figure 10 An example of real EEG signal taken from Fp1 Fp2 Cz O1 and O2 electrode channels

Table 2 cc between filtered EOG and UDWT component decomposed by UDWT dictionary

EOG channels EEG channelsFp1 Fp2 Cz O1 O2

Correlation coefficientUDWT-DST-DIRACV1d 06777 0657 07267 09223 06445V1u 06814 0646 06606 09419 06354V2d 0916 0906 09402 0882 05402V2u 02332 02268 02353 06388 08494H1 08582 0847 08444 06902 05839H2 09419 09468 09559 07476 04752

UDWT-DCT-DIRACV1d 06792 06595 068 09213 06352V1u 06835 06396 06424 09581 06585V2d 09193 0902 09362 08764 05145V2u 02331 02183 02316 06639 08919H1 08593 08507 08626 06759 05376H2 09442 09465 09662 07266 04346

UDWT-LDCT-DIRACV1d 06794 06403 07219 08892 065V1u 06443 06279 06459 08196 05381V2d 09142 09072 09395 09592 06506V2u 02351 02235 02383 03747 06804H1 08637 08449 08471 07638 05734H2 09586 09558 09577 08826 05598

Computational and Mathematical Methods in Medicine 13

0

50

0

20

UDWT

DCT

DIRAC

0

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus30

(a)

UDWT

DST

DIRAC

0

0

20

0

50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus20

minus20

(b)

0

0

50

100

0

UDWT

LDCT

DIRAC

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus20

minus40

minus80

(c)

Figure 11 Component separated fromEEG (Fp1 electrode) signal by explicit dictionaries (a)UDWT-DCT-DIRAC (b)UDWT-DST-DIRACand (c) UDWT-LDCT-DIRAC respectively

This study revealed the nature of EEG signals in the senseof morphologies contained in the original signal by usingMCA The UDWT was used to decompose the slow andbump morphology The DCT DST and LDCT transformwere used to decompose the EEG signal Spike typemorphol-ogy was decomposed by DIRAC Redundant transforms ofDCT and DST have a similar capability in representing themorphology of oscillatory activities Therefore we used theDCT LDCT and DST dictionaries for validations of EEGsignal The detailed significant differences in morphology ofDCT and DST were given in past studies [56 57] while inour analysis there were no significant differences The rightcombination of redundant transforms to form overcompletedictionary revealed the desired decomposition in principle

In Section 42 ldquoBlocksrdquo ldquoBumpsrdquo similar to simulatedEOG signal defined in past studies [59ndash61] as shown in

Figure 4 and EEG data [58] were used to validate ourpurposed method The ldquoBlocksrdquo with abrupt changes weresimilar to the horizontal and vertical eye movements sim-ply as described by past studies [25 51] For the sake ofsimplicity in the present study ldquoBumpsrdquo were used as arepresentative signal form as eye blinks that happens inunexpected timings as illustrated in Figure 5 The separationof components by given dictionary works well in this evalu-ation but the further analysis is necessary for the evaluationof the signal decomposition with complex eye movementswhich requires presumably various redundant dictionariesIn the verification of the component discrimination as shownin Figures 6 and 7 the accuracy of the averaged EOGcomponent decomposition was above 90 which suggests aplausible performance even in the complex eye movementsThe combined DST and DIRAC dictionaries had better

14 Computational and Mathematical Methods in Medicine

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

Samples20000 1000

V1u

H1

(a) UDWT components separated by UDWT-DST-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(b) UDWT components separated by UDWT-DCT-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(c) UDWT components separated by UDWT-LDCT-DIRAC

Figure 12 UDWT component taken from Fp1 Fp2 Cz O1 and O2 separated by UDWT-DCT-DIRAC UDWT-DST-DIRAC and UDWT-LDCT-DIRAC respectively

decomposition performance than others while DST andDCT theoretically have no meaningful difference The usageof iEEG as the true EEG signal had a large benefit whichcan be used for the performance test for past proposedmethods like ICA and PCA consistently Our proposedmethod successfully demonstrated the performance in cc andthe frequency profile especially in Section 42 while in theserious discussion of the real EEG and EOG signals the DSTor DCT component exhibited a baseline fluctuation of thesignal which denotes the persistence of the EOG componentor other slow frequency artifacts noises and the factor willbe improved by the fine-tuned design of the DST or DCTdictionary with a band pass filter function In addition thethreshold problem exits in the optimization algorithm andnumber of iterations [37]

The EEG decomposition had not mark with a combi-nation of a second and a third component of EEG signal

decomposed by ldquoDST DCT and LDCTrdquo andDIRAC respec-tively based on the morphology Therefore the accuratecombination in the further perspective will be considerableEven the combination of all components and the mixedsignal or real EEG signal had cc above 97 for all redundanttransforms as is analyzed in the frequency spectrum thesignal morphology has further meaning in the viewpointof the signal transmission The MCA method has such anextended and flexible availability for signal analyses

6 Conclusion

Morphological Component Analysis methodology wasapplied to the simulated semisimulated and real EOGand EEG signal The successful decomposition of the EOGand EEG signal into their morphological component wasdemonstrated It seems to be that the EEG signals and

Computational and Mathematical Methods in Medicine 15

artifacts in EEG have been represented by different explicitdictionaries We analyzed the EEG signals involved with theEOG artifacts which were influenced by task conditionsTheDIRAC explicit dictionary decomposed the EEG signal intospike-like activities which may be related to the transientproperty of EEG UDWT explicit dictionary representsslow movement or bumps DCT DST and LDCT explicitdictionaries represent dominant signal that represents EEGsor pure tones signals as monomorphic and polymorphicactivities These results suggested that the effectivenessof MCA in ocular artifacts removal from the EEG rawsignal was derived from signal morphology characterizedas slow and smooth change of EOG time series In thefurther analysis the MCA is required to compare withother competing methods for the EEG and EOG signaldecomposition

Competing Interests

The authors have declared that no competing interests exist

Acknowledgments

This work was partly supported by JSPS KAKENHI 16H01616and 26240032 and theNewEnergy and Industrial TechnologyDevelopment Organization (NEDO) ldquoNext-Generation Arti-ficial Intelligence (3) Base Technology for Next-GenerationAIrdquo (Automated Driving Task) and the collaborative researchproject with Fujitsu Ten Limited

References

[1] J P Donoghue J N Sanes N G Hatsopoulos and G GaalldquoNeural discharge and local field potential oscillations in pri-mate motor cortex during voluntary movementsrdquo Journal ofNeurophysiology vol 79 no 1 pp 159ndash173 1998

[2] J A Uriguen and B Garcia-Zapirain ldquoEEG artifact removalmdashstate-of-the-art and guidelinesrdquo Journal of Neural Engineeringvol 12 no 3 Article ID 031001 2015

[3] C Kamarajan and B Porjesz ldquoAdvances in electrophysiologicalresearchrdquoAlcohol Research Current Reviews vol 37 no 1 article53 2015

[4] L F Nicolas-Alonso and J Gomez-Gil ldquoBrain computer inter-faces a reviewrdquo Sensors vol 12 no 2 pp 1211ndash1279 2012

[5] L Mayaud M Congedo A Van Laghenhove et al ldquoA compar-ison of recording modalities of P300 event-related potentials(ERP) for brain-computer interface (BCI) paradigmrdquo Neuro-physiologie CliniqueClinical Neurophysiology vol 43 no 4 pp217ndash227 2013

[6] X-Y Wang J Jin Y Zhang and B Wang ldquoBrain controlhuman-computer integration control based on brain-computerinterfacerdquo Acta Automatica Sinica vol 39 no 3 pp 208ndash2212013

[7] G Al-Hudhud ldquoAffective command-based control system inte-grating brain signals in commands control systemsrdquo Computersin Human Behavior vol 30 pp 535ndash541 2014

[8] J L Sirvent Blasco E Ianez A Ubeda and JM Azorın ldquoVisualevoked potential-based brain-machine interface applications toassist disabled peoplerdquo Expert Systems with Applications vol 39no 9 pp 7908ndash7918 2012

[9] H Cecotti ldquoSpelling with non-invasive Brain-Computer Inter-facesmdashcurrent and future trendsrdquo Journal of Physiology Parisvol 105 no 1ndash3 pp 106ndash114 2011

[10] I S Kotchetkov B Y Hwang G Appelboom C P Kellnerand E S Connolly Jr ldquoBrain-computer interfaces militaryneurosurgical and ethical perspectiverdquo Neurosurgical Focusvol 28 no 5 article no E25 2010

[11] R N Vigario ldquoExtraction of ocular artefacts from EEG usingindependent component analysisrdquo Electroencephalography andClinical Neurophysiology vol 103 no 3 pp 395ndash404 1997

[12] W Zhou and J Gotman ldquoAutomatic removal of eye movementartifacts from the EEG using ICA and the dipole modelrdquoProgress in Natural Science vol 19 no 9 pp 1165ndash1170 2009

[13] R Sameni andCGouy-Pailler ldquoAn iterative subspace denoisingalgorithm for removing electroencephalogram ocular artifactsrdquoJournal of Neuroscience Methods vol 225 pp 97ndash105 2014

[14] M Breakspear and J R Terry ldquoDetection and description ofnon-linear interdependence in normal multichannel humanEEG datardquo Clinical Neurophysiology vol 113 no 5 pp 735ndash7532002

[15] U R Acharya O Faust N Kannathal T Chua and S Laxmin-arayan ldquoNon-linear analysis of EEG signals at various sleepstagesrdquo Computer Methods and Programs in Biomedicine vol80 no 1 pp 37ndash45 2005

[16] L I Aftanas and S A Golocheikine ldquoNon-linear dynamiccomplexity of the human EEGduringmeditationrdquoNeuroscienceLetters vol 330 no 2 pp 143ndash146 2002

[17] M J Fadili J-L Starck J Bobin and Y Moudden ldquoImagedecomposition and separation using sparse representations anoverviewrdquo Proceedings of the IEEE vol 98 no 6 pp 983ndash9942010

[18] K J Blinowska and P J Durka ldquoUnbiased high resolutionmethod of EEG analysis in time-frequency spacerdquo Acta Neuro-biologiae Experimentalis vol 61 no 3 pp 157ndash174 2001

[19] E Imani H-R Pourreza and T Banaee ldquoFully automateddiabetic retinopathy screening usingmorphological componentanalysisrdquo Computerized Medical Imaging and Graphics vol 43pp 78ndash88 2015

[20] E Imani M Javidi and H-R Pourreza ldquoImprovement ofretinal blood vessel detection using morphological componentanalysisrdquo Computer Methods and Programs in Biomedicine vol118 no 3 pp 263ndash279 2016

[21] A S Al-Fahoum and A A Al-Fraihat ldquoMethods of EEG signalfeatures extraction using linear analysis in frequency and time-frequency domainsrdquo ISRN Neuroscience vol 2014 Article ID730218 7 pages 2014

[22] M Zibulevsky and B A Pearlmutter ldquoBlind source separationby sparse decomposition in a signal dictionaryrdquoNeural Compu-tation vol 13 no 4 pp 863ndash882 2001

[23] N P Castellanos andVAMakarov ldquoRecovering EEGbrain sig-nals artifact suppression with wavelet enhanced independentcomponent analysisrdquo Journal of Neuroscience Methods vol 158no 2 pp 300ndash312 2006

[24] J Hou K Morgan D M Tucker et al ldquoAn improved artifactsremoval method for high dimensional EEGrdquo Journal of Neuro-science Methods vol 268 pp 31ndash42 2016

[25] P Berg and M Scherg ldquoA multiple source approach to thecorrection of eye artifactsrdquo Electroencephalography and ClinicalNeurophysiology vol 90 no 3 pp 229ndash241 1994

[26] P K Sadasivan and D Narayana Dutt ldquoSVD based techniquefor noise reduction in electroencephalographic signalsrdquo SignalProcessing vol 55 no 2 pp 179ndash189 1996

16 Computational and Mathematical Methods in Medicine

[27] C A Joyce I F Gorodnitsky andMKutas ldquoAutomatic removalof eye movement and blink artifacts from EEG data using blindcomponent separationrdquo Psychophysiology vol 41 no 2 pp 313ndash325 2004

[28] G L Wallstrom R E Kass A Miller J F Cohn and N A FoxldquoAutomatic correction of ocular artifacts in the EEG a com-parison of regression-based and component-based methodsrdquoInternational Journal of Psychophysiology vol 53 no 2 pp 105ndash119 2004

[29] S M Gordon V Lawhern A D Passaro and K McDowellldquoInformed decomposition of electroencephalographic datardquoJournal of Neuroscience Methods vol 256 pp 41ndash55 2015

[30] D StuderUHoffmann andTKoenig ldquoFromEEGdependencymultichannel matching pursuit to sparse topographic EEGdecompositionrdquo Journal of Neuroscience Methods vol 153 no2 pp 261ndash275 2006

[31] J-L Starck M Elad and D Donoho ldquoRedundant multiscaletransforms and their application for morphological componentseparationrdquo Advances in Imaging and Electron Physics vol 132pp 287ndash348 2004

[32] P J Franaszczuk G K Bergey P J Durka andHM EisenbergldquoTime-frequency analysis using thematching pursuit algorithmapplied to seizures originating from the mesial temporal loberdquoElectroencephalography and Clinical Neurophysiology vol 106no 6 pp 513ndash521 1998

[33] P J Durka A Matysiak E M Montes P V Sosa and K JBlinowska ldquoMultichannel matching pursuit and EEG inversesolutionsrdquo Journal of Neuroscience Methods vol 148 no 1 pp49ndash59 2005

[34] J Bobin J-L Starck J Fadili and Y Moudden ldquoSparsityand morphological diversity in blind source separationrdquo IEEETransactions on Image Processing vol 16 no 11 pp 2662ndash26742007

[35] P J Durka D Ircha and K J Blinowska ldquoStochastic time-frequency dictionaries formatching pursuitrdquo IEEE Transactionson Signal Processing vol 49 no 3 pp 507ndash510 2001

[36] X Yong R K Ward and G E Birch ldquoGeneralized morpholog-ical component analysis for EEG source separation and artifactremovalrdquo in Proceedings of the 4th International IEEEEMBSConference on Neural Engineering (NER rsquo09) pp 343ndash346Antalya Turkey May 2009

[37] B Singh G Ai and H Wagatsuma ldquoAn electrooculographyanalysis in the time-frequency domain using morphologicalcomponent analysis toward the development of mobile BCIsystemsrdquo in Universal Access in Human-Computer InteractionAccess to Interaction 9th International Conference UAHCI 2015Held as Part of HCI International 2015 Los Angeles CA USAAugust 2ndash7 2015 Proceedings Part II vol 9176 of Lecture Notesin Computer Science pp 528ndash537 Springer Berlin Germany2015

[38] S S Chen D L Donoho and M A Saunders ldquoAtomicdecomposition by basis pursuitrdquo SIAM Review vol 43 no 1pp 129ndash159 2001

[39] D L Donoho and X Huo ldquoUncertainty principles and idealatomic decompositionrdquo IEEE Transactions on InformationThe-ory vol 47 no 7 pp 2845ndash2862 2001

[40] F Miwakeichi E Martınez-Montes P A Valdes-Sosa NNishiyama H Mizuhara and Y Yamaguchi ldquoDecomposingEEG data into spacendashtimendashfrequency components using par-allel factor analysisrdquo NeuroImage vol 22 no 3 pp 1035ndash10452004

[41] K J Friston C D Frith P F Liddle and R S J FrackowiakldquoFunctional connectivity the principal-component analysis oflarge (PET) data setsrdquo Journal of Cerebral Blood Flow andMetabolism vol 13 no 1 pp 5ndash14 1993

[42] S Makeig T-P Jung A J Bell D Ghahremani and T JSejnowski ldquoBlind separation of auditory event-related brainresponses into independent componentsrdquo Proceedings of theNational Academy of Sciences of the United States of Americavol 94 no 20 pp 10979ndash10984 1997

[43] Biomedical Signal httpwwwmedicinemcgillcaphysiovlabbiomed signalseeg nhtm

[44] S E G Nilsson and B E Andersson ldquoCorneal DC recordingsof slow ocular potential changes such as the ERG c-wave and thelight peak in clinical workmdashequipment and examples of resultsrdquoDocumenta Ophthalmologica vol 68 no 3-4 pp 313ndash325 1988

[45] OG Lins TW Picton P Berg andM Scherg ldquoOcular artifactsin EEG and event-related potentials I scalp topographyrdquo BrainTopography vol 6 no 1 pp 51ndash63 1993

[46] T W Picton P Van Roon M L Armilio P Berg N Ille andM Scherg ldquoThe correction of ocular artifacts a topographicperspectiverdquo Clinical Neurophysiology vol 111 no 1 pp 53ndash652000

[47] A S Keren S Yuval-Greenberg and L Y Deouell ldquoSaccadicspike potentials in gamma-band EEG characterization detec-tion and suppressionrdquo NeuroImage vol 49 no 3 pp 2248ndash2263 2010

[48] M Plochl J P Ossandon and P Konig ldquoCombining EEG andeye tracking identification characterization and correctionof eye movement artifacts in electroencephalographic datardquoFrontiers in Human Neuroscience vol 6 article 278 2012

[49] S Dandekar C Privitera T Carney and S A Klein ldquoNeuralsaccadic response estimation during natural viewingrdquo Journalof Neurophysiology vol 107 no 6 pp 1776ndash1790 2012

[50] G Ai N Sato B Singh and H Wagatsuma ldquoDirection andviewing area-sensitive influence of EOGartifacts revealed in theEEG topographic pattern analysisrdquo Cognitive Neurodynamicsvol 10 no 4 pp 301ndash314 2016

[51] P Berg and M Scherg ldquoDipole models of eye movements andblinksrdquo Electroencephalography and Clinical Neurophysiologyvol 79 no 1 pp 36ndash44 1991

[52] R J Croft and R J Barry ldquoRemoval of ocular artifact from theEEG a reviewrdquo Neurophysiologie Clinique vol 30 no 1 pp 5ndash19 2000

[53] I J Rampil ldquoA primer for EEG signal processing in anesthesiardquoAnesthesiology vol 89 no 4 pp 980ndash1002 1998

[54] J L Starck Y Moudden J Bobin M Elad and D DonoholdquoMorphological component analysisrdquo in Optics amp Photonics2005 p 59140Q International Society forOptics and Photonics2005

[55] S Sardy A Bruce and P Tseng ldquoBlock coordinate relaxationmethods for nonparametric signal denoising with waveletdictionariesrdquo Journal of Computational and Graphical Statisticsvol 9 pp 361ndash379 2000

[56] M Puschel and J M F Moura ldquoThe algebraic approach to thediscrete cosine and sine transforms and their fast algorithmsrdquoSIAM Journal on Computing vol 32 no 5 pp 1280ndash1316 2003

[57] X Shao and S G Johnson ldquoType-IV DCT DST and MDCTalgorithms with reduced numbers of arithmetic operationsrdquoSignal Processing vol 88 no 6 pp 1313ndash1326 2008

[58] R G Andrzejak K Lehnertz F Mormann C Rieke P Davidand C E Elger ldquoIndications of nonlinear deterministic and

Computational and Mathematical Methods in Medicine 7

200

0

minus200Pote

ntia

l (V

)

Samples40003000200010000

Intracranial real EEG signal

(a)

500

0

minus500Pote

ntia

l (V

)

Samples40003000200010000

Artificial eye movement-related EOG signal

(b)

500

0

minus500Pote

ntia

l (V

)

Samples40003000200010000

Artificial blink EOG signal

(c)

Samples

1000

0

minus1000Pote

ntia

l (V

)

40003000200010000

Combined signal (EEG + EOG)

(d)

Figure 4 A systemic representation of differentmorphological signals (a) intracranial EEG signal (b) artificial block EOG signal (c) artificialblink EOG signal and (d) combined signal

Figures 6(a) and 6(b) showed the averaged cc of decom-posed component by a respective combination of explicitdictionaries with hard and soft thresholds For EEG signaldecomposition performance cc between iEEG and eitherDST DCT or LDCT component was evaluated dependingon the three combination types (Figure 6(a)) For EOGsignal decomposition performance cc between EOG andUDWT component was evaluated (Figure 6(b)) In compari-son between hard and soft thresholds the average value of thehard threshold is around 06 which is larger than that in thesoft threshold while the average value of the soft threshold isaround 095 demonstrating fewer variances than those in thehard thresholdThismethod indicates thatUDWTdictionarywith a soft threshold is the stable performance according tothe fitness of the morphological property in this case

There were similar variances and average values in theevaluation of EEG signal decomposition using the timedomain and then we introduced a measure in the frequencydomain As mentioned in Section 22 EEG signals carryinformation to represent the current brain stage in thespecific tendency in the frequency domain such as having asynchronized neural activities by showing the existence of apeak in the frequency spectrum The EEG data used in theevaluation showed a peak around 10Hz under the closingeye condition and a peak around 50Hz under the openingeye condition Therefore in the frequency analysis a 10Hzpeak will be an index to tell how much the reconstructedsignal preserves the original information contained in theoriginal iEEG data under closing eye condition Figure 7showed the averaged normalized FFT as the comparisonbetween three combinations of the dictionaries InterestinglyalthoughDSTDCT and LDCT single components seemed toreconstruct the EEGs because of a high cc value in the timedomain the frequency spectrum analysis clarified the factthat the single component cannot reproduce the necessarytendency of EEG signals peak Meanwhile the combination

of 2nd and 3rd components which means oscillatory andspike components successfully reproduced the EEG signaltendency suggesting the importance of the spike informa-tion that presumably synchronizes background oscillatorybehaviors The 10Hz peak can be reproduced according toparameter conditions easily However 50Hz peak is difficultto be reproduced especially for LDCT-DIRAC componentin every case In the viewpoint of the tolerance in thechange of the threshold value the soft threshold methodshowed the robust performance of the signal informationpreservation which is consistent with the result of EOGsshown in Figure 6 As shown in Figure 8 the reconstructionaccuracy of the frequency profile by two dictionaries wasproved by a significant difference between the results of twomorphological and single morphological components (119905-test119901 lt 001 in both hard and soft thresholds) This evidencesuggests the importance of the DIRAC component for EEGsignals which was not equivalent to the noise or rathercarrying some information

43 Decomposition of EOG from Real EEG Data

431 EEG Data The real scalp EEG and EOG data wereobtained from the data demonstrated in the paper writtenby Ai et al (2016) [50] These data were recorded from23 EEG channels (FP1 FP2 F7 F3 Fz F4 F8 FC5 FC1FC2 FC4 T7 C3 Cz C4 T8 CP1 CP2 P3 Pz P4 O1and O2) and 7 EOG channels (V1u V1d V2u and V2dvertical EOG ⟨VEOG⟩ electrodeswere placed on supraorbitaland infraorbital rims of each eye HL and HR horizontalEOG ⟨HEOG⟩ electrodes were on the left and right outercanthi Vz was on the forehead approximately 25mm abovethe nasion) respectively according to 10ndash20 InternationalSystem (BrainAmp amplifier Brain Products GmbH) fromthe 8 participants seated in a comfortable armchair withthe base adjusted according to a participant height Theeyes of the participants were fixed straightly to the fixation

8 Computational and Mathematical Methods in Medicine

UDWT DST DIRAC400

0

minus400

Pote

ntia

l (V

)

200

0

minus200

0

100

minus100

Samples400020000

Samples400020000

Samples400020000

(a)

DCTUDWT DIRAC

400

0

minus400

Pote

ntia

l (V

)

200

0

minus200

0

100

minus100

Samples400020000

Samples400020000

Samples400020000

(b)

UDWT LDCT DIRAC400

0

minus400

Pote

ntia

l (V

)

200

0

200

0

minus200

Samples400020000

Samples400020000

Samples400020000

(c)

Figure 5 Components separation byMCA (a) explicit dictionaries are UDWT DST andDIRAC (b) UDWT DCT andDIRAC (c) UDWTLDCT and DIRAC respectively at 120582 = 4 The original signal for decomposition was shown in Figure 4(d) as combined signal

cross in the center of the monitor screen The stimulus wasdisplayed by a CRT monitor A chin support frame wasused to keep the participantrsquos head position fixed and fixtheir head to the supporting frame without laying their chinson the supporting bar to avoid the jaw clenching artifactThe distance between eyes and monitor was set to 70 cmThe sampling rate was 500Hz The whole details of theexperiment protocols were given in Ai et al (2016) [50]

432 Results with Real EEG-EOG According toAi et al [50]the real EEG-EOG data were divided into 4 sessions Eachsession had 12 tasks of eye movement The two EOG signalswere collected from ldquoV1d-V1urdquo and ldquoV2d-V2urdquo at right andleft sides of the eye as shown in Figure 9 and both signalsshowed the same kind of tendency because vertical EOG

propagated symmetrically in an anterior-posterior directionFigure 10 showed the real EEG signals were taken from someelectrodes for example Fp1 Fp2 Cz O1 and O2 whichrepresent EOG influence depending on the frontal centraland occipital parts of the brain

The selected explicit dictionaries were used to representthe targeted component for the EEG and EOG signal EEGand EOG were distinguished based on the morphologythat was observed in the EEG and EOG The lateral eyemovements mostly affect frontal electrodes [45] ThereforeFp1 electrode was used to decompose and demonstratethe effectiveness of our proposed method with MCA asshowed in Figure 11 and the same method was applied toall the 23 electrodes All EEG signals were morphologicallydecomposed with redundant transform

Computational and Mathematical Methods in Medicine 9

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

Aver

aged

corr

elat

ion

coeffi

cien

t

06

04

08

1

(a) cc between iEEG and 2nd comp (hard)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5Av

erag

ed co

rrel

atio

n co

effici

ent

06

04

08

1

(b) cc between iEEG and 2nd comp (soft)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

06

04

08

1

Aver

aged

corr

elat

ion

coeffi

cien

t

(c) cc between EOG and UDWT (hard)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

Aver

aged

corr

elat

ion

coeffi

cien

t

06

04

08

1

(d) cc between EOG and UDWT (soft)

Figure 6 A comparison between cc of decomposed morphological component with iEEG signal and artificial EOG with hard and softthresholds The mean value and standard deviation were calculated from all 100 decomposed datasets by explicit dictionaries (a) Secondmorphological component was decomposed by DST DCT and LDCT with hard and (b) soft threshold respectively (c) First morphologicalcomponent was decomposed by UDWT with a hard threshold and (d) soft threshold respectively 100 trials of iEEG and artificial EOG wereused

10 Computational and Mathematical Methods in Medicine

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

0 20 40 60 80

0

2

4

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(a) Hard (120582 = 3)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(b) Hard (120582 = 4)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(c) Hard (120582 = 5)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(d) Soft (120582 = 3)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(e) Soft (120582 = 4)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Nor

mal

ized

pow

er (d

B)

Frequency (Hz)

minus2

(f) Soft (120582 = 5)

Figure 7 An averaged normalized FFT obtained from 100 of iEEG and combination of two morphological components and singlemorphological component at 120582 varies from 3 to 5 with hard and soft thresholds

Figure 11(a) demonstrated the decomposition of compo-nents by the first explicit dictionary it was divided into threedifferent morphologies of the EEG signal Figures 11(b) and11(c) showed the second and the third explicit dictionary ofredundant transform respectively The overcomplete dictio-nary was a combination of redundant transforms that char-acterized the component in a different morphology Accord-ingly one of redundant transforms can be differentiated intodecomposed components by overcomplete dictionaries Thefirst component was decomposed by ldquoUDWTrdquo of each over-complete dictionary and was analyzed via the slow and blinktype morphology The second component was decomposedby ldquoDCTrdquo ldquoDSTrdquo and ldquoLDCTrdquo and was analyzed via thebackground of the signal which was similar to the EEG signal

and the third component was decomposed by ldquoDIRACrdquo andwas analyzed via the unexpected spikeThe first overcompletedictionary decomposed the EEG signal without changingthe monomorphic polymorphic and transient propertiesThe cc between the original signal and the summation of alldecomposed components was close to one Figure 12 showedthe raw EOG signal taken from the vertical and horizontalchannel and first decomposed component taken from Fp1Fp2 Cz O1 and O2 respectively

Table 1 showed individual cc of original EEG signals andrecomposed EEG signals from the combination of compo-nents with respect to different channels and combinationsof dictionaries Table 2 showed the cc between filter rawEOG signal taken from vertical and horizontal channels and

Computational and Mathematical Methods in Medicine 11

3 4 5

02

03

04

05

06

07

08

09

Aver

aged

FFT

corr

elat

ion

coeffi

cien

t

01

1

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

lowast lowast lowast

(a) Hard threshold

3 4 5

Aver

aged

FFT

corr

elat

ion

coeffi

cien

t02

03

04

05

06

07

08

09

01

1

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

lowast lowast lowast

(b) Soft threshold

Figure 8 A comparison of FFT correlation coefficients between iEEG data and morphological component decomposed by explicitdictionaries lowastSignificant differences (119901 lt 005) (a) Combined two morphological components and (b) single morphological componentMean value and standard deviation calculated from all 100 decomposed datasets by explicit dictionaries with hard and soft thresholds

400

Pote

ntia

l (V

)

200

0

minus200

400

Pote

ntia

l (V

)

200

0

minus200

Samples20000 1000

EOG (V1u-V1d)

EOG (V2u-V2d)

Figure 9 An example of EOG signal taken from right and left sideof eyes

decomposed first component from Fp1 Fp2 Cz O1 and O2respectively

5 Discussion

Artifact contamination in EEG signal has been a com-mon important issue in neurobiological event diagnosis and

Table 1 cc of original signal and sum of the decomposed compo-nents

EEG channelCorrelation coefficient

UDWT-DST-DIRAC

UDWT-DCT-DIRAC

UDWT-LDCT-DIRAC

Fp1 09921 plusmn 0014 09921 plusmn 0014 09932 plusmn 0013Fp2 0992 plusmn 017 09919 plusmn 018 09932 plusmn 014Cz 09898 plusmn 01 09899 plusmn 01 09908 plusmn 009O1 09836 plusmn 015 09836 plusmn 016 09869 plusmn 012O2 09855 plusmn 013 09856 plusmn 013 09849 plusmn 015

neuroscientific researchThevariousmethodswere applied toremove the artifacts from EEG [2 11ndash13 21 23 24 26ndash28 52]The decomposition based analysis was used in removal ofEOG artifacts in EEG [22 27 28 30 40 42] Howeverthose methods lack the elucidation of what the nature ofEEG signals is in the viewpoint of the signal analysis and asystematic approach was required by treating the sparsity andnonlinearity of the signal in the time domain

12 Computational and Mathematical Methods in Medicine

0

0

50

Fp1

Fp2

Cz

O1

O2

100

0

minus100

minus50

minus40

Pote

ntia

l (V

)

0

50

minus50

Pote

ntia

l (V

)

050

minus50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

Figure 10 An example of real EEG signal taken from Fp1 Fp2 Cz O1 and O2 electrode channels

Table 2 cc between filtered EOG and UDWT component decomposed by UDWT dictionary

EOG channels EEG channelsFp1 Fp2 Cz O1 O2

Correlation coefficientUDWT-DST-DIRACV1d 06777 0657 07267 09223 06445V1u 06814 0646 06606 09419 06354V2d 0916 0906 09402 0882 05402V2u 02332 02268 02353 06388 08494H1 08582 0847 08444 06902 05839H2 09419 09468 09559 07476 04752

UDWT-DCT-DIRACV1d 06792 06595 068 09213 06352V1u 06835 06396 06424 09581 06585V2d 09193 0902 09362 08764 05145V2u 02331 02183 02316 06639 08919H1 08593 08507 08626 06759 05376H2 09442 09465 09662 07266 04346

UDWT-LDCT-DIRACV1d 06794 06403 07219 08892 065V1u 06443 06279 06459 08196 05381V2d 09142 09072 09395 09592 06506V2u 02351 02235 02383 03747 06804H1 08637 08449 08471 07638 05734H2 09586 09558 09577 08826 05598

Computational and Mathematical Methods in Medicine 13

0

50

0

20

UDWT

DCT

DIRAC

0

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus30

(a)

UDWT

DST

DIRAC

0

0

20

0

50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus20

minus20

(b)

0

0

50

100

0

UDWT

LDCT

DIRAC

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus20

minus40

minus80

(c)

Figure 11 Component separated fromEEG (Fp1 electrode) signal by explicit dictionaries (a)UDWT-DCT-DIRAC (b)UDWT-DST-DIRACand (c) UDWT-LDCT-DIRAC respectively

This study revealed the nature of EEG signals in the senseof morphologies contained in the original signal by usingMCA The UDWT was used to decompose the slow andbump morphology The DCT DST and LDCT transformwere used to decompose the EEG signal Spike typemorphol-ogy was decomposed by DIRAC Redundant transforms ofDCT and DST have a similar capability in representing themorphology of oscillatory activities Therefore we used theDCT LDCT and DST dictionaries for validations of EEGsignal The detailed significant differences in morphology ofDCT and DST were given in past studies [56 57] while inour analysis there were no significant differences The rightcombination of redundant transforms to form overcompletedictionary revealed the desired decomposition in principle

In Section 42 ldquoBlocksrdquo ldquoBumpsrdquo similar to simulatedEOG signal defined in past studies [59ndash61] as shown in

Figure 4 and EEG data [58] were used to validate ourpurposed method The ldquoBlocksrdquo with abrupt changes weresimilar to the horizontal and vertical eye movements sim-ply as described by past studies [25 51] For the sake ofsimplicity in the present study ldquoBumpsrdquo were used as arepresentative signal form as eye blinks that happens inunexpected timings as illustrated in Figure 5 The separationof components by given dictionary works well in this evalu-ation but the further analysis is necessary for the evaluationof the signal decomposition with complex eye movementswhich requires presumably various redundant dictionariesIn the verification of the component discrimination as shownin Figures 6 and 7 the accuracy of the averaged EOGcomponent decomposition was above 90 which suggests aplausible performance even in the complex eye movementsThe combined DST and DIRAC dictionaries had better

14 Computational and Mathematical Methods in Medicine

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

Samples20000 1000

V1u

H1

(a) UDWT components separated by UDWT-DST-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(b) UDWT components separated by UDWT-DCT-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(c) UDWT components separated by UDWT-LDCT-DIRAC

Figure 12 UDWT component taken from Fp1 Fp2 Cz O1 and O2 separated by UDWT-DCT-DIRAC UDWT-DST-DIRAC and UDWT-LDCT-DIRAC respectively

decomposition performance than others while DST andDCT theoretically have no meaningful difference The usageof iEEG as the true EEG signal had a large benefit whichcan be used for the performance test for past proposedmethods like ICA and PCA consistently Our proposedmethod successfully demonstrated the performance in cc andthe frequency profile especially in Section 42 while in theserious discussion of the real EEG and EOG signals the DSTor DCT component exhibited a baseline fluctuation of thesignal which denotes the persistence of the EOG componentor other slow frequency artifacts noises and the factor willbe improved by the fine-tuned design of the DST or DCTdictionary with a band pass filter function In addition thethreshold problem exits in the optimization algorithm andnumber of iterations [37]

The EEG decomposition had not mark with a combi-nation of a second and a third component of EEG signal

decomposed by ldquoDST DCT and LDCTrdquo andDIRAC respec-tively based on the morphology Therefore the accuratecombination in the further perspective will be considerableEven the combination of all components and the mixedsignal or real EEG signal had cc above 97 for all redundanttransforms as is analyzed in the frequency spectrum thesignal morphology has further meaning in the viewpointof the signal transmission The MCA method has such anextended and flexible availability for signal analyses

6 Conclusion

Morphological Component Analysis methodology wasapplied to the simulated semisimulated and real EOGand EEG signal The successful decomposition of the EOGand EEG signal into their morphological component wasdemonstrated It seems to be that the EEG signals and

Computational and Mathematical Methods in Medicine 15

artifacts in EEG have been represented by different explicitdictionaries We analyzed the EEG signals involved with theEOG artifacts which were influenced by task conditionsTheDIRAC explicit dictionary decomposed the EEG signal intospike-like activities which may be related to the transientproperty of EEG UDWT explicit dictionary representsslow movement or bumps DCT DST and LDCT explicitdictionaries represent dominant signal that represents EEGsor pure tones signals as monomorphic and polymorphicactivities These results suggested that the effectivenessof MCA in ocular artifacts removal from the EEG rawsignal was derived from signal morphology characterizedas slow and smooth change of EOG time series In thefurther analysis the MCA is required to compare withother competing methods for the EEG and EOG signaldecomposition

Competing Interests

The authors have declared that no competing interests exist

Acknowledgments

This work was partly supported by JSPS KAKENHI 16H01616and 26240032 and theNewEnergy and Industrial TechnologyDevelopment Organization (NEDO) ldquoNext-Generation Arti-ficial Intelligence (3) Base Technology for Next-GenerationAIrdquo (Automated Driving Task) and the collaborative researchproject with Fujitsu Ten Limited

References

[1] J P Donoghue J N Sanes N G Hatsopoulos and G GaalldquoNeural discharge and local field potential oscillations in pri-mate motor cortex during voluntary movementsrdquo Journal ofNeurophysiology vol 79 no 1 pp 159ndash173 1998

[2] J A Uriguen and B Garcia-Zapirain ldquoEEG artifact removalmdashstate-of-the-art and guidelinesrdquo Journal of Neural Engineeringvol 12 no 3 Article ID 031001 2015

[3] C Kamarajan and B Porjesz ldquoAdvances in electrophysiologicalresearchrdquoAlcohol Research Current Reviews vol 37 no 1 article53 2015

[4] L F Nicolas-Alonso and J Gomez-Gil ldquoBrain computer inter-faces a reviewrdquo Sensors vol 12 no 2 pp 1211ndash1279 2012

[5] L Mayaud M Congedo A Van Laghenhove et al ldquoA compar-ison of recording modalities of P300 event-related potentials(ERP) for brain-computer interface (BCI) paradigmrdquo Neuro-physiologie CliniqueClinical Neurophysiology vol 43 no 4 pp217ndash227 2013

[6] X-Y Wang J Jin Y Zhang and B Wang ldquoBrain controlhuman-computer integration control based on brain-computerinterfacerdquo Acta Automatica Sinica vol 39 no 3 pp 208ndash2212013

[7] G Al-Hudhud ldquoAffective command-based control system inte-grating brain signals in commands control systemsrdquo Computersin Human Behavior vol 30 pp 535ndash541 2014

[8] J L Sirvent Blasco E Ianez A Ubeda and JM Azorın ldquoVisualevoked potential-based brain-machine interface applications toassist disabled peoplerdquo Expert Systems with Applications vol 39no 9 pp 7908ndash7918 2012

[9] H Cecotti ldquoSpelling with non-invasive Brain-Computer Inter-facesmdashcurrent and future trendsrdquo Journal of Physiology Parisvol 105 no 1ndash3 pp 106ndash114 2011

[10] I S Kotchetkov B Y Hwang G Appelboom C P Kellnerand E S Connolly Jr ldquoBrain-computer interfaces militaryneurosurgical and ethical perspectiverdquo Neurosurgical Focusvol 28 no 5 article no E25 2010

[11] R N Vigario ldquoExtraction of ocular artefacts from EEG usingindependent component analysisrdquo Electroencephalography andClinical Neurophysiology vol 103 no 3 pp 395ndash404 1997

[12] W Zhou and J Gotman ldquoAutomatic removal of eye movementartifacts from the EEG using ICA and the dipole modelrdquoProgress in Natural Science vol 19 no 9 pp 1165ndash1170 2009

[13] R Sameni andCGouy-Pailler ldquoAn iterative subspace denoisingalgorithm for removing electroencephalogram ocular artifactsrdquoJournal of Neuroscience Methods vol 225 pp 97ndash105 2014

[14] M Breakspear and J R Terry ldquoDetection and description ofnon-linear interdependence in normal multichannel humanEEG datardquo Clinical Neurophysiology vol 113 no 5 pp 735ndash7532002

[15] U R Acharya O Faust N Kannathal T Chua and S Laxmin-arayan ldquoNon-linear analysis of EEG signals at various sleepstagesrdquo Computer Methods and Programs in Biomedicine vol80 no 1 pp 37ndash45 2005

[16] L I Aftanas and S A Golocheikine ldquoNon-linear dynamiccomplexity of the human EEGduringmeditationrdquoNeuroscienceLetters vol 330 no 2 pp 143ndash146 2002

[17] M J Fadili J-L Starck J Bobin and Y Moudden ldquoImagedecomposition and separation using sparse representations anoverviewrdquo Proceedings of the IEEE vol 98 no 6 pp 983ndash9942010

[18] K J Blinowska and P J Durka ldquoUnbiased high resolutionmethod of EEG analysis in time-frequency spacerdquo Acta Neuro-biologiae Experimentalis vol 61 no 3 pp 157ndash174 2001

[19] E Imani H-R Pourreza and T Banaee ldquoFully automateddiabetic retinopathy screening usingmorphological componentanalysisrdquo Computerized Medical Imaging and Graphics vol 43pp 78ndash88 2015

[20] E Imani M Javidi and H-R Pourreza ldquoImprovement ofretinal blood vessel detection using morphological componentanalysisrdquo Computer Methods and Programs in Biomedicine vol118 no 3 pp 263ndash279 2016

[21] A S Al-Fahoum and A A Al-Fraihat ldquoMethods of EEG signalfeatures extraction using linear analysis in frequency and time-frequency domainsrdquo ISRN Neuroscience vol 2014 Article ID730218 7 pages 2014

[22] M Zibulevsky and B A Pearlmutter ldquoBlind source separationby sparse decomposition in a signal dictionaryrdquoNeural Compu-tation vol 13 no 4 pp 863ndash882 2001

[23] N P Castellanos andVAMakarov ldquoRecovering EEGbrain sig-nals artifact suppression with wavelet enhanced independentcomponent analysisrdquo Journal of Neuroscience Methods vol 158no 2 pp 300ndash312 2006

[24] J Hou K Morgan D M Tucker et al ldquoAn improved artifactsremoval method for high dimensional EEGrdquo Journal of Neuro-science Methods vol 268 pp 31ndash42 2016

[25] P Berg and M Scherg ldquoA multiple source approach to thecorrection of eye artifactsrdquo Electroencephalography and ClinicalNeurophysiology vol 90 no 3 pp 229ndash241 1994

[26] P K Sadasivan and D Narayana Dutt ldquoSVD based techniquefor noise reduction in electroencephalographic signalsrdquo SignalProcessing vol 55 no 2 pp 179ndash189 1996

16 Computational and Mathematical Methods in Medicine

[27] C A Joyce I F Gorodnitsky andMKutas ldquoAutomatic removalof eye movement and blink artifacts from EEG data using blindcomponent separationrdquo Psychophysiology vol 41 no 2 pp 313ndash325 2004

[28] G L Wallstrom R E Kass A Miller J F Cohn and N A FoxldquoAutomatic correction of ocular artifacts in the EEG a com-parison of regression-based and component-based methodsrdquoInternational Journal of Psychophysiology vol 53 no 2 pp 105ndash119 2004

[29] S M Gordon V Lawhern A D Passaro and K McDowellldquoInformed decomposition of electroencephalographic datardquoJournal of Neuroscience Methods vol 256 pp 41ndash55 2015

[30] D StuderUHoffmann andTKoenig ldquoFromEEGdependencymultichannel matching pursuit to sparse topographic EEGdecompositionrdquo Journal of Neuroscience Methods vol 153 no2 pp 261ndash275 2006

[31] J-L Starck M Elad and D Donoho ldquoRedundant multiscaletransforms and their application for morphological componentseparationrdquo Advances in Imaging and Electron Physics vol 132pp 287ndash348 2004

[32] P J Franaszczuk G K Bergey P J Durka andHM EisenbergldquoTime-frequency analysis using thematching pursuit algorithmapplied to seizures originating from the mesial temporal loberdquoElectroencephalography and Clinical Neurophysiology vol 106no 6 pp 513ndash521 1998

[33] P J Durka A Matysiak E M Montes P V Sosa and K JBlinowska ldquoMultichannel matching pursuit and EEG inversesolutionsrdquo Journal of Neuroscience Methods vol 148 no 1 pp49ndash59 2005

[34] J Bobin J-L Starck J Fadili and Y Moudden ldquoSparsityand morphological diversity in blind source separationrdquo IEEETransactions on Image Processing vol 16 no 11 pp 2662ndash26742007

[35] P J Durka D Ircha and K J Blinowska ldquoStochastic time-frequency dictionaries formatching pursuitrdquo IEEE Transactionson Signal Processing vol 49 no 3 pp 507ndash510 2001

[36] X Yong R K Ward and G E Birch ldquoGeneralized morpholog-ical component analysis for EEG source separation and artifactremovalrdquo in Proceedings of the 4th International IEEEEMBSConference on Neural Engineering (NER rsquo09) pp 343ndash346Antalya Turkey May 2009

[37] B Singh G Ai and H Wagatsuma ldquoAn electrooculographyanalysis in the time-frequency domain using morphologicalcomponent analysis toward the development of mobile BCIsystemsrdquo in Universal Access in Human-Computer InteractionAccess to Interaction 9th International Conference UAHCI 2015Held as Part of HCI International 2015 Los Angeles CA USAAugust 2ndash7 2015 Proceedings Part II vol 9176 of Lecture Notesin Computer Science pp 528ndash537 Springer Berlin Germany2015

[38] S S Chen D L Donoho and M A Saunders ldquoAtomicdecomposition by basis pursuitrdquo SIAM Review vol 43 no 1pp 129ndash159 2001

[39] D L Donoho and X Huo ldquoUncertainty principles and idealatomic decompositionrdquo IEEE Transactions on InformationThe-ory vol 47 no 7 pp 2845ndash2862 2001

[40] F Miwakeichi E Martınez-Montes P A Valdes-Sosa NNishiyama H Mizuhara and Y Yamaguchi ldquoDecomposingEEG data into spacendashtimendashfrequency components using par-allel factor analysisrdquo NeuroImage vol 22 no 3 pp 1035ndash10452004

[41] K J Friston C D Frith P F Liddle and R S J FrackowiakldquoFunctional connectivity the principal-component analysis oflarge (PET) data setsrdquo Journal of Cerebral Blood Flow andMetabolism vol 13 no 1 pp 5ndash14 1993

[42] S Makeig T-P Jung A J Bell D Ghahremani and T JSejnowski ldquoBlind separation of auditory event-related brainresponses into independent componentsrdquo Proceedings of theNational Academy of Sciences of the United States of Americavol 94 no 20 pp 10979ndash10984 1997

[43] Biomedical Signal httpwwwmedicinemcgillcaphysiovlabbiomed signalseeg nhtm

[44] S E G Nilsson and B E Andersson ldquoCorneal DC recordingsof slow ocular potential changes such as the ERG c-wave and thelight peak in clinical workmdashequipment and examples of resultsrdquoDocumenta Ophthalmologica vol 68 no 3-4 pp 313ndash325 1988

[45] OG Lins TW Picton P Berg andM Scherg ldquoOcular artifactsin EEG and event-related potentials I scalp topographyrdquo BrainTopography vol 6 no 1 pp 51ndash63 1993

[46] T W Picton P Van Roon M L Armilio P Berg N Ille andM Scherg ldquoThe correction of ocular artifacts a topographicperspectiverdquo Clinical Neurophysiology vol 111 no 1 pp 53ndash652000

[47] A S Keren S Yuval-Greenberg and L Y Deouell ldquoSaccadicspike potentials in gamma-band EEG characterization detec-tion and suppressionrdquo NeuroImage vol 49 no 3 pp 2248ndash2263 2010

[48] M Plochl J P Ossandon and P Konig ldquoCombining EEG andeye tracking identification characterization and correctionof eye movement artifacts in electroencephalographic datardquoFrontiers in Human Neuroscience vol 6 article 278 2012

[49] S Dandekar C Privitera T Carney and S A Klein ldquoNeuralsaccadic response estimation during natural viewingrdquo Journalof Neurophysiology vol 107 no 6 pp 1776ndash1790 2012

[50] G Ai N Sato B Singh and H Wagatsuma ldquoDirection andviewing area-sensitive influence of EOGartifacts revealed in theEEG topographic pattern analysisrdquo Cognitive Neurodynamicsvol 10 no 4 pp 301ndash314 2016

[51] P Berg and M Scherg ldquoDipole models of eye movements andblinksrdquo Electroencephalography and Clinical Neurophysiologyvol 79 no 1 pp 36ndash44 1991

[52] R J Croft and R J Barry ldquoRemoval of ocular artifact from theEEG a reviewrdquo Neurophysiologie Clinique vol 30 no 1 pp 5ndash19 2000

[53] I J Rampil ldquoA primer for EEG signal processing in anesthesiardquoAnesthesiology vol 89 no 4 pp 980ndash1002 1998

[54] J L Starck Y Moudden J Bobin M Elad and D DonoholdquoMorphological component analysisrdquo in Optics amp Photonics2005 p 59140Q International Society forOptics and Photonics2005

[55] S Sardy A Bruce and P Tseng ldquoBlock coordinate relaxationmethods for nonparametric signal denoising with waveletdictionariesrdquo Journal of Computational and Graphical Statisticsvol 9 pp 361ndash379 2000

[56] M Puschel and J M F Moura ldquoThe algebraic approach to thediscrete cosine and sine transforms and their fast algorithmsrdquoSIAM Journal on Computing vol 32 no 5 pp 1280ndash1316 2003

[57] X Shao and S G Johnson ldquoType-IV DCT DST and MDCTalgorithms with reduced numbers of arithmetic operationsrdquoSignal Processing vol 88 no 6 pp 1313ndash1326 2008

[58] R G Andrzejak K Lehnertz F Mormann C Rieke P Davidand C E Elger ldquoIndications of nonlinear deterministic and

8 Computational and Mathematical Methods in Medicine

UDWT DST DIRAC400

0

minus400

Pote

ntia

l (V

)

200

0

minus200

0

100

minus100

Samples400020000

Samples400020000

Samples400020000

(a)

DCTUDWT DIRAC

400

0

minus400

Pote

ntia

l (V

)

200

0

minus200

0

100

minus100

Samples400020000

Samples400020000

Samples400020000

(b)

UDWT LDCT DIRAC400

0

minus400

Pote

ntia

l (V

)

200

0

200

0

minus200

Samples400020000

Samples400020000

Samples400020000

(c)

Figure 5 Components separation byMCA (a) explicit dictionaries are UDWT DST andDIRAC (b) UDWT DCT andDIRAC (c) UDWTLDCT and DIRAC respectively at 120582 = 4 The original signal for decomposition was shown in Figure 4(d) as combined signal

cross in the center of the monitor screen The stimulus wasdisplayed by a CRT monitor A chin support frame wasused to keep the participantrsquos head position fixed and fixtheir head to the supporting frame without laying their chinson the supporting bar to avoid the jaw clenching artifactThe distance between eyes and monitor was set to 70 cmThe sampling rate was 500Hz The whole details of theexperiment protocols were given in Ai et al (2016) [50]

432 Results with Real EEG-EOG According toAi et al [50]the real EEG-EOG data were divided into 4 sessions Eachsession had 12 tasks of eye movement The two EOG signalswere collected from ldquoV1d-V1urdquo and ldquoV2d-V2urdquo at right andleft sides of the eye as shown in Figure 9 and both signalsshowed the same kind of tendency because vertical EOG

propagated symmetrically in an anterior-posterior directionFigure 10 showed the real EEG signals were taken from someelectrodes for example Fp1 Fp2 Cz O1 and O2 whichrepresent EOG influence depending on the frontal centraland occipital parts of the brain

The selected explicit dictionaries were used to representthe targeted component for the EEG and EOG signal EEGand EOG were distinguished based on the morphologythat was observed in the EEG and EOG The lateral eyemovements mostly affect frontal electrodes [45] ThereforeFp1 electrode was used to decompose and demonstratethe effectiveness of our proposed method with MCA asshowed in Figure 11 and the same method was applied toall the 23 electrodes All EEG signals were morphologicallydecomposed with redundant transform

Computational and Mathematical Methods in Medicine 9

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

Aver

aged

corr

elat

ion

coeffi

cien

t

06

04

08

1

(a) cc between iEEG and 2nd comp (hard)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5Av

erag

ed co

rrel

atio

n co

effici

ent

06

04

08

1

(b) cc between iEEG and 2nd comp (soft)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

06

04

08

1

Aver

aged

corr

elat

ion

coeffi

cien

t

(c) cc between EOG and UDWT (hard)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

Aver

aged

corr

elat

ion

coeffi

cien

t

06

04

08

1

(d) cc between EOG and UDWT (soft)

Figure 6 A comparison between cc of decomposed morphological component with iEEG signal and artificial EOG with hard and softthresholds The mean value and standard deviation were calculated from all 100 decomposed datasets by explicit dictionaries (a) Secondmorphological component was decomposed by DST DCT and LDCT with hard and (b) soft threshold respectively (c) First morphologicalcomponent was decomposed by UDWT with a hard threshold and (d) soft threshold respectively 100 trials of iEEG and artificial EOG wereused

10 Computational and Mathematical Methods in Medicine

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

0 20 40 60 80

0

2

4

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(a) Hard (120582 = 3)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(b) Hard (120582 = 4)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(c) Hard (120582 = 5)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(d) Soft (120582 = 3)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(e) Soft (120582 = 4)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Nor

mal

ized

pow

er (d

B)

Frequency (Hz)

minus2

(f) Soft (120582 = 5)

Figure 7 An averaged normalized FFT obtained from 100 of iEEG and combination of two morphological components and singlemorphological component at 120582 varies from 3 to 5 with hard and soft thresholds

Figure 11(a) demonstrated the decomposition of compo-nents by the first explicit dictionary it was divided into threedifferent morphologies of the EEG signal Figures 11(b) and11(c) showed the second and the third explicit dictionary ofredundant transform respectively The overcomplete dictio-nary was a combination of redundant transforms that char-acterized the component in a different morphology Accord-ingly one of redundant transforms can be differentiated intodecomposed components by overcomplete dictionaries Thefirst component was decomposed by ldquoUDWTrdquo of each over-complete dictionary and was analyzed via the slow and blinktype morphology The second component was decomposedby ldquoDCTrdquo ldquoDSTrdquo and ldquoLDCTrdquo and was analyzed via thebackground of the signal which was similar to the EEG signal

and the third component was decomposed by ldquoDIRACrdquo andwas analyzed via the unexpected spikeThe first overcompletedictionary decomposed the EEG signal without changingthe monomorphic polymorphic and transient propertiesThe cc between the original signal and the summation of alldecomposed components was close to one Figure 12 showedthe raw EOG signal taken from the vertical and horizontalchannel and first decomposed component taken from Fp1Fp2 Cz O1 and O2 respectively

Table 1 showed individual cc of original EEG signals andrecomposed EEG signals from the combination of compo-nents with respect to different channels and combinationsof dictionaries Table 2 showed the cc between filter rawEOG signal taken from vertical and horizontal channels and

Computational and Mathematical Methods in Medicine 11

3 4 5

02

03

04

05

06

07

08

09

Aver

aged

FFT

corr

elat

ion

coeffi

cien

t

01

1

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

lowast lowast lowast

(a) Hard threshold

3 4 5

Aver

aged

FFT

corr

elat

ion

coeffi

cien

t02

03

04

05

06

07

08

09

01

1

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

lowast lowast lowast

(b) Soft threshold

Figure 8 A comparison of FFT correlation coefficients between iEEG data and morphological component decomposed by explicitdictionaries lowastSignificant differences (119901 lt 005) (a) Combined two morphological components and (b) single morphological componentMean value and standard deviation calculated from all 100 decomposed datasets by explicit dictionaries with hard and soft thresholds

400

Pote

ntia

l (V

)

200

0

minus200

400

Pote

ntia

l (V

)

200

0

minus200

Samples20000 1000

EOG (V1u-V1d)

EOG (V2u-V2d)

Figure 9 An example of EOG signal taken from right and left sideof eyes

decomposed first component from Fp1 Fp2 Cz O1 and O2respectively

5 Discussion

Artifact contamination in EEG signal has been a com-mon important issue in neurobiological event diagnosis and

Table 1 cc of original signal and sum of the decomposed compo-nents

EEG channelCorrelation coefficient

UDWT-DST-DIRAC

UDWT-DCT-DIRAC

UDWT-LDCT-DIRAC

Fp1 09921 plusmn 0014 09921 plusmn 0014 09932 plusmn 0013Fp2 0992 plusmn 017 09919 plusmn 018 09932 plusmn 014Cz 09898 plusmn 01 09899 plusmn 01 09908 plusmn 009O1 09836 plusmn 015 09836 plusmn 016 09869 plusmn 012O2 09855 plusmn 013 09856 plusmn 013 09849 plusmn 015

neuroscientific researchThevariousmethodswere applied toremove the artifacts from EEG [2 11ndash13 21 23 24 26ndash28 52]The decomposition based analysis was used in removal ofEOG artifacts in EEG [22 27 28 30 40 42] Howeverthose methods lack the elucidation of what the nature ofEEG signals is in the viewpoint of the signal analysis and asystematic approach was required by treating the sparsity andnonlinearity of the signal in the time domain

12 Computational and Mathematical Methods in Medicine

0

0

50

Fp1

Fp2

Cz

O1

O2

100

0

minus100

minus50

minus40

Pote

ntia

l (V

)

0

50

minus50

Pote

ntia

l (V

)

050

minus50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

Figure 10 An example of real EEG signal taken from Fp1 Fp2 Cz O1 and O2 electrode channels

Table 2 cc between filtered EOG and UDWT component decomposed by UDWT dictionary

EOG channels EEG channelsFp1 Fp2 Cz O1 O2

Correlation coefficientUDWT-DST-DIRACV1d 06777 0657 07267 09223 06445V1u 06814 0646 06606 09419 06354V2d 0916 0906 09402 0882 05402V2u 02332 02268 02353 06388 08494H1 08582 0847 08444 06902 05839H2 09419 09468 09559 07476 04752

UDWT-DCT-DIRACV1d 06792 06595 068 09213 06352V1u 06835 06396 06424 09581 06585V2d 09193 0902 09362 08764 05145V2u 02331 02183 02316 06639 08919H1 08593 08507 08626 06759 05376H2 09442 09465 09662 07266 04346

UDWT-LDCT-DIRACV1d 06794 06403 07219 08892 065V1u 06443 06279 06459 08196 05381V2d 09142 09072 09395 09592 06506V2u 02351 02235 02383 03747 06804H1 08637 08449 08471 07638 05734H2 09586 09558 09577 08826 05598

Computational and Mathematical Methods in Medicine 13

0

50

0

20

UDWT

DCT

DIRAC

0

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus30

(a)

UDWT

DST

DIRAC

0

0

20

0

50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus20

minus20

(b)

0

0

50

100

0

UDWT

LDCT

DIRAC

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus20

minus40

minus80

(c)

Figure 11 Component separated fromEEG (Fp1 electrode) signal by explicit dictionaries (a)UDWT-DCT-DIRAC (b)UDWT-DST-DIRACand (c) UDWT-LDCT-DIRAC respectively

This study revealed the nature of EEG signals in the senseof morphologies contained in the original signal by usingMCA The UDWT was used to decompose the slow andbump morphology The DCT DST and LDCT transformwere used to decompose the EEG signal Spike typemorphol-ogy was decomposed by DIRAC Redundant transforms ofDCT and DST have a similar capability in representing themorphology of oscillatory activities Therefore we used theDCT LDCT and DST dictionaries for validations of EEGsignal The detailed significant differences in morphology ofDCT and DST were given in past studies [56 57] while inour analysis there were no significant differences The rightcombination of redundant transforms to form overcompletedictionary revealed the desired decomposition in principle

In Section 42 ldquoBlocksrdquo ldquoBumpsrdquo similar to simulatedEOG signal defined in past studies [59ndash61] as shown in

Figure 4 and EEG data [58] were used to validate ourpurposed method The ldquoBlocksrdquo with abrupt changes weresimilar to the horizontal and vertical eye movements sim-ply as described by past studies [25 51] For the sake ofsimplicity in the present study ldquoBumpsrdquo were used as arepresentative signal form as eye blinks that happens inunexpected timings as illustrated in Figure 5 The separationof components by given dictionary works well in this evalu-ation but the further analysis is necessary for the evaluationof the signal decomposition with complex eye movementswhich requires presumably various redundant dictionariesIn the verification of the component discrimination as shownin Figures 6 and 7 the accuracy of the averaged EOGcomponent decomposition was above 90 which suggests aplausible performance even in the complex eye movementsThe combined DST and DIRAC dictionaries had better

14 Computational and Mathematical Methods in Medicine

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

Samples20000 1000

V1u

H1

(a) UDWT components separated by UDWT-DST-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(b) UDWT components separated by UDWT-DCT-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(c) UDWT components separated by UDWT-LDCT-DIRAC

Figure 12 UDWT component taken from Fp1 Fp2 Cz O1 and O2 separated by UDWT-DCT-DIRAC UDWT-DST-DIRAC and UDWT-LDCT-DIRAC respectively

decomposition performance than others while DST andDCT theoretically have no meaningful difference The usageof iEEG as the true EEG signal had a large benefit whichcan be used for the performance test for past proposedmethods like ICA and PCA consistently Our proposedmethod successfully demonstrated the performance in cc andthe frequency profile especially in Section 42 while in theserious discussion of the real EEG and EOG signals the DSTor DCT component exhibited a baseline fluctuation of thesignal which denotes the persistence of the EOG componentor other slow frequency artifacts noises and the factor willbe improved by the fine-tuned design of the DST or DCTdictionary with a band pass filter function In addition thethreshold problem exits in the optimization algorithm andnumber of iterations [37]

The EEG decomposition had not mark with a combi-nation of a second and a third component of EEG signal

decomposed by ldquoDST DCT and LDCTrdquo andDIRAC respec-tively based on the morphology Therefore the accuratecombination in the further perspective will be considerableEven the combination of all components and the mixedsignal or real EEG signal had cc above 97 for all redundanttransforms as is analyzed in the frequency spectrum thesignal morphology has further meaning in the viewpointof the signal transmission The MCA method has such anextended and flexible availability for signal analyses

6 Conclusion

Morphological Component Analysis methodology wasapplied to the simulated semisimulated and real EOGand EEG signal The successful decomposition of the EOGand EEG signal into their morphological component wasdemonstrated It seems to be that the EEG signals and

Computational and Mathematical Methods in Medicine 15

artifacts in EEG have been represented by different explicitdictionaries We analyzed the EEG signals involved with theEOG artifacts which were influenced by task conditionsTheDIRAC explicit dictionary decomposed the EEG signal intospike-like activities which may be related to the transientproperty of EEG UDWT explicit dictionary representsslow movement or bumps DCT DST and LDCT explicitdictionaries represent dominant signal that represents EEGsor pure tones signals as monomorphic and polymorphicactivities These results suggested that the effectivenessof MCA in ocular artifacts removal from the EEG rawsignal was derived from signal morphology characterizedas slow and smooth change of EOG time series In thefurther analysis the MCA is required to compare withother competing methods for the EEG and EOG signaldecomposition

Competing Interests

The authors have declared that no competing interests exist

Acknowledgments

This work was partly supported by JSPS KAKENHI 16H01616and 26240032 and theNewEnergy and Industrial TechnologyDevelopment Organization (NEDO) ldquoNext-Generation Arti-ficial Intelligence (3) Base Technology for Next-GenerationAIrdquo (Automated Driving Task) and the collaborative researchproject with Fujitsu Ten Limited

References

[1] J P Donoghue J N Sanes N G Hatsopoulos and G GaalldquoNeural discharge and local field potential oscillations in pri-mate motor cortex during voluntary movementsrdquo Journal ofNeurophysiology vol 79 no 1 pp 159ndash173 1998

[2] J A Uriguen and B Garcia-Zapirain ldquoEEG artifact removalmdashstate-of-the-art and guidelinesrdquo Journal of Neural Engineeringvol 12 no 3 Article ID 031001 2015

[3] C Kamarajan and B Porjesz ldquoAdvances in electrophysiologicalresearchrdquoAlcohol Research Current Reviews vol 37 no 1 article53 2015

[4] L F Nicolas-Alonso and J Gomez-Gil ldquoBrain computer inter-faces a reviewrdquo Sensors vol 12 no 2 pp 1211ndash1279 2012

[5] L Mayaud M Congedo A Van Laghenhove et al ldquoA compar-ison of recording modalities of P300 event-related potentials(ERP) for brain-computer interface (BCI) paradigmrdquo Neuro-physiologie CliniqueClinical Neurophysiology vol 43 no 4 pp217ndash227 2013

[6] X-Y Wang J Jin Y Zhang and B Wang ldquoBrain controlhuman-computer integration control based on brain-computerinterfacerdquo Acta Automatica Sinica vol 39 no 3 pp 208ndash2212013

[7] G Al-Hudhud ldquoAffective command-based control system inte-grating brain signals in commands control systemsrdquo Computersin Human Behavior vol 30 pp 535ndash541 2014

[8] J L Sirvent Blasco E Ianez A Ubeda and JM Azorın ldquoVisualevoked potential-based brain-machine interface applications toassist disabled peoplerdquo Expert Systems with Applications vol 39no 9 pp 7908ndash7918 2012

[9] H Cecotti ldquoSpelling with non-invasive Brain-Computer Inter-facesmdashcurrent and future trendsrdquo Journal of Physiology Parisvol 105 no 1ndash3 pp 106ndash114 2011

[10] I S Kotchetkov B Y Hwang G Appelboom C P Kellnerand E S Connolly Jr ldquoBrain-computer interfaces militaryneurosurgical and ethical perspectiverdquo Neurosurgical Focusvol 28 no 5 article no E25 2010

[11] R N Vigario ldquoExtraction of ocular artefacts from EEG usingindependent component analysisrdquo Electroencephalography andClinical Neurophysiology vol 103 no 3 pp 395ndash404 1997

[12] W Zhou and J Gotman ldquoAutomatic removal of eye movementartifacts from the EEG using ICA and the dipole modelrdquoProgress in Natural Science vol 19 no 9 pp 1165ndash1170 2009

[13] R Sameni andCGouy-Pailler ldquoAn iterative subspace denoisingalgorithm for removing electroencephalogram ocular artifactsrdquoJournal of Neuroscience Methods vol 225 pp 97ndash105 2014

[14] M Breakspear and J R Terry ldquoDetection and description ofnon-linear interdependence in normal multichannel humanEEG datardquo Clinical Neurophysiology vol 113 no 5 pp 735ndash7532002

[15] U R Acharya O Faust N Kannathal T Chua and S Laxmin-arayan ldquoNon-linear analysis of EEG signals at various sleepstagesrdquo Computer Methods and Programs in Biomedicine vol80 no 1 pp 37ndash45 2005

[16] L I Aftanas and S A Golocheikine ldquoNon-linear dynamiccomplexity of the human EEGduringmeditationrdquoNeuroscienceLetters vol 330 no 2 pp 143ndash146 2002

[17] M J Fadili J-L Starck J Bobin and Y Moudden ldquoImagedecomposition and separation using sparse representations anoverviewrdquo Proceedings of the IEEE vol 98 no 6 pp 983ndash9942010

[18] K J Blinowska and P J Durka ldquoUnbiased high resolutionmethod of EEG analysis in time-frequency spacerdquo Acta Neuro-biologiae Experimentalis vol 61 no 3 pp 157ndash174 2001

[19] E Imani H-R Pourreza and T Banaee ldquoFully automateddiabetic retinopathy screening usingmorphological componentanalysisrdquo Computerized Medical Imaging and Graphics vol 43pp 78ndash88 2015

[20] E Imani M Javidi and H-R Pourreza ldquoImprovement ofretinal blood vessel detection using morphological componentanalysisrdquo Computer Methods and Programs in Biomedicine vol118 no 3 pp 263ndash279 2016

[21] A S Al-Fahoum and A A Al-Fraihat ldquoMethods of EEG signalfeatures extraction using linear analysis in frequency and time-frequency domainsrdquo ISRN Neuroscience vol 2014 Article ID730218 7 pages 2014

[22] M Zibulevsky and B A Pearlmutter ldquoBlind source separationby sparse decomposition in a signal dictionaryrdquoNeural Compu-tation vol 13 no 4 pp 863ndash882 2001

[23] N P Castellanos andVAMakarov ldquoRecovering EEGbrain sig-nals artifact suppression with wavelet enhanced independentcomponent analysisrdquo Journal of Neuroscience Methods vol 158no 2 pp 300ndash312 2006

[24] J Hou K Morgan D M Tucker et al ldquoAn improved artifactsremoval method for high dimensional EEGrdquo Journal of Neuro-science Methods vol 268 pp 31ndash42 2016

[25] P Berg and M Scherg ldquoA multiple source approach to thecorrection of eye artifactsrdquo Electroencephalography and ClinicalNeurophysiology vol 90 no 3 pp 229ndash241 1994

[26] P K Sadasivan and D Narayana Dutt ldquoSVD based techniquefor noise reduction in electroencephalographic signalsrdquo SignalProcessing vol 55 no 2 pp 179ndash189 1996

16 Computational and Mathematical Methods in Medicine

[27] C A Joyce I F Gorodnitsky andMKutas ldquoAutomatic removalof eye movement and blink artifacts from EEG data using blindcomponent separationrdquo Psychophysiology vol 41 no 2 pp 313ndash325 2004

[28] G L Wallstrom R E Kass A Miller J F Cohn and N A FoxldquoAutomatic correction of ocular artifacts in the EEG a com-parison of regression-based and component-based methodsrdquoInternational Journal of Psychophysiology vol 53 no 2 pp 105ndash119 2004

[29] S M Gordon V Lawhern A D Passaro and K McDowellldquoInformed decomposition of electroencephalographic datardquoJournal of Neuroscience Methods vol 256 pp 41ndash55 2015

[30] D StuderUHoffmann andTKoenig ldquoFromEEGdependencymultichannel matching pursuit to sparse topographic EEGdecompositionrdquo Journal of Neuroscience Methods vol 153 no2 pp 261ndash275 2006

[31] J-L Starck M Elad and D Donoho ldquoRedundant multiscaletransforms and their application for morphological componentseparationrdquo Advances in Imaging and Electron Physics vol 132pp 287ndash348 2004

[32] P J Franaszczuk G K Bergey P J Durka andHM EisenbergldquoTime-frequency analysis using thematching pursuit algorithmapplied to seizures originating from the mesial temporal loberdquoElectroencephalography and Clinical Neurophysiology vol 106no 6 pp 513ndash521 1998

[33] P J Durka A Matysiak E M Montes P V Sosa and K JBlinowska ldquoMultichannel matching pursuit and EEG inversesolutionsrdquo Journal of Neuroscience Methods vol 148 no 1 pp49ndash59 2005

[34] J Bobin J-L Starck J Fadili and Y Moudden ldquoSparsityand morphological diversity in blind source separationrdquo IEEETransactions on Image Processing vol 16 no 11 pp 2662ndash26742007

[35] P J Durka D Ircha and K J Blinowska ldquoStochastic time-frequency dictionaries formatching pursuitrdquo IEEE Transactionson Signal Processing vol 49 no 3 pp 507ndash510 2001

[36] X Yong R K Ward and G E Birch ldquoGeneralized morpholog-ical component analysis for EEG source separation and artifactremovalrdquo in Proceedings of the 4th International IEEEEMBSConference on Neural Engineering (NER rsquo09) pp 343ndash346Antalya Turkey May 2009

[37] B Singh G Ai and H Wagatsuma ldquoAn electrooculographyanalysis in the time-frequency domain using morphologicalcomponent analysis toward the development of mobile BCIsystemsrdquo in Universal Access in Human-Computer InteractionAccess to Interaction 9th International Conference UAHCI 2015Held as Part of HCI International 2015 Los Angeles CA USAAugust 2ndash7 2015 Proceedings Part II vol 9176 of Lecture Notesin Computer Science pp 528ndash537 Springer Berlin Germany2015

[38] S S Chen D L Donoho and M A Saunders ldquoAtomicdecomposition by basis pursuitrdquo SIAM Review vol 43 no 1pp 129ndash159 2001

[39] D L Donoho and X Huo ldquoUncertainty principles and idealatomic decompositionrdquo IEEE Transactions on InformationThe-ory vol 47 no 7 pp 2845ndash2862 2001

[40] F Miwakeichi E Martınez-Montes P A Valdes-Sosa NNishiyama H Mizuhara and Y Yamaguchi ldquoDecomposingEEG data into spacendashtimendashfrequency components using par-allel factor analysisrdquo NeuroImage vol 22 no 3 pp 1035ndash10452004

[41] K J Friston C D Frith P F Liddle and R S J FrackowiakldquoFunctional connectivity the principal-component analysis oflarge (PET) data setsrdquo Journal of Cerebral Blood Flow andMetabolism vol 13 no 1 pp 5ndash14 1993

[42] S Makeig T-P Jung A J Bell D Ghahremani and T JSejnowski ldquoBlind separation of auditory event-related brainresponses into independent componentsrdquo Proceedings of theNational Academy of Sciences of the United States of Americavol 94 no 20 pp 10979ndash10984 1997

[43] Biomedical Signal httpwwwmedicinemcgillcaphysiovlabbiomed signalseeg nhtm

[44] S E G Nilsson and B E Andersson ldquoCorneal DC recordingsof slow ocular potential changes such as the ERG c-wave and thelight peak in clinical workmdashequipment and examples of resultsrdquoDocumenta Ophthalmologica vol 68 no 3-4 pp 313ndash325 1988

[45] OG Lins TW Picton P Berg andM Scherg ldquoOcular artifactsin EEG and event-related potentials I scalp topographyrdquo BrainTopography vol 6 no 1 pp 51ndash63 1993

[46] T W Picton P Van Roon M L Armilio P Berg N Ille andM Scherg ldquoThe correction of ocular artifacts a topographicperspectiverdquo Clinical Neurophysiology vol 111 no 1 pp 53ndash652000

[47] A S Keren S Yuval-Greenberg and L Y Deouell ldquoSaccadicspike potentials in gamma-band EEG characterization detec-tion and suppressionrdquo NeuroImage vol 49 no 3 pp 2248ndash2263 2010

[48] M Plochl J P Ossandon and P Konig ldquoCombining EEG andeye tracking identification characterization and correctionof eye movement artifacts in electroencephalographic datardquoFrontiers in Human Neuroscience vol 6 article 278 2012

[49] S Dandekar C Privitera T Carney and S A Klein ldquoNeuralsaccadic response estimation during natural viewingrdquo Journalof Neurophysiology vol 107 no 6 pp 1776ndash1790 2012

[50] G Ai N Sato B Singh and H Wagatsuma ldquoDirection andviewing area-sensitive influence of EOGartifacts revealed in theEEG topographic pattern analysisrdquo Cognitive Neurodynamicsvol 10 no 4 pp 301ndash314 2016

[51] P Berg and M Scherg ldquoDipole models of eye movements andblinksrdquo Electroencephalography and Clinical Neurophysiologyvol 79 no 1 pp 36ndash44 1991

[52] R J Croft and R J Barry ldquoRemoval of ocular artifact from theEEG a reviewrdquo Neurophysiologie Clinique vol 30 no 1 pp 5ndash19 2000

[53] I J Rampil ldquoA primer for EEG signal processing in anesthesiardquoAnesthesiology vol 89 no 4 pp 980ndash1002 1998

[54] J L Starck Y Moudden J Bobin M Elad and D DonoholdquoMorphological component analysisrdquo in Optics amp Photonics2005 p 59140Q International Society forOptics and Photonics2005

[55] S Sardy A Bruce and P Tseng ldquoBlock coordinate relaxationmethods for nonparametric signal denoising with waveletdictionariesrdquo Journal of Computational and Graphical Statisticsvol 9 pp 361ndash379 2000

[56] M Puschel and J M F Moura ldquoThe algebraic approach to thediscrete cosine and sine transforms and their fast algorithmsrdquoSIAM Journal on Computing vol 32 no 5 pp 1280ndash1316 2003

[57] X Shao and S G Johnson ldquoType-IV DCT DST and MDCTalgorithms with reduced numbers of arithmetic operationsrdquoSignal Processing vol 88 no 6 pp 1313ndash1326 2008

[58] R G Andrzejak K Lehnertz F Mormann C Rieke P Davidand C E Elger ldquoIndications of nonlinear deterministic and

Computational and Mathematical Methods in Medicine 9

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

Aver

aged

corr

elat

ion

coeffi

cien

t

06

04

08

1

(a) cc between iEEG and 2nd comp (hard)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5Av

erag

ed co

rrel

atio

n co

effici

ent

06

04

08

1

(b) cc between iEEG and 2nd comp (soft)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

06

04

08

1

Aver

aged

corr

elat

ion

coeffi

cien

t

(c) cc between EOG and UDWT (hard)

UDWT-DST-DIRACUDWT-DCT-DIRACUDWT-LDCT-DIRAC

3 4 5

Aver

aged

corr

elat

ion

coeffi

cien

t

06

04

08

1

(d) cc between EOG and UDWT (soft)

Figure 6 A comparison between cc of decomposed morphological component with iEEG signal and artificial EOG with hard and softthresholds The mean value and standard deviation were calculated from all 100 decomposed datasets by explicit dictionaries (a) Secondmorphological component was decomposed by DST DCT and LDCT with hard and (b) soft threshold respectively (c) First morphologicalcomponent was decomposed by UDWT with a hard threshold and (d) soft threshold respectively 100 trials of iEEG and artificial EOG wereused

10 Computational and Mathematical Methods in Medicine

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

0 20 40 60 80

0

2

4

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(a) Hard (120582 = 3)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(b) Hard (120582 = 4)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(c) Hard (120582 = 5)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(d) Soft (120582 = 3)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(e) Soft (120582 = 4)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Nor

mal

ized

pow

er (d

B)

Frequency (Hz)

minus2

(f) Soft (120582 = 5)

Figure 7 An averaged normalized FFT obtained from 100 of iEEG and combination of two morphological components and singlemorphological component at 120582 varies from 3 to 5 with hard and soft thresholds

Figure 11(a) demonstrated the decomposition of compo-nents by the first explicit dictionary it was divided into threedifferent morphologies of the EEG signal Figures 11(b) and11(c) showed the second and the third explicit dictionary ofredundant transform respectively The overcomplete dictio-nary was a combination of redundant transforms that char-acterized the component in a different morphology Accord-ingly one of redundant transforms can be differentiated intodecomposed components by overcomplete dictionaries Thefirst component was decomposed by ldquoUDWTrdquo of each over-complete dictionary and was analyzed via the slow and blinktype morphology The second component was decomposedby ldquoDCTrdquo ldquoDSTrdquo and ldquoLDCTrdquo and was analyzed via thebackground of the signal which was similar to the EEG signal

and the third component was decomposed by ldquoDIRACrdquo andwas analyzed via the unexpected spikeThe first overcompletedictionary decomposed the EEG signal without changingthe monomorphic polymorphic and transient propertiesThe cc between the original signal and the summation of alldecomposed components was close to one Figure 12 showedthe raw EOG signal taken from the vertical and horizontalchannel and first decomposed component taken from Fp1Fp2 Cz O1 and O2 respectively

Table 1 showed individual cc of original EEG signals andrecomposed EEG signals from the combination of compo-nents with respect to different channels and combinationsof dictionaries Table 2 showed the cc between filter rawEOG signal taken from vertical and horizontal channels and

Computational and Mathematical Methods in Medicine 11

3 4 5

02

03

04

05

06

07

08

09

Aver

aged

FFT

corr

elat

ion

coeffi

cien

t

01

1

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

lowast lowast lowast

(a) Hard threshold

3 4 5

Aver

aged

FFT

corr

elat

ion

coeffi

cien

t02

03

04

05

06

07

08

09

01

1

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

lowast lowast lowast

(b) Soft threshold

Figure 8 A comparison of FFT correlation coefficients between iEEG data and morphological component decomposed by explicitdictionaries lowastSignificant differences (119901 lt 005) (a) Combined two morphological components and (b) single morphological componentMean value and standard deviation calculated from all 100 decomposed datasets by explicit dictionaries with hard and soft thresholds

400

Pote

ntia

l (V

)

200

0

minus200

400

Pote

ntia

l (V

)

200

0

minus200

Samples20000 1000

EOG (V1u-V1d)

EOG (V2u-V2d)

Figure 9 An example of EOG signal taken from right and left sideof eyes

decomposed first component from Fp1 Fp2 Cz O1 and O2respectively

5 Discussion

Artifact contamination in EEG signal has been a com-mon important issue in neurobiological event diagnosis and

Table 1 cc of original signal and sum of the decomposed compo-nents

EEG channelCorrelation coefficient

UDWT-DST-DIRAC

UDWT-DCT-DIRAC

UDWT-LDCT-DIRAC

Fp1 09921 plusmn 0014 09921 plusmn 0014 09932 plusmn 0013Fp2 0992 plusmn 017 09919 plusmn 018 09932 plusmn 014Cz 09898 plusmn 01 09899 plusmn 01 09908 plusmn 009O1 09836 plusmn 015 09836 plusmn 016 09869 plusmn 012O2 09855 plusmn 013 09856 plusmn 013 09849 plusmn 015

neuroscientific researchThevariousmethodswere applied toremove the artifacts from EEG [2 11ndash13 21 23 24 26ndash28 52]The decomposition based analysis was used in removal ofEOG artifacts in EEG [22 27 28 30 40 42] Howeverthose methods lack the elucidation of what the nature ofEEG signals is in the viewpoint of the signal analysis and asystematic approach was required by treating the sparsity andnonlinearity of the signal in the time domain

12 Computational and Mathematical Methods in Medicine

0

0

50

Fp1

Fp2

Cz

O1

O2

100

0

minus100

minus50

minus40

Pote

ntia

l (V

)

0

50

minus50

Pote

ntia

l (V

)

050

minus50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

Figure 10 An example of real EEG signal taken from Fp1 Fp2 Cz O1 and O2 electrode channels

Table 2 cc between filtered EOG and UDWT component decomposed by UDWT dictionary

EOG channels EEG channelsFp1 Fp2 Cz O1 O2

Correlation coefficientUDWT-DST-DIRACV1d 06777 0657 07267 09223 06445V1u 06814 0646 06606 09419 06354V2d 0916 0906 09402 0882 05402V2u 02332 02268 02353 06388 08494H1 08582 0847 08444 06902 05839H2 09419 09468 09559 07476 04752

UDWT-DCT-DIRACV1d 06792 06595 068 09213 06352V1u 06835 06396 06424 09581 06585V2d 09193 0902 09362 08764 05145V2u 02331 02183 02316 06639 08919H1 08593 08507 08626 06759 05376H2 09442 09465 09662 07266 04346

UDWT-LDCT-DIRACV1d 06794 06403 07219 08892 065V1u 06443 06279 06459 08196 05381V2d 09142 09072 09395 09592 06506V2u 02351 02235 02383 03747 06804H1 08637 08449 08471 07638 05734H2 09586 09558 09577 08826 05598

Computational and Mathematical Methods in Medicine 13

0

50

0

20

UDWT

DCT

DIRAC

0

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus30

(a)

UDWT

DST

DIRAC

0

0

20

0

50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus20

minus20

(b)

0

0

50

100

0

UDWT

LDCT

DIRAC

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus20

minus40

minus80

(c)

Figure 11 Component separated fromEEG (Fp1 electrode) signal by explicit dictionaries (a)UDWT-DCT-DIRAC (b)UDWT-DST-DIRACand (c) UDWT-LDCT-DIRAC respectively

This study revealed the nature of EEG signals in the senseof morphologies contained in the original signal by usingMCA The UDWT was used to decompose the slow andbump morphology The DCT DST and LDCT transformwere used to decompose the EEG signal Spike typemorphol-ogy was decomposed by DIRAC Redundant transforms ofDCT and DST have a similar capability in representing themorphology of oscillatory activities Therefore we used theDCT LDCT and DST dictionaries for validations of EEGsignal The detailed significant differences in morphology ofDCT and DST were given in past studies [56 57] while inour analysis there were no significant differences The rightcombination of redundant transforms to form overcompletedictionary revealed the desired decomposition in principle

In Section 42 ldquoBlocksrdquo ldquoBumpsrdquo similar to simulatedEOG signal defined in past studies [59ndash61] as shown in

Figure 4 and EEG data [58] were used to validate ourpurposed method The ldquoBlocksrdquo with abrupt changes weresimilar to the horizontal and vertical eye movements sim-ply as described by past studies [25 51] For the sake ofsimplicity in the present study ldquoBumpsrdquo were used as arepresentative signal form as eye blinks that happens inunexpected timings as illustrated in Figure 5 The separationof components by given dictionary works well in this evalu-ation but the further analysis is necessary for the evaluationof the signal decomposition with complex eye movementswhich requires presumably various redundant dictionariesIn the verification of the component discrimination as shownin Figures 6 and 7 the accuracy of the averaged EOGcomponent decomposition was above 90 which suggests aplausible performance even in the complex eye movementsThe combined DST and DIRAC dictionaries had better

14 Computational and Mathematical Methods in Medicine

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

Samples20000 1000

V1u

H1

(a) UDWT components separated by UDWT-DST-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(b) UDWT components separated by UDWT-DCT-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(c) UDWT components separated by UDWT-LDCT-DIRAC

Figure 12 UDWT component taken from Fp1 Fp2 Cz O1 and O2 separated by UDWT-DCT-DIRAC UDWT-DST-DIRAC and UDWT-LDCT-DIRAC respectively

decomposition performance than others while DST andDCT theoretically have no meaningful difference The usageof iEEG as the true EEG signal had a large benefit whichcan be used for the performance test for past proposedmethods like ICA and PCA consistently Our proposedmethod successfully demonstrated the performance in cc andthe frequency profile especially in Section 42 while in theserious discussion of the real EEG and EOG signals the DSTor DCT component exhibited a baseline fluctuation of thesignal which denotes the persistence of the EOG componentor other slow frequency artifacts noises and the factor willbe improved by the fine-tuned design of the DST or DCTdictionary with a band pass filter function In addition thethreshold problem exits in the optimization algorithm andnumber of iterations [37]

The EEG decomposition had not mark with a combi-nation of a second and a third component of EEG signal

decomposed by ldquoDST DCT and LDCTrdquo andDIRAC respec-tively based on the morphology Therefore the accuratecombination in the further perspective will be considerableEven the combination of all components and the mixedsignal or real EEG signal had cc above 97 for all redundanttransforms as is analyzed in the frequency spectrum thesignal morphology has further meaning in the viewpointof the signal transmission The MCA method has such anextended and flexible availability for signal analyses

6 Conclusion

Morphological Component Analysis methodology wasapplied to the simulated semisimulated and real EOGand EEG signal The successful decomposition of the EOGand EEG signal into their morphological component wasdemonstrated It seems to be that the EEG signals and

Computational and Mathematical Methods in Medicine 15

artifacts in EEG have been represented by different explicitdictionaries We analyzed the EEG signals involved with theEOG artifacts which were influenced by task conditionsTheDIRAC explicit dictionary decomposed the EEG signal intospike-like activities which may be related to the transientproperty of EEG UDWT explicit dictionary representsslow movement or bumps DCT DST and LDCT explicitdictionaries represent dominant signal that represents EEGsor pure tones signals as monomorphic and polymorphicactivities These results suggested that the effectivenessof MCA in ocular artifacts removal from the EEG rawsignal was derived from signal morphology characterizedas slow and smooth change of EOG time series In thefurther analysis the MCA is required to compare withother competing methods for the EEG and EOG signaldecomposition

Competing Interests

The authors have declared that no competing interests exist

Acknowledgments

This work was partly supported by JSPS KAKENHI 16H01616and 26240032 and theNewEnergy and Industrial TechnologyDevelopment Organization (NEDO) ldquoNext-Generation Arti-ficial Intelligence (3) Base Technology for Next-GenerationAIrdquo (Automated Driving Task) and the collaborative researchproject with Fujitsu Ten Limited

References

[1] J P Donoghue J N Sanes N G Hatsopoulos and G GaalldquoNeural discharge and local field potential oscillations in pri-mate motor cortex during voluntary movementsrdquo Journal ofNeurophysiology vol 79 no 1 pp 159ndash173 1998

[2] J A Uriguen and B Garcia-Zapirain ldquoEEG artifact removalmdashstate-of-the-art and guidelinesrdquo Journal of Neural Engineeringvol 12 no 3 Article ID 031001 2015

[3] C Kamarajan and B Porjesz ldquoAdvances in electrophysiologicalresearchrdquoAlcohol Research Current Reviews vol 37 no 1 article53 2015

[4] L F Nicolas-Alonso and J Gomez-Gil ldquoBrain computer inter-faces a reviewrdquo Sensors vol 12 no 2 pp 1211ndash1279 2012

[5] L Mayaud M Congedo A Van Laghenhove et al ldquoA compar-ison of recording modalities of P300 event-related potentials(ERP) for brain-computer interface (BCI) paradigmrdquo Neuro-physiologie CliniqueClinical Neurophysiology vol 43 no 4 pp217ndash227 2013

[6] X-Y Wang J Jin Y Zhang and B Wang ldquoBrain controlhuman-computer integration control based on brain-computerinterfacerdquo Acta Automatica Sinica vol 39 no 3 pp 208ndash2212013

[7] G Al-Hudhud ldquoAffective command-based control system inte-grating brain signals in commands control systemsrdquo Computersin Human Behavior vol 30 pp 535ndash541 2014

[8] J L Sirvent Blasco E Ianez A Ubeda and JM Azorın ldquoVisualevoked potential-based brain-machine interface applications toassist disabled peoplerdquo Expert Systems with Applications vol 39no 9 pp 7908ndash7918 2012

[9] H Cecotti ldquoSpelling with non-invasive Brain-Computer Inter-facesmdashcurrent and future trendsrdquo Journal of Physiology Parisvol 105 no 1ndash3 pp 106ndash114 2011

[10] I S Kotchetkov B Y Hwang G Appelboom C P Kellnerand E S Connolly Jr ldquoBrain-computer interfaces militaryneurosurgical and ethical perspectiverdquo Neurosurgical Focusvol 28 no 5 article no E25 2010

[11] R N Vigario ldquoExtraction of ocular artefacts from EEG usingindependent component analysisrdquo Electroencephalography andClinical Neurophysiology vol 103 no 3 pp 395ndash404 1997

[12] W Zhou and J Gotman ldquoAutomatic removal of eye movementartifacts from the EEG using ICA and the dipole modelrdquoProgress in Natural Science vol 19 no 9 pp 1165ndash1170 2009

[13] R Sameni andCGouy-Pailler ldquoAn iterative subspace denoisingalgorithm for removing electroencephalogram ocular artifactsrdquoJournal of Neuroscience Methods vol 225 pp 97ndash105 2014

[14] M Breakspear and J R Terry ldquoDetection and description ofnon-linear interdependence in normal multichannel humanEEG datardquo Clinical Neurophysiology vol 113 no 5 pp 735ndash7532002

[15] U R Acharya O Faust N Kannathal T Chua and S Laxmin-arayan ldquoNon-linear analysis of EEG signals at various sleepstagesrdquo Computer Methods and Programs in Biomedicine vol80 no 1 pp 37ndash45 2005

[16] L I Aftanas and S A Golocheikine ldquoNon-linear dynamiccomplexity of the human EEGduringmeditationrdquoNeuroscienceLetters vol 330 no 2 pp 143ndash146 2002

[17] M J Fadili J-L Starck J Bobin and Y Moudden ldquoImagedecomposition and separation using sparse representations anoverviewrdquo Proceedings of the IEEE vol 98 no 6 pp 983ndash9942010

[18] K J Blinowska and P J Durka ldquoUnbiased high resolutionmethod of EEG analysis in time-frequency spacerdquo Acta Neuro-biologiae Experimentalis vol 61 no 3 pp 157ndash174 2001

[19] E Imani H-R Pourreza and T Banaee ldquoFully automateddiabetic retinopathy screening usingmorphological componentanalysisrdquo Computerized Medical Imaging and Graphics vol 43pp 78ndash88 2015

[20] E Imani M Javidi and H-R Pourreza ldquoImprovement ofretinal blood vessel detection using morphological componentanalysisrdquo Computer Methods and Programs in Biomedicine vol118 no 3 pp 263ndash279 2016

[21] A S Al-Fahoum and A A Al-Fraihat ldquoMethods of EEG signalfeatures extraction using linear analysis in frequency and time-frequency domainsrdquo ISRN Neuroscience vol 2014 Article ID730218 7 pages 2014

[22] M Zibulevsky and B A Pearlmutter ldquoBlind source separationby sparse decomposition in a signal dictionaryrdquoNeural Compu-tation vol 13 no 4 pp 863ndash882 2001

[23] N P Castellanos andVAMakarov ldquoRecovering EEGbrain sig-nals artifact suppression with wavelet enhanced independentcomponent analysisrdquo Journal of Neuroscience Methods vol 158no 2 pp 300ndash312 2006

[24] J Hou K Morgan D M Tucker et al ldquoAn improved artifactsremoval method for high dimensional EEGrdquo Journal of Neuro-science Methods vol 268 pp 31ndash42 2016

[25] P Berg and M Scherg ldquoA multiple source approach to thecorrection of eye artifactsrdquo Electroencephalography and ClinicalNeurophysiology vol 90 no 3 pp 229ndash241 1994

[26] P K Sadasivan and D Narayana Dutt ldquoSVD based techniquefor noise reduction in electroencephalographic signalsrdquo SignalProcessing vol 55 no 2 pp 179ndash189 1996

16 Computational and Mathematical Methods in Medicine

[27] C A Joyce I F Gorodnitsky andMKutas ldquoAutomatic removalof eye movement and blink artifacts from EEG data using blindcomponent separationrdquo Psychophysiology vol 41 no 2 pp 313ndash325 2004

[28] G L Wallstrom R E Kass A Miller J F Cohn and N A FoxldquoAutomatic correction of ocular artifacts in the EEG a com-parison of regression-based and component-based methodsrdquoInternational Journal of Psychophysiology vol 53 no 2 pp 105ndash119 2004

[29] S M Gordon V Lawhern A D Passaro and K McDowellldquoInformed decomposition of electroencephalographic datardquoJournal of Neuroscience Methods vol 256 pp 41ndash55 2015

[30] D StuderUHoffmann andTKoenig ldquoFromEEGdependencymultichannel matching pursuit to sparse topographic EEGdecompositionrdquo Journal of Neuroscience Methods vol 153 no2 pp 261ndash275 2006

[31] J-L Starck M Elad and D Donoho ldquoRedundant multiscaletransforms and their application for morphological componentseparationrdquo Advances in Imaging and Electron Physics vol 132pp 287ndash348 2004

[32] P J Franaszczuk G K Bergey P J Durka andHM EisenbergldquoTime-frequency analysis using thematching pursuit algorithmapplied to seizures originating from the mesial temporal loberdquoElectroencephalography and Clinical Neurophysiology vol 106no 6 pp 513ndash521 1998

[33] P J Durka A Matysiak E M Montes P V Sosa and K JBlinowska ldquoMultichannel matching pursuit and EEG inversesolutionsrdquo Journal of Neuroscience Methods vol 148 no 1 pp49ndash59 2005

[34] J Bobin J-L Starck J Fadili and Y Moudden ldquoSparsityand morphological diversity in blind source separationrdquo IEEETransactions on Image Processing vol 16 no 11 pp 2662ndash26742007

[35] P J Durka D Ircha and K J Blinowska ldquoStochastic time-frequency dictionaries formatching pursuitrdquo IEEE Transactionson Signal Processing vol 49 no 3 pp 507ndash510 2001

[36] X Yong R K Ward and G E Birch ldquoGeneralized morpholog-ical component analysis for EEG source separation and artifactremovalrdquo in Proceedings of the 4th International IEEEEMBSConference on Neural Engineering (NER rsquo09) pp 343ndash346Antalya Turkey May 2009

[37] B Singh G Ai and H Wagatsuma ldquoAn electrooculographyanalysis in the time-frequency domain using morphologicalcomponent analysis toward the development of mobile BCIsystemsrdquo in Universal Access in Human-Computer InteractionAccess to Interaction 9th International Conference UAHCI 2015Held as Part of HCI International 2015 Los Angeles CA USAAugust 2ndash7 2015 Proceedings Part II vol 9176 of Lecture Notesin Computer Science pp 528ndash537 Springer Berlin Germany2015

[38] S S Chen D L Donoho and M A Saunders ldquoAtomicdecomposition by basis pursuitrdquo SIAM Review vol 43 no 1pp 129ndash159 2001

[39] D L Donoho and X Huo ldquoUncertainty principles and idealatomic decompositionrdquo IEEE Transactions on InformationThe-ory vol 47 no 7 pp 2845ndash2862 2001

[40] F Miwakeichi E Martınez-Montes P A Valdes-Sosa NNishiyama H Mizuhara and Y Yamaguchi ldquoDecomposingEEG data into spacendashtimendashfrequency components using par-allel factor analysisrdquo NeuroImage vol 22 no 3 pp 1035ndash10452004

[41] K J Friston C D Frith P F Liddle and R S J FrackowiakldquoFunctional connectivity the principal-component analysis oflarge (PET) data setsrdquo Journal of Cerebral Blood Flow andMetabolism vol 13 no 1 pp 5ndash14 1993

[42] S Makeig T-P Jung A J Bell D Ghahremani and T JSejnowski ldquoBlind separation of auditory event-related brainresponses into independent componentsrdquo Proceedings of theNational Academy of Sciences of the United States of Americavol 94 no 20 pp 10979ndash10984 1997

[43] Biomedical Signal httpwwwmedicinemcgillcaphysiovlabbiomed signalseeg nhtm

[44] S E G Nilsson and B E Andersson ldquoCorneal DC recordingsof slow ocular potential changes such as the ERG c-wave and thelight peak in clinical workmdashequipment and examples of resultsrdquoDocumenta Ophthalmologica vol 68 no 3-4 pp 313ndash325 1988

[45] OG Lins TW Picton P Berg andM Scherg ldquoOcular artifactsin EEG and event-related potentials I scalp topographyrdquo BrainTopography vol 6 no 1 pp 51ndash63 1993

[46] T W Picton P Van Roon M L Armilio P Berg N Ille andM Scherg ldquoThe correction of ocular artifacts a topographicperspectiverdquo Clinical Neurophysiology vol 111 no 1 pp 53ndash652000

[47] A S Keren S Yuval-Greenberg and L Y Deouell ldquoSaccadicspike potentials in gamma-band EEG characterization detec-tion and suppressionrdquo NeuroImage vol 49 no 3 pp 2248ndash2263 2010

[48] M Plochl J P Ossandon and P Konig ldquoCombining EEG andeye tracking identification characterization and correctionof eye movement artifacts in electroencephalographic datardquoFrontiers in Human Neuroscience vol 6 article 278 2012

[49] S Dandekar C Privitera T Carney and S A Klein ldquoNeuralsaccadic response estimation during natural viewingrdquo Journalof Neurophysiology vol 107 no 6 pp 1776ndash1790 2012

[50] G Ai N Sato B Singh and H Wagatsuma ldquoDirection andviewing area-sensitive influence of EOGartifacts revealed in theEEG topographic pattern analysisrdquo Cognitive Neurodynamicsvol 10 no 4 pp 301ndash314 2016

[51] P Berg and M Scherg ldquoDipole models of eye movements andblinksrdquo Electroencephalography and Clinical Neurophysiologyvol 79 no 1 pp 36ndash44 1991

[52] R J Croft and R J Barry ldquoRemoval of ocular artifact from theEEG a reviewrdquo Neurophysiologie Clinique vol 30 no 1 pp 5ndash19 2000

[53] I J Rampil ldquoA primer for EEG signal processing in anesthesiardquoAnesthesiology vol 89 no 4 pp 980ndash1002 1998

[54] J L Starck Y Moudden J Bobin M Elad and D DonoholdquoMorphological component analysisrdquo in Optics amp Photonics2005 p 59140Q International Society forOptics and Photonics2005

[55] S Sardy A Bruce and P Tseng ldquoBlock coordinate relaxationmethods for nonparametric signal denoising with waveletdictionariesrdquo Journal of Computational and Graphical Statisticsvol 9 pp 361ndash379 2000

[56] M Puschel and J M F Moura ldquoThe algebraic approach to thediscrete cosine and sine transforms and their fast algorithmsrdquoSIAM Journal on Computing vol 32 no 5 pp 1280ndash1316 2003

[57] X Shao and S G Johnson ldquoType-IV DCT DST and MDCTalgorithms with reduced numbers of arithmetic operationsrdquoSignal Processing vol 88 no 6 pp 1313ndash1326 2008

[58] R G Andrzejak K Lehnertz F Mormann C Rieke P Davidand C E Elger ldquoIndications of nonlinear deterministic and

10 Computational and Mathematical Methods in Medicine

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

0 20 40 60 80

0

2

4

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(a) Hard (120582 = 3)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(b) Hard (120582 = 4)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(c) Hard (120582 = 5)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(d) Soft (120582 = 3)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Frequency (Hz)

minus2

Nor

mal

ized

pow

er (d

B)

(e) Soft (120582 = 4)

0 20 40 60 80

0

2

4

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

iEEG Signal

Nor

mal

ized

pow

er (d

B)

Frequency (Hz)

minus2

(f) Soft (120582 = 5)

Figure 7 An averaged normalized FFT obtained from 100 of iEEG and combination of two morphological components and singlemorphological component at 120582 varies from 3 to 5 with hard and soft thresholds

Figure 11(a) demonstrated the decomposition of compo-nents by the first explicit dictionary it was divided into threedifferent morphologies of the EEG signal Figures 11(b) and11(c) showed the second and the third explicit dictionary ofredundant transform respectively The overcomplete dictio-nary was a combination of redundant transforms that char-acterized the component in a different morphology Accord-ingly one of redundant transforms can be differentiated intodecomposed components by overcomplete dictionaries Thefirst component was decomposed by ldquoUDWTrdquo of each over-complete dictionary and was analyzed via the slow and blinktype morphology The second component was decomposedby ldquoDCTrdquo ldquoDSTrdquo and ldquoLDCTrdquo and was analyzed via thebackground of the signal which was similar to the EEG signal

and the third component was decomposed by ldquoDIRACrdquo andwas analyzed via the unexpected spikeThe first overcompletedictionary decomposed the EEG signal without changingthe monomorphic polymorphic and transient propertiesThe cc between the original signal and the summation of alldecomposed components was close to one Figure 12 showedthe raw EOG signal taken from the vertical and horizontalchannel and first decomposed component taken from Fp1Fp2 Cz O1 and O2 respectively

Table 1 showed individual cc of original EEG signals andrecomposed EEG signals from the combination of compo-nents with respect to different channels and combinationsof dictionaries Table 2 showed the cc between filter rawEOG signal taken from vertical and horizontal channels and

Computational and Mathematical Methods in Medicine 11

3 4 5

02

03

04

05

06

07

08

09

Aver

aged

FFT

corr

elat

ion

coeffi

cien

t

01

1

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

lowast lowast lowast

(a) Hard threshold

3 4 5

Aver

aged

FFT

corr

elat

ion

coeffi

cien

t02

03

04

05

06

07

08

09

01

1

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

lowast lowast lowast

(b) Soft threshold

Figure 8 A comparison of FFT correlation coefficients between iEEG data and morphological component decomposed by explicitdictionaries lowastSignificant differences (119901 lt 005) (a) Combined two morphological components and (b) single morphological componentMean value and standard deviation calculated from all 100 decomposed datasets by explicit dictionaries with hard and soft thresholds

400

Pote

ntia

l (V

)

200

0

minus200

400

Pote

ntia

l (V

)

200

0

minus200

Samples20000 1000

EOG (V1u-V1d)

EOG (V2u-V2d)

Figure 9 An example of EOG signal taken from right and left sideof eyes

decomposed first component from Fp1 Fp2 Cz O1 and O2respectively

5 Discussion

Artifact contamination in EEG signal has been a com-mon important issue in neurobiological event diagnosis and

Table 1 cc of original signal and sum of the decomposed compo-nents

EEG channelCorrelation coefficient

UDWT-DST-DIRAC

UDWT-DCT-DIRAC

UDWT-LDCT-DIRAC

Fp1 09921 plusmn 0014 09921 plusmn 0014 09932 plusmn 0013Fp2 0992 plusmn 017 09919 plusmn 018 09932 plusmn 014Cz 09898 plusmn 01 09899 plusmn 01 09908 plusmn 009O1 09836 plusmn 015 09836 plusmn 016 09869 plusmn 012O2 09855 plusmn 013 09856 plusmn 013 09849 plusmn 015

neuroscientific researchThevariousmethodswere applied toremove the artifacts from EEG [2 11ndash13 21 23 24 26ndash28 52]The decomposition based analysis was used in removal ofEOG artifacts in EEG [22 27 28 30 40 42] Howeverthose methods lack the elucidation of what the nature ofEEG signals is in the viewpoint of the signal analysis and asystematic approach was required by treating the sparsity andnonlinearity of the signal in the time domain

12 Computational and Mathematical Methods in Medicine

0

0

50

Fp1

Fp2

Cz

O1

O2

100

0

minus100

minus50

minus40

Pote

ntia

l (V

)

0

50

minus50

Pote

ntia

l (V

)

050

minus50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

Figure 10 An example of real EEG signal taken from Fp1 Fp2 Cz O1 and O2 electrode channels

Table 2 cc between filtered EOG and UDWT component decomposed by UDWT dictionary

EOG channels EEG channelsFp1 Fp2 Cz O1 O2

Correlation coefficientUDWT-DST-DIRACV1d 06777 0657 07267 09223 06445V1u 06814 0646 06606 09419 06354V2d 0916 0906 09402 0882 05402V2u 02332 02268 02353 06388 08494H1 08582 0847 08444 06902 05839H2 09419 09468 09559 07476 04752

UDWT-DCT-DIRACV1d 06792 06595 068 09213 06352V1u 06835 06396 06424 09581 06585V2d 09193 0902 09362 08764 05145V2u 02331 02183 02316 06639 08919H1 08593 08507 08626 06759 05376H2 09442 09465 09662 07266 04346

UDWT-LDCT-DIRACV1d 06794 06403 07219 08892 065V1u 06443 06279 06459 08196 05381V2d 09142 09072 09395 09592 06506V2u 02351 02235 02383 03747 06804H1 08637 08449 08471 07638 05734H2 09586 09558 09577 08826 05598

Computational and Mathematical Methods in Medicine 13

0

50

0

20

UDWT

DCT

DIRAC

0

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus30

(a)

UDWT

DST

DIRAC

0

0

20

0

50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus20

minus20

(b)

0

0

50

100

0

UDWT

LDCT

DIRAC

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus20

minus40

minus80

(c)

Figure 11 Component separated fromEEG (Fp1 electrode) signal by explicit dictionaries (a)UDWT-DCT-DIRAC (b)UDWT-DST-DIRACand (c) UDWT-LDCT-DIRAC respectively

This study revealed the nature of EEG signals in the senseof morphologies contained in the original signal by usingMCA The UDWT was used to decompose the slow andbump morphology The DCT DST and LDCT transformwere used to decompose the EEG signal Spike typemorphol-ogy was decomposed by DIRAC Redundant transforms ofDCT and DST have a similar capability in representing themorphology of oscillatory activities Therefore we used theDCT LDCT and DST dictionaries for validations of EEGsignal The detailed significant differences in morphology ofDCT and DST were given in past studies [56 57] while inour analysis there were no significant differences The rightcombination of redundant transforms to form overcompletedictionary revealed the desired decomposition in principle

In Section 42 ldquoBlocksrdquo ldquoBumpsrdquo similar to simulatedEOG signal defined in past studies [59ndash61] as shown in

Figure 4 and EEG data [58] were used to validate ourpurposed method The ldquoBlocksrdquo with abrupt changes weresimilar to the horizontal and vertical eye movements sim-ply as described by past studies [25 51] For the sake ofsimplicity in the present study ldquoBumpsrdquo were used as arepresentative signal form as eye blinks that happens inunexpected timings as illustrated in Figure 5 The separationof components by given dictionary works well in this evalu-ation but the further analysis is necessary for the evaluationof the signal decomposition with complex eye movementswhich requires presumably various redundant dictionariesIn the verification of the component discrimination as shownin Figures 6 and 7 the accuracy of the averaged EOGcomponent decomposition was above 90 which suggests aplausible performance even in the complex eye movementsThe combined DST and DIRAC dictionaries had better

14 Computational and Mathematical Methods in Medicine

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

Samples20000 1000

V1u

H1

(a) UDWT components separated by UDWT-DST-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(b) UDWT components separated by UDWT-DCT-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(c) UDWT components separated by UDWT-LDCT-DIRAC

Figure 12 UDWT component taken from Fp1 Fp2 Cz O1 and O2 separated by UDWT-DCT-DIRAC UDWT-DST-DIRAC and UDWT-LDCT-DIRAC respectively

decomposition performance than others while DST andDCT theoretically have no meaningful difference The usageof iEEG as the true EEG signal had a large benefit whichcan be used for the performance test for past proposedmethods like ICA and PCA consistently Our proposedmethod successfully demonstrated the performance in cc andthe frequency profile especially in Section 42 while in theserious discussion of the real EEG and EOG signals the DSTor DCT component exhibited a baseline fluctuation of thesignal which denotes the persistence of the EOG componentor other slow frequency artifacts noises and the factor willbe improved by the fine-tuned design of the DST or DCTdictionary with a band pass filter function In addition thethreshold problem exits in the optimization algorithm andnumber of iterations [37]

The EEG decomposition had not mark with a combi-nation of a second and a third component of EEG signal

decomposed by ldquoDST DCT and LDCTrdquo andDIRAC respec-tively based on the morphology Therefore the accuratecombination in the further perspective will be considerableEven the combination of all components and the mixedsignal or real EEG signal had cc above 97 for all redundanttransforms as is analyzed in the frequency spectrum thesignal morphology has further meaning in the viewpointof the signal transmission The MCA method has such anextended and flexible availability for signal analyses

6 Conclusion

Morphological Component Analysis methodology wasapplied to the simulated semisimulated and real EOGand EEG signal The successful decomposition of the EOGand EEG signal into their morphological component wasdemonstrated It seems to be that the EEG signals and

Computational and Mathematical Methods in Medicine 15

artifacts in EEG have been represented by different explicitdictionaries We analyzed the EEG signals involved with theEOG artifacts which were influenced by task conditionsTheDIRAC explicit dictionary decomposed the EEG signal intospike-like activities which may be related to the transientproperty of EEG UDWT explicit dictionary representsslow movement or bumps DCT DST and LDCT explicitdictionaries represent dominant signal that represents EEGsor pure tones signals as monomorphic and polymorphicactivities These results suggested that the effectivenessof MCA in ocular artifacts removal from the EEG rawsignal was derived from signal morphology characterizedas slow and smooth change of EOG time series In thefurther analysis the MCA is required to compare withother competing methods for the EEG and EOG signaldecomposition

Competing Interests

The authors have declared that no competing interests exist

Acknowledgments

This work was partly supported by JSPS KAKENHI 16H01616and 26240032 and theNewEnergy and Industrial TechnologyDevelopment Organization (NEDO) ldquoNext-Generation Arti-ficial Intelligence (3) Base Technology for Next-GenerationAIrdquo (Automated Driving Task) and the collaborative researchproject with Fujitsu Ten Limited

References

[1] J P Donoghue J N Sanes N G Hatsopoulos and G GaalldquoNeural discharge and local field potential oscillations in pri-mate motor cortex during voluntary movementsrdquo Journal ofNeurophysiology vol 79 no 1 pp 159ndash173 1998

[2] J A Uriguen and B Garcia-Zapirain ldquoEEG artifact removalmdashstate-of-the-art and guidelinesrdquo Journal of Neural Engineeringvol 12 no 3 Article ID 031001 2015

[3] C Kamarajan and B Porjesz ldquoAdvances in electrophysiologicalresearchrdquoAlcohol Research Current Reviews vol 37 no 1 article53 2015

[4] L F Nicolas-Alonso and J Gomez-Gil ldquoBrain computer inter-faces a reviewrdquo Sensors vol 12 no 2 pp 1211ndash1279 2012

[5] L Mayaud M Congedo A Van Laghenhove et al ldquoA compar-ison of recording modalities of P300 event-related potentials(ERP) for brain-computer interface (BCI) paradigmrdquo Neuro-physiologie CliniqueClinical Neurophysiology vol 43 no 4 pp217ndash227 2013

[6] X-Y Wang J Jin Y Zhang and B Wang ldquoBrain controlhuman-computer integration control based on brain-computerinterfacerdquo Acta Automatica Sinica vol 39 no 3 pp 208ndash2212013

[7] G Al-Hudhud ldquoAffective command-based control system inte-grating brain signals in commands control systemsrdquo Computersin Human Behavior vol 30 pp 535ndash541 2014

[8] J L Sirvent Blasco E Ianez A Ubeda and JM Azorın ldquoVisualevoked potential-based brain-machine interface applications toassist disabled peoplerdquo Expert Systems with Applications vol 39no 9 pp 7908ndash7918 2012

[9] H Cecotti ldquoSpelling with non-invasive Brain-Computer Inter-facesmdashcurrent and future trendsrdquo Journal of Physiology Parisvol 105 no 1ndash3 pp 106ndash114 2011

[10] I S Kotchetkov B Y Hwang G Appelboom C P Kellnerand E S Connolly Jr ldquoBrain-computer interfaces militaryneurosurgical and ethical perspectiverdquo Neurosurgical Focusvol 28 no 5 article no E25 2010

[11] R N Vigario ldquoExtraction of ocular artefacts from EEG usingindependent component analysisrdquo Electroencephalography andClinical Neurophysiology vol 103 no 3 pp 395ndash404 1997

[12] W Zhou and J Gotman ldquoAutomatic removal of eye movementartifacts from the EEG using ICA and the dipole modelrdquoProgress in Natural Science vol 19 no 9 pp 1165ndash1170 2009

[13] R Sameni andCGouy-Pailler ldquoAn iterative subspace denoisingalgorithm for removing electroencephalogram ocular artifactsrdquoJournal of Neuroscience Methods vol 225 pp 97ndash105 2014

[14] M Breakspear and J R Terry ldquoDetection and description ofnon-linear interdependence in normal multichannel humanEEG datardquo Clinical Neurophysiology vol 113 no 5 pp 735ndash7532002

[15] U R Acharya O Faust N Kannathal T Chua and S Laxmin-arayan ldquoNon-linear analysis of EEG signals at various sleepstagesrdquo Computer Methods and Programs in Biomedicine vol80 no 1 pp 37ndash45 2005

[16] L I Aftanas and S A Golocheikine ldquoNon-linear dynamiccomplexity of the human EEGduringmeditationrdquoNeuroscienceLetters vol 330 no 2 pp 143ndash146 2002

[17] M J Fadili J-L Starck J Bobin and Y Moudden ldquoImagedecomposition and separation using sparse representations anoverviewrdquo Proceedings of the IEEE vol 98 no 6 pp 983ndash9942010

[18] K J Blinowska and P J Durka ldquoUnbiased high resolutionmethod of EEG analysis in time-frequency spacerdquo Acta Neuro-biologiae Experimentalis vol 61 no 3 pp 157ndash174 2001

[19] E Imani H-R Pourreza and T Banaee ldquoFully automateddiabetic retinopathy screening usingmorphological componentanalysisrdquo Computerized Medical Imaging and Graphics vol 43pp 78ndash88 2015

[20] E Imani M Javidi and H-R Pourreza ldquoImprovement ofretinal blood vessel detection using morphological componentanalysisrdquo Computer Methods and Programs in Biomedicine vol118 no 3 pp 263ndash279 2016

[21] A S Al-Fahoum and A A Al-Fraihat ldquoMethods of EEG signalfeatures extraction using linear analysis in frequency and time-frequency domainsrdquo ISRN Neuroscience vol 2014 Article ID730218 7 pages 2014

[22] M Zibulevsky and B A Pearlmutter ldquoBlind source separationby sparse decomposition in a signal dictionaryrdquoNeural Compu-tation vol 13 no 4 pp 863ndash882 2001

[23] N P Castellanos andVAMakarov ldquoRecovering EEGbrain sig-nals artifact suppression with wavelet enhanced independentcomponent analysisrdquo Journal of Neuroscience Methods vol 158no 2 pp 300ndash312 2006

[24] J Hou K Morgan D M Tucker et al ldquoAn improved artifactsremoval method for high dimensional EEGrdquo Journal of Neuro-science Methods vol 268 pp 31ndash42 2016

[25] P Berg and M Scherg ldquoA multiple source approach to thecorrection of eye artifactsrdquo Electroencephalography and ClinicalNeurophysiology vol 90 no 3 pp 229ndash241 1994

[26] P K Sadasivan and D Narayana Dutt ldquoSVD based techniquefor noise reduction in electroencephalographic signalsrdquo SignalProcessing vol 55 no 2 pp 179ndash189 1996

16 Computational and Mathematical Methods in Medicine

[27] C A Joyce I F Gorodnitsky andMKutas ldquoAutomatic removalof eye movement and blink artifacts from EEG data using blindcomponent separationrdquo Psychophysiology vol 41 no 2 pp 313ndash325 2004

[28] G L Wallstrom R E Kass A Miller J F Cohn and N A FoxldquoAutomatic correction of ocular artifacts in the EEG a com-parison of regression-based and component-based methodsrdquoInternational Journal of Psychophysiology vol 53 no 2 pp 105ndash119 2004

[29] S M Gordon V Lawhern A D Passaro and K McDowellldquoInformed decomposition of electroencephalographic datardquoJournal of Neuroscience Methods vol 256 pp 41ndash55 2015

[30] D StuderUHoffmann andTKoenig ldquoFromEEGdependencymultichannel matching pursuit to sparse topographic EEGdecompositionrdquo Journal of Neuroscience Methods vol 153 no2 pp 261ndash275 2006

[31] J-L Starck M Elad and D Donoho ldquoRedundant multiscaletransforms and their application for morphological componentseparationrdquo Advances in Imaging and Electron Physics vol 132pp 287ndash348 2004

[32] P J Franaszczuk G K Bergey P J Durka andHM EisenbergldquoTime-frequency analysis using thematching pursuit algorithmapplied to seizures originating from the mesial temporal loberdquoElectroencephalography and Clinical Neurophysiology vol 106no 6 pp 513ndash521 1998

[33] P J Durka A Matysiak E M Montes P V Sosa and K JBlinowska ldquoMultichannel matching pursuit and EEG inversesolutionsrdquo Journal of Neuroscience Methods vol 148 no 1 pp49ndash59 2005

[34] J Bobin J-L Starck J Fadili and Y Moudden ldquoSparsityand morphological diversity in blind source separationrdquo IEEETransactions on Image Processing vol 16 no 11 pp 2662ndash26742007

[35] P J Durka D Ircha and K J Blinowska ldquoStochastic time-frequency dictionaries formatching pursuitrdquo IEEE Transactionson Signal Processing vol 49 no 3 pp 507ndash510 2001

[36] X Yong R K Ward and G E Birch ldquoGeneralized morpholog-ical component analysis for EEG source separation and artifactremovalrdquo in Proceedings of the 4th International IEEEEMBSConference on Neural Engineering (NER rsquo09) pp 343ndash346Antalya Turkey May 2009

[37] B Singh G Ai and H Wagatsuma ldquoAn electrooculographyanalysis in the time-frequency domain using morphologicalcomponent analysis toward the development of mobile BCIsystemsrdquo in Universal Access in Human-Computer InteractionAccess to Interaction 9th International Conference UAHCI 2015Held as Part of HCI International 2015 Los Angeles CA USAAugust 2ndash7 2015 Proceedings Part II vol 9176 of Lecture Notesin Computer Science pp 528ndash537 Springer Berlin Germany2015

[38] S S Chen D L Donoho and M A Saunders ldquoAtomicdecomposition by basis pursuitrdquo SIAM Review vol 43 no 1pp 129ndash159 2001

[39] D L Donoho and X Huo ldquoUncertainty principles and idealatomic decompositionrdquo IEEE Transactions on InformationThe-ory vol 47 no 7 pp 2845ndash2862 2001

[40] F Miwakeichi E Martınez-Montes P A Valdes-Sosa NNishiyama H Mizuhara and Y Yamaguchi ldquoDecomposingEEG data into spacendashtimendashfrequency components using par-allel factor analysisrdquo NeuroImage vol 22 no 3 pp 1035ndash10452004

[41] K J Friston C D Frith P F Liddle and R S J FrackowiakldquoFunctional connectivity the principal-component analysis oflarge (PET) data setsrdquo Journal of Cerebral Blood Flow andMetabolism vol 13 no 1 pp 5ndash14 1993

[42] S Makeig T-P Jung A J Bell D Ghahremani and T JSejnowski ldquoBlind separation of auditory event-related brainresponses into independent componentsrdquo Proceedings of theNational Academy of Sciences of the United States of Americavol 94 no 20 pp 10979ndash10984 1997

[43] Biomedical Signal httpwwwmedicinemcgillcaphysiovlabbiomed signalseeg nhtm

[44] S E G Nilsson and B E Andersson ldquoCorneal DC recordingsof slow ocular potential changes such as the ERG c-wave and thelight peak in clinical workmdashequipment and examples of resultsrdquoDocumenta Ophthalmologica vol 68 no 3-4 pp 313ndash325 1988

[45] OG Lins TW Picton P Berg andM Scherg ldquoOcular artifactsin EEG and event-related potentials I scalp topographyrdquo BrainTopography vol 6 no 1 pp 51ndash63 1993

[46] T W Picton P Van Roon M L Armilio P Berg N Ille andM Scherg ldquoThe correction of ocular artifacts a topographicperspectiverdquo Clinical Neurophysiology vol 111 no 1 pp 53ndash652000

[47] A S Keren S Yuval-Greenberg and L Y Deouell ldquoSaccadicspike potentials in gamma-band EEG characterization detec-tion and suppressionrdquo NeuroImage vol 49 no 3 pp 2248ndash2263 2010

[48] M Plochl J P Ossandon and P Konig ldquoCombining EEG andeye tracking identification characterization and correctionof eye movement artifacts in electroencephalographic datardquoFrontiers in Human Neuroscience vol 6 article 278 2012

[49] S Dandekar C Privitera T Carney and S A Klein ldquoNeuralsaccadic response estimation during natural viewingrdquo Journalof Neurophysiology vol 107 no 6 pp 1776ndash1790 2012

[50] G Ai N Sato B Singh and H Wagatsuma ldquoDirection andviewing area-sensitive influence of EOGartifacts revealed in theEEG topographic pattern analysisrdquo Cognitive Neurodynamicsvol 10 no 4 pp 301ndash314 2016

[51] P Berg and M Scherg ldquoDipole models of eye movements andblinksrdquo Electroencephalography and Clinical Neurophysiologyvol 79 no 1 pp 36ndash44 1991

[52] R J Croft and R J Barry ldquoRemoval of ocular artifact from theEEG a reviewrdquo Neurophysiologie Clinique vol 30 no 1 pp 5ndash19 2000

[53] I J Rampil ldquoA primer for EEG signal processing in anesthesiardquoAnesthesiology vol 89 no 4 pp 980ndash1002 1998

[54] J L Starck Y Moudden J Bobin M Elad and D DonoholdquoMorphological component analysisrdquo in Optics amp Photonics2005 p 59140Q International Society forOptics and Photonics2005

[55] S Sardy A Bruce and P Tseng ldquoBlock coordinate relaxationmethods for nonparametric signal denoising with waveletdictionariesrdquo Journal of Computational and Graphical Statisticsvol 9 pp 361ndash379 2000

[56] M Puschel and J M F Moura ldquoThe algebraic approach to thediscrete cosine and sine transforms and their fast algorithmsrdquoSIAM Journal on Computing vol 32 no 5 pp 1280ndash1316 2003

[57] X Shao and S G Johnson ldquoType-IV DCT DST and MDCTalgorithms with reduced numbers of arithmetic operationsrdquoSignal Processing vol 88 no 6 pp 1313ndash1326 2008

[58] R G Andrzejak K Lehnertz F Mormann C Rieke P Davidand C E Elger ldquoIndications of nonlinear deterministic and

Computational and Mathematical Methods in Medicine 11

3 4 5

02

03

04

05

06

07

08

09

Aver

aged

FFT

corr

elat

ion

coeffi

cien

t

01

1

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

lowast lowast lowast

(a) Hard threshold

3 4 5

Aver

aged

FFT

corr

elat

ion

coeffi

cien

t02

03

04

05

06

07

08

09

01

1

DST-DIRACDCT-DIRACLDCT-DIRAC

DSTDCTLDCT

lowast lowast lowast

(b) Soft threshold

Figure 8 A comparison of FFT correlation coefficients between iEEG data and morphological component decomposed by explicitdictionaries lowastSignificant differences (119901 lt 005) (a) Combined two morphological components and (b) single morphological componentMean value and standard deviation calculated from all 100 decomposed datasets by explicit dictionaries with hard and soft thresholds

400

Pote

ntia

l (V

)

200

0

minus200

400

Pote

ntia

l (V

)

200

0

minus200

Samples20000 1000

EOG (V1u-V1d)

EOG (V2u-V2d)

Figure 9 An example of EOG signal taken from right and left sideof eyes

decomposed first component from Fp1 Fp2 Cz O1 and O2respectively

5 Discussion

Artifact contamination in EEG signal has been a com-mon important issue in neurobiological event diagnosis and

Table 1 cc of original signal and sum of the decomposed compo-nents

EEG channelCorrelation coefficient

UDWT-DST-DIRAC

UDWT-DCT-DIRAC

UDWT-LDCT-DIRAC

Fp1 09921 plusmn 0014 09921 plusmn 0014 09932 plusmn 0013Fp2 0992 plusmn 017 09919 plusmn 018 09932 plusmn 014Cz 09898 plusmn 01 09899 plusmn 01 09908 plusmn 009O1 09836 plusmn 015 09836 plusmn 016 09869 plusmn 012O2 09855 plusmn 013 09856 plusmn 013 09849 plusmn 015

neuroscientific researchThevariousmethodswere applied toremove the artifacts from EEG [2 11ndash13 21 23 24 26ndash28 52]The decomposition based analysis was used in removal ofEOG artifacts in EEG [22 27 28 30 40 42] Howeverthose methods lack the elucidation of what the nature ofEEG signals is in the viewpoint of the signal analysis and asystematic approach was required by treating the sparsity andnonlinearity of the signal in the time domain

12 Computational and Mathematical Methods in Medicine

0

0

50

Fp1

Fp2

Cz

O1

O2

100

0

minus100

minus50

minus40

Pote

ntia

l (V

)

0

50

minus50

Pote

ntia

l (V

)

050

minus50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

Figure 10 An example of real EEG signal taken from Fp1 Fp2 Cz O1 and O2 electrode channels

Table 2 cc between filtered EOG and UDWT component decomposed by UDWT dictionary

EOG channels EEG channelsFp1 Fp2 Cz O1 O2

Correlation coefficientUDWT-DST-DIRACV1d 06777 0657 07267 09223 06445V1u 06814 0646 06606 09419 06354V2d 0916 0906 09402 0882 05402V2u 02332 02268 02353 06388 08494H1 08582 0847 08444 06902 05839H2 09419 09468 09559 07476 04752

UDWT-DCT-DIRACV1d 06792 06595 068 09213 06352V1u 06835 06396 06424 09581 06585V2d 09193 0902 09362 08764 05145V2u 02331 02183 02316 06639 08919H1 08593 08507 08626 06759 05376H2 09442 09465 09662 07266 04346

UDWT-LDCT-DIRACV1d 06794 06403 07219 08892 065V1u 06443 06279 06459 08196 05381V2d 09142 09072 09395 09592 06506V2u 02351 02235 02383 03747 06804H1 08637 08449 08471 07638 05734H2 09586 09558 09577 08826 05598

Computational and Mathematical Methods in Medicine 13

0

50

0

20

UDWT

DCT

DIRAC

0

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus30

(a)

UDWT

DST

DIRAC

0

0

20

0

50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus20

minus20

(b)

0

0

50

100

0

UDWT

LDCT

DIRAC

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus20

minus40

minus80

(c)

Figure 11 Component separated fromEEG (Fp1 electrode) signal by explicit dictionaries (a)UDWT-DCT-DIRAC (b)UDWT-DST-DIRACand (c) UDWT-LDCT-DIRAC respectively

This study revealed the nature of EEG signals in the senseof morphologies contained in the original signal by usingMCA The UDWT was used to decompose the slow andbump morphology The DCT DST and LDCT transformwere used to decompose the EEG signal Spike typemorphol-ogy was decomposed by DIRAC Redundant transforms ofDCT and DST have a similar capability in representing themorphology of oscillatory activities Therefore we used theDCT LDCT and DST dictionaries for validations of EEGsignal The detailed significant differences in morphology ofDCT and DST were given in past studies [56 57] while inour analysis there were no significant differences The rightcombination of redundant transforms to form overcompletedictionary revealed the desired decomposition in principle

In Section 42 ldquoBlocksrdquo ldquoBumpsrdquo similar to simulatedEOG signal defined in past studies [59ndash61] as shown in

Figure 4 and EEG data [58] were used to validate ourpurposed method The ldquoBlocksrdquo with abrupt changes weresimilar to the horizontal and vertical eye movements sim-ply as described by past studies [25 51] For the sake ofsimplicity in the present study ldquoBumpsrdquo were used as arepresentative signal form as eye blinks that happens inunexpected timings as illustrated in Figure 5 The separationof components by given dictionary works well in this evalu-ation but the further analysis is necessary for the evaluationof the signal decomposition with complex eye movementswhich requires presumably various redundant dictionariesIn the verification of the component discrimination as shownin Figures 6 and 7 the accuracy of the averaged EOGcomponent decomposition was above 90 which suggests aplausible performance even in the complex eye movementsThe combined DST and DIRAC dictionaries had better

14 Computational and Mathematical Methods in Medicine

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

Samples20000 1000

V1u

H1

(a) UDWT components separated by UDWT-DST-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(b) UDWT components separated by UDWT-DCT-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(c) UDWT components separated by UDWT-LDCT-DIRAC

Figure 12 UDWT component taken from Fp1 Fp2 Cz O1 and O2 separated by UDWT-DCT-DIRAC UDWT-DST-DIRAC and UDWT-LDCT-DIRAC respectively

decomposition performance than others while DST andDCT theoretically have no meaningful difference The usageof iEEG as the true EEG signal had a large benefit whichcan be used for the performance test for past proposedmethods like ICA and PCA consistently Our proposedmethod successfully demonstrated the performance in cc andthe frequency profile especially in Section 42 while in theserious discussion of the real EEG and EOG signals the DSTor DCT component exhibited a baseline fluctuation of thesignal which denotes the persistence of the EOG componentor other slow frequency artifacts noises and the factor willbe improved by the fine-tuned design of the DST or DCTdictionary with a band pass filter function In addition thethreshold problem exits in the optimization algorithm andnumber of iterations [37]

The EEG decomposition had not mark with a combi-nation of a second and a third component of EEG signal

decomposed by ldquoDST DCT and LDCTrdquo andDIRAC respec-tively based on the morphology Therefore the accuratecombination in the further perspective will be considerableEven the combination of all components and the mixedsignal or real EEG signal had cc above 97 for all redundanttransforms as is analyzed in the frequency spectrum thesignal morphology has further meaning in the viewpointof the signal transmission The MCA method has such anextended and flexible availability for signal analyses

6 Conclusion

Morphological Component Analysis methodology wasapplied to the simulated semisimulated and real EOGand EEG signal The successful decomposition of the EOGand EEG signal into their morphological component wasdemonstrated It seems to be that the EEG signals and

Computational and Mathematical Methods in Medicine 15

artifacts in EEG have been represented by different explicitdictionaries We analyzed the EEG signals involved with theEOG artifacts which were influenced by task conditionsTheDIRAC explicit dictionary decomposed the EEG signal intospike-like activities which may be related to the transientproperty of EEG UDWT explicit dictionary representsslow movement or bumps DCT DST and LDCT explicitdictionaries represent dominant signal that represents EEGsor pure tones signals as monomorphic and polymorphicactivities These results suggested that the effectivenessof MCA in ocular artifacts removal from the EEG rawsignal was derived from signal morphology characterizedas slow and smooth change of EOG time series In thefurther analysis the MCA is required to compare withother competing methods for the EEG and EOG signaldecomposition

Competing Interests

The authors have declared that no competing interests exist

Acknowledgments

This work was partly supported by JSPS KAKENHI 16H01616and 26240032 and theNewEnergy and Industrial TechnologyDevelopment Organization (NEDO) ldquoNext-Generation Arti-ficial Intelligence (3) Base Technology for Next-GenerationAIrdquo (Automated Driving Task) and the collaborative researchproject with Fujitsu Ten Limited

References

[1] J P Donoghue J N Sanes N G Hatsopoulos and G GaalldquoNeural discharge and local field potential oscillations in pri-mate motor cortex during voluntary movementsrdquo Journal ofNeurophysiology vol 79 no 1 pp 159ndash173 1998

[2] J A Uriguen and B Garcia-Zapirain ldquoEEG artifact removalmdashstate-of-the-art and guidelinesrdquo Journal of Neural Engineeringvol 12 no 3 Article ID 031001 2015

[3] C Kamarajan and B Porjesz ldquoAdvances in electrophysiologicalresearchrdquoAlcohol Research Current Reviews vol 37 no 1 article53 2015

[4] L F Nicolas-Alonso and J Gomez-Gil ldquoBrain computer inter-faces a reviewrdquo Sensors vol 12 no 2 pp 1211ndash1279 2012

[5] L Mayaud M Congedo A Van Laghenhove et al ldquoA compar-ison of recording modalities of P300 event-related potentials(ERP) for brain-computer interface (BCI) paradigmrdquo Neuro-physiologie CliniqueClinical Neurophysiology vol 43 no 4 pp217ndash227 2013

[6] X-Y Wang J Jin Y Zhang and B Wang ldquoBrain controlhuman-computer integration control based on brain-computerinterfacerdquo Acta Automatica Sinica vol 39 no 3 pp 208ndash2212013

[7] G Al-Hudhud ldquoAffective command-based control system inte-grating brain signals in commands control systemsrdquo Computersin Human Behavior vol 30 pp 535ndash541 2014

[8] J L Sirvent Blasco E Ianez A Ubeda and JM Azorın ldquoVisualevoked potential-based brain-machine interface applications toassist disabled peoplerdquo Expert Systems with Applications vol 39no 9 pp 7908ndash7918 2012

[9] H Cecotti ldquoSpelling with non-invasive Brain-Computer Inter-facesmdashcurrent and future trendsrdquo Journal of Physiology Parisvol 105 no 1ndash3 pp 106ndash114 2011

[10] I S Kotchetkov B Y Hwang G Appelboom C P Kellnerand E S Connolly Jr ldquoBrain-computer interfaces militaryneurosurgical and ethical perspectiverdquo Neurosurgical Focusvol 28 no 5 article no E25 2010

[11] R N Vigario ldquoExtraction of ocular artefacts from EEG usingindependent component analysisrdquo Electroencephalography andClinical Neurophysiology vol 103 no 3 pp 395ndash404 1997

[12] W Zhou and J Gotman ldquoAutomatic removal of eye movementartifacts from the EEG using ICA and the dipole modelrdquoProgress in Natural Science vol 19 no 9 pp 1165ndash1170 2009

[13] R Sameni andCGouy-Pailler ldquoAn iterative subspace denoisingalgorithm for removing electroencephalogram ocular artifactsrdquoJournal of Neuroscience Methods vol 225 pp 97ndash105 2014

[14] M Breakspear and J R Terry ldquoDetection and description ofnon-linear interdependence in normal multichannel humanEEG datardquo Clinical Neurophysiology vol 113 no 5 pp 735ndash7532002

[15] U R Acharya O Faust N Kannathal T Chua and S Laxmin-arayan ldquoNon-linear analysis of EEG signals at various sleepstagesrdquo Computer Methods and Programs in Biomedicine vol80 no 1 pp 37ndash45 2005

[16] L I Aftanas and S A Golocheikine ldquoNon-linear dynamiccomplexity of the human EEGduringmeditationrdquoNeuroscienceLetters vol 330 no 2 pp 143ndash146 2002

[17] M J Fadili J-L Starck J Bobin and Y Moudden ldquoImagedecomposition and separation using sparse representations anoverviewrdquo Proceedings of the IEEE vol 98 no 6 pp 983ndash9942010

[18] K J Blinowska and P J Durka ldquoUnbiased high resolutionmethod of EEG analysis in time-frequency spacerdquo Acta Neuro-biologiae Experimentalis vol 61 no 3 pp 157ndash174 2001

[19] E Imani H-R Pourreza and T Banaee ldquoFully automateddiabetic retinopathy screening usingmorphological componentanalysisrdquo Computerized Medical Imaging and Graphics vol 43pp 78ndash88 2015

[20] E Imani M Javidi and H-R Pourreza ldquoImprovement ofretinal blood vessel detection using morphological componentanalysisrdquo Computer Methods and Programs in Biomedicine vol118 no 3 pp 263ndash279 2016

[21] A S Al-Fahoum and A A Al-Fraihat ldquoMethods of EEG signalfeatures extraction using linear analysis in frequency and time-frequency domainsrdquo ISRN Neuroscience vol 2014 Article ID730218 7 pages 2014

[22] M Zibulevsky and B A Pearlmutter ldquoBlind source separationby sparse decomposition in a signal dictionaryrdquoNeural Compu-tation vol 13 no 4 pp 863ndash882 2001

[23] N P Castellanos andVAMakarov ldquoRecovering EEGbrain sig-nals artifact suppression with wavelet enhanced independentcomponent analysisrdquo Journal of Neuroscience Methods vol 158no 2 pp 300ndash312 2006

[24] J Hou K Morgan D M Tucker et al ldquoAn improved artifactsremoval method for high dimensional EEGrdquo Journal of Neuro-science Methods vol 268 pp 31ndash42 2016

[25] P Berg and M Scherg ldquoA multiple source approach to thecorrection of eye artifactsrdquo Electroencephalography and ClinicalNeurophysiology vol 90 no 3 pp 229ndash241 1994

[26] P K Sadasivan and D Narayana Dutt ldquoSVD based techniquefor noise reduction in electroencephalographic signalsrdquo SignalProcessing vol 55 no 2 pp 179ndash189 1996

16 Computational and Mathematical Methods in Medicine

[27] C A Joyce I F Gorodnitsky andMKutas ldquoAutomatic removalof eye movement and blink artifacts from EEG data using blindcomponent separationrdquo Psychophysiology vol 41 no 2 pp 313ndash325 2004

[28] G L Wallstrom R E Kass A Miller J F Cohn and N A FoxldquoAutomatic correction of ocular artifacts in the EEG a com-parison of regression-based and component-based methodsrdquoInternational Journal of Psychophysiology vol 53 no 2 pp 105ndash119 2004

[29] S M Gordon V Lawhern A D Passaro and K McDowellldquoInformed decomposition of electroencephalographic datardquoJournal of Neuroscience Methods vol 256 pp 41ndash55 2015

[30] D StuderUHoffmann andTKoenig ldquoFromEEGdependencymultichannel matching pursuit to sparse topographic EEGdecompositionrdquo Journal of Neuroscience Methods vol 153 no2 pp 261ndash275 2006

[31] J-L Starck M Elad and D Donoho ldquoRedundant multiscaletransforms and their application for morphological componentseparationrdquo Advances in Imaging and Electron Physics vol 132pp 287ndash348 2004

[32] P J Franaszczuk G K Bergey P J Durka andHM EisenbergldquoTime-frequency analysis using thematching pursuit algorithmapplied to seizures originating from the mesial temporal loberdquoElectroencephalography and Clinical Neurophysiology vol 106no 6 pp 513ndash521 1998

[33] P J Durka A Matysiak E M Montes P V Sosa and K JBlinowska ldquoMultichannel matching pursuit and EEG inversesolutionsrdquo Journal of Neuroscience Methods vol 148 no 1 pp49ndash59 2005

[34] J Bobin J-L Starck J Fadili and Y Moudden ldquoSparsityand morphological diversity in blind source separationrdquo IEEETransactions on Image Processing vol 16 no 11 pp 2662ndash26742007

[35] P J Durka D Ircha and K J Blinowska ldquoStochastic time-frequency dictionaries formatching pursuitrdquo IEEE Transactionson Signal Processing vol 49 no 3 pp 507ndash510 2001

[36] X Yong R K Ward and G E Birch ldquoGeneralized morpholog-ical component analysis for EEG source separation and artifactremovalrdquo in Proceedings of the 4th International IEEEEMBSConference on Neural Engineering (NER rsquo09) pp 343ndash346Antalya Turkey May 2009

[37] B Singh G Ai and H Wagatsuma ldquoAn electrooculographyanalysis in the time-frequency domain using morphologicalcomponent analysis toward the development of mobile BCIsystemsrdquo in Universal Access in Human-Computer InteractionAccess to Interaction 9th International Conference UAHCI 2015Held as Part of HCI International 2015 Los Angeles CA USAAugust 2ndash7 2015 Proceedings Part II vol 9176 of Lecture Notesin Computer Science pp 528ndash537 Springer Berlin Germany2015

[38] S S Chen D L Donoho and M A Saunders ldquoAtomicdecomposition by basis pursuitrdquo SIAM Review vol 43 no 1pp 129ndash159 2001

[39] D L Donoho and X Huo ldquoUncertainty principles and idealatomic decompositionrdquo IEEE Transactions on InformationThe-ory vol 47 no 7 pp 2845ndash2862 2001

[40] F Miwakeichi E Martınez-Montes P A Valdes-Sosa NNishiyama H Mizuhara and Y Yamaguchi ldquoDecomposingEEG data into spacendashtimendashfrequency components using par-allel factor analysisrdquo NeuroImage vol 22 no 3 pp 1035ndash10452004

[41] K J Friston C D Frith P F Liddle and R S J FrackowiakldquoFunctional connectivity the principal-component analysis oflarge (PET) data setsrdquo Journal of Cerebral Blood Flow andMetabolism vol 13 no 1 pp 5ndash14 1993

[42] S Makeig T-P Jung A J Bell D Ghahremani and T JSejnowski ldquoBlind separation of auditory event-related brainresponses into independent componentsrdquo Proceedings of theNational Academy of Sciences of the United States of Americavol 94 no 20 pp 10979ndash10984 1997

[43] Biomedical Signal httpwwwmedicinemcgillcaphysiovlabbiomed signalseeg nhtm

[44] S E G Nilsson and B E Andersson ldquoCorneal DC recordingsof slow ocular potential changes such as the ERG c-wave and thelight peak in clinical workmdashequipment and examples of resultsrdquoDocumenta Ophthalmologica vol 68 no 3-4 pp 313ndash325 1988

[45] OG Lins TW Picton P Berg andM Scherg ldquoOcular artifactsin EEG and event-related potentials I scalp topographyrdquo BrainTopography vol 6 no 1 pp 51ndash63 1993

[46] T W Picton P Van Roon M L Armilio P Berg N Ille andM Scherg ldquoThe correction of ocular artifacts a topographicperspectiverdquo Clinical Neurophysiology vol 111 no 1 pp 53ndash652000

[47] A S Keren S Yuval-Greenberg and L Y Deouell ldquoSaccadicspike potentials in gamma-band EEG characterization detec-tion and suppressionrdquo NeuroImage vol 49 no 3 pp 2248ndash2263 2010

[48] M Plochl J P Ossandon and P Konig ldquoCombining EEG andeye tracking identification characterization and correctionof eye movement artifacts in electroencephalographic datardquoFrontiers in Human Neuroscience vol 6 article 278 2012

[49] S Dandekar C Privitera T Carney and S A Klein ldquoNeuralsaccadic response estimation during natural viewingrdquo Journalof Neurophysiology vol 107 no 6 pp 1776ndash1790 2012

[50] G Ai N Sato B Singh and H Wagatsuma ldquoDirection andviewing area-sensitive influence of EOGartifacts revealed in theEEG topographic pattern analysisrdquo Cognitive Neurodynamicsvol 10 no 4 pp 301ndash314 2016

[51] P Berg and M Scherg ldquoDipole models of eye movements andblinksrdquo Electroencephalography and Clinical Neurophysiologyvol 79 no 1 pp 36ndash44 1991

[52] R J Croft and R J Barry ldquoRemoval of ocular artifact from theEEG a reviewrdquo Neurophysiologie Clinique vol 30 no 1 pp 5ndash19 2000

[53] I J Rampil ldquoA primer for EEG signal processing in anesthesiardquoAnesthesiology vol 89 no 4 pp 980ndash1002 1998

[54] J L Starck Y Moudden J Bobin M Elad and D DonoholdquoMorphological component analysisrdquo in Optics amp Photonics2005 p 59140Q International Society forOptics and Photonics2005

[55] S Sardy A Bruce and P Tseng ldquoBlock coordinate relaxationmethods for nonparametric signal denoising with waveletdictionariesrdquo Journal of Computational and Graphical Statisticsvol 9 pp 361ndash379 2000

[56] M Puschel and J M F Moura ldquoThe algebraic approach to thediscrete cosine and sine transforms and their fast algorithmsrdquoSIAM Journal on Computing vol 32 no 5 pp 1280ndash1316 2003

[57] X Shao and S G Johnson ldquoType-IV DCT DST and MDCTalgorithms with reduced numbers of arithmetic operationsrdquoSignal Processing vol 88 no 6 pp 1313ndash1326 2008

[58] R G Andrzejak K Lehnertz F Mormann C Rieke P Davidand C E Elger ldquoIndications of nonlinear deterministic and

12 Computational and Mathematical Methods in Medicine

0

0

50

Fp1

Fp2

Cz

O1

O2

100

0

minus100

minus50

minus40

Pote

ntia

l (V

)

0

50

minus50

Pote

ntia

l (V

)

050

minus50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

Figure 10 An example of real EEG signal taken from Fp1 Fp2 Cz O1 and O2 electrode channels

Table 2 cc between filtered EOG and UDWT component decomposed by UDWT dictionary

EOG channels EEG channelsFp1 Fp2 Cz O1 O2

Correlation coefficientUDWT-DST-DIRACV1d 06777 0657 07267 09223 06445V1u 06814 0646 06606 09419 06354V2d 0916 0906 09402 0882 05402V2u 02332 02268 02353 06388 08494H1 08582 0847 08444 06902 05839H2 09419 09468 09559 07476 04752

UDWT-DCT-DIRACV1d 06792 06595 068 09213 06352V1u 06835 06396 06424 09581 06585V2d 09193 0902 09362 08764 05145V2u 02331 02183 02316 06639 08919H1 08593 08507 08626 06759 05376H2 09442 09465 09662 07266 04346

UDWT-LDCT-DIRACV1d 06794 06403 07219 08892 065V1u 06443 06279 06459 08196 05381V2d 09142 09072 09395 09592 06506V2u 02351 02235 02383 03747 06804H1 08637 08449 08471 07638 05734H2 09586 09558 09577 08826 05598

Computational and Mathematical Methods in Medicine 13

0

50

0

20

UDWT

DCT

DIRAC

0

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus30

(a)

UDWT

DST

DIRAC

0

0

20

0

50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus20

minus20

(b)

0

0

50

100

0

UDWT

LDCT

DIRAC

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus20

minus40

minus80

(c)

Figure 11 Component separated fromEEG (Fp1 electrode) signal by explicit dictionaries (a)UDWT-DCT-DIRAC (b)UDWT-DST-DIRACand (c) UDWT-LDCT-DIRAC respectively

This study revealed the nature of EEG signals in the senseof morphologies contained in the original signal by usingMCA The UDWT was used to decompose the slow andbump morphology The DCT DST and LDCT transformwere used to decompose the EEG signal Spike typemorphol-ogy was decomposed by DIRAC Redundant transforms ofDCT and DST have a similar capability in representing themorphology of oscillatory activities Therefore we used theDCT LDCT and DST dictionaries for validations of EEGsignal The detailed significant differences in morphology ofDCT and DST were given in past studies [56 57] while inour analysis there were no significant differences The rightcombination of redundant transforms to form overcompletedictionary revealed the desired decomposition in principle

In Section 42 ldquoBlocksrdquo ldquoBumpsrdquo similar to simulatedEOG signal defined in past studies [59ndash61] as shown in

Figure 4 and EEG data [58] were used to validate ourpurposed method The ldquoBlocksrdquo with abrupt changes weresimilar to the horizontal and vertical eye movements sim-ply as described by past studies [25 51] For the sake ofsimplicity in the present study ldquoBumpsrdquo were used as arepresentative signal form as eye blinks that happens inunexpected timings as illustrated in Figure 5 The separationof components by given dictionary works well in this evalu-ation but the further analysis is necessary for the evaluationof the signal decomposition with complex eye movementswhich requires presumably various redundant dictionariesIn the verification of the component discrimination as shownin Figures 6 and 7 the accuracy of the averaged EOGcomponent decomposition was above 90 which suggests aplausible performance even in the complex eye movementsThe combined DST and DIRAC dictionaries had better

14 Computational and Mathematical Methods in Medicine

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

Samples20000 1000

V1u

H1

(a) UDWT components separated by UDWT-DST-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(b) UDWT components separated by UDWT-DCT-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(c) UDWT components separated by UDWT-LDCT-DIRAC

Figure 12 UDWT component taken from Fp1 Fp2 Cz O1 and O2 separated by UDWT-DCT-DIRAC UDWT-DST-DIRAC and UDWT-LDCT-DIRAC respectively

decomposition performance than others while DST andDCT theoretically have no meaningful difference The usageof iEEG as the true EEG signal had a large benefit whichcan be used for the performance test for past proposedmethods like ICA and PCA consistently Our proposedmethod successfully demonstrated the performance in cc andthe frequency profile especially in Section 42 while in theserious discussion of the real EEG and EOG signals the DSTor DCT component exhibited a baseline fluctuation of thesignal which denotes the persistence of the EOG componentor other slow frequency artifacts noises and the factor willbe improved by the fine-tuned design of the DST or DCTdictionary with a band pass filter function In addition thethreshold problem exits in the optimization algorithm andnumber of iterations [37]

The EEG decomposition had not mark with a combi-nation of a second and a third component of EEG signal

decomposed by ldquoDST DCT and LDCTrdquo andDIRAC respec-tively based on the morphology Therefore the accuratecombination in the further perspective will be considerableEven the combination of all components and the mixedsignal or real EEG signal had cc above 97 for all redundanttransforms as is analyzed in the frequency spectrum thesignal morphology has further meaning in the viewpointof the signal transmission The MCA method has such anextended and flexible availability for signal analyses

6 Conclusion

Morphological Component Analysis methodology wasapplied to the simulated semisimulated and real EOGand EEG signal The successful decomposition of the EOGand EEG signal into their morphological component wasdemonstrated It seems to be that the EEG signals and

Computational and Mathematical Methods in Medicine 15

artifacts in EEG have been represented by different explicitdictionaries We analyzed the EEG signals involved with theEOG artifacts which were influenced by task conditionsTheDIRAC explicit dictionary decomposed the EEG signal intospike-like activities which may be related to the transientproperty of EEG UDWT explicit dictionary representsslow movement or bumps DCT DST and LDCT explicitdictionaries represent dominant signal that represents EEGsor pure tones signals as monomorphic and polymorphicactivities These results suggested that the effectivenessof MCA in ocular artifacts removal from the EEG rawsignal was derived from signal morphology characterizedas slow and smooth change of EOG time series In thefurther analysis the MCA is required to compare withother competing methods for the EEG and EOG signaldecomposition

Competing Interests

The authors have declared that no competing interests exist

Acknowledgments

This work was partly supported by JSPS KAKENHI 16H01616and 26240032 and theNewEnergy and Industrial TechnologyDevelopment Organization (NEDO) ldquoNext-Generation Arti-ficial Intelligence (3) Base Technology for Next-GenerationAIrdquo (Automated Driving Task) and the collaborative researchproject with Fujitsu Ten Limited

References

[1] J P Donoghue J N Sanes N G Hatsopoulos and G GaalldquoNeural discharge and local field potential oscillations in pri-mate motor cortex during voluntary movementsrdquo Journal ofNeurophysiology vol 79 no 1 pp 159ndash173 1998

[2] J A Uriguen and B Garcia-Zapirain ldquoEEG artifact removalmdashstate-of-the-art and guidelinesrdquo Journal of Neural Engineeringvol 12 no 3 Article ID 031001 2015

[3] C Kamarajan and B Porjesz ldquoAdvances in electrophysiologicalresearchrdquoAlcohol Research Current Reviews vol 37 no 1 article53 2015

[4] L F Nicolas-Alonso and J Gomez-Gil ldquoBrain computer inter-faces a reviewrdquo Sensors vol 12 no 2 pp 1211ndash1279 2012

[5] L Mayaud M Congedo A Van Laghenhove et al ldquoA compar-ison of recording modalities of P300 event-related potentials(ERP) for brain-computer interface (BCI) paradigmrdquo Neuro-physiologie CliniqueClinical Neurophysiology vol 43 no 4 pp217ndash227 2013

[6] X-Y Wang J Jin Y Zhang and B Wang ldquoBrain controlhuman-computer integration control based on brain-computerinterfacerdquo Acta Automatica Sinica vol 39 no 3 pp 208ndash2212013

[7] G Al-Hudhud ldquoAffective command-based control system inte-grating brain signals in commands control systemsrdquo Computersin Human Behavior vol 30 pp 535ndash541 2014

[8] J L Sirvent Blasco E Ianez A Ubeda and JM Azorın ldquoVisualevoked potential-based brain-machine interface applications toassist disabled peoplerdquo Expert Systems with Applications vol 39no 9 pp 7908ndash7918 2012

[9] H Cecotti ldquoSpelling with non-invasive Brain-Computer Inter-facesmdashcurrent and future trendsrdquo Journal of Physiology Parisvol 105 no 1ndash3 pp 106ndash114 2011

[10] I S Kotchetkov B Y Hwang G Appelboom C P Kellnerand E S Connolly Jr ldquoBrain-computer interfaces militaryneurosurgical and ethical perspectiverdquo Neurosurgical Focusvol 28 no 5 article no E25 2010

[11] R N Vigario ldquoExtraction of ocular artefacts from EEG usingindependent component analysisrdquo Electroencephalography andClinical Neurophysiology vol 103 no 3 pp 395ndash404 1997

[12] W Zhou and J Gotman ldquoAutomatic removal of eye movementartifacts from the EEG using ICA and the dipole modelrdquoProgress in Natural Science vol 19 no 9 pp 1165ndash1170 2009

[13] R Sameni andCGouy-Pailler ldquoAn iterative subspace denoisingalgorithm for removing electroencephalogram ocular artifactsrdquoJournal of Neuroscience Methods vol 225 pp 97ndash105 2014

[14] M Breakspear and J R Terry ldquoDetection and description ofnon-linear interdependence in normal multichannel humanEEG datardquo Clinical Neurophysiology vol 113 no 5 pp 735ndash7532002

[15] U R Acharya O Faust N Kannathal T Chua and S Laxmin-arayan ldquoNon-linear analysis of EEG signals at various sleepstagesrdquo Computer Methods and Programs in Biomedicine vol80 no 1 pp 37ndash45 2005

[16] L I Aftanas and S A Golocheikine ldquoNon-linear dynamiccomplexity of the human EEGduringmeditationrdquoNeuroscienceLetters vol 330 no 2 pp 143ndash146 2002

[17] M J Fadili J-L Starck J Bobin and Y Moudden ldquoImagedecomposition and separation using sparse representations anoverviewrdquo Proceedings of the IEEE vol 98 no 6 pp 983ndash9942010

[18] K J Blinowska and P J Durka ldquoUnbiased high resolutionmethod of EEG analysis in time-frequency spacerdquo Acta Neuro-biologiae Experimentalis vol 61 no 3 pp 157ndash174 2001

[19] E Imani H-R Pourreza and T Banaee ldquoFully automateddiabetic retinopathy screening usingmorphological componentanalysisrdquo Computerized Medical Imaging and Graphics vol 43pp 78ndash88 2015

[20] E Imani M Javidi and H-R Pourreza ldquoImprovement ofretinal blood vessel detection using morphological componentanalysisrdquo Computer Methods and Programs in Biomedicine vol118 no 3 pp 263ndash279 2016

[21] A S Al-Fahoum and A A Al-Fraihat ldquoMethods of EEG signalfeatures extraction using linear analysis in frequency and time-frequency domainsrdquo ISRN Neuroscience vol 2014 Article ID730218 7 pages 2014

[22] M Zibulevsky and B A Pearlmutter ldquoBlind source separationby sparse decomposition in a signal dictionaryrdquoNeural Compu-tation vol 13 no 4 pp 863ndash882 2001

[23] N P Castellanos andVAMakarov ldquoRecovering EEGbrain sig-nals artifact suppression with wavelet enhanced independentcomponent analysisrdquo Journal of Neuroscience Methods vol 158no 2 pp 300ndash312 2006

[24] J Hou K Morgan D M Tucker et al ldquoAn improved artifactsremoval method for high dimensional EEGrdquo Journal of Neuro-science Methods vol 268 pp 31ndash42 2016

[25] P Berg and M Scherg ldquoA multiple source approach to thecorrection of eye artifactsrdquo Electroencephalography and ClinicalNeurophysiology vol 90 no 3 pp 229ndash241 1994

[26] P K Sadasivan and D Narayana Dutt ldquoSVD based techniquefor noise reduction in electroencephalographic signalsrdquo SignalProcessing vol 55 no 2 pp 179ndash189 1996

16 Computational and Mathematical Methods in Medicine

[27] C A Joyce I F Gorodnitsky andMKutas ldquoAutomatic removalof eye movement and blink artifacts from EEG data using blindcomponent separationrdquo Psychophysiology vol 41 no 2 pp 313ndash325 2004

[28] G L Wallstrom R E Kass A Miller J F Cohn and N A FoxldquoAutomatic correction of ocular artifacts in the EEG a com-parison of regression-based and component-based methodsrdquoInternational Journal of Psychophysiology vol 53 no 2 pp 105ndash119 2004

[29] S M Gordon V Lawhern A D Passaro and K McDowellldquoInformed decomposition of electroencephalographic datardquoJournal of Neuroscience Methods vol 256 pp 41ndash55 2015

[30] D StuderUHoffmann andTKoenig ldquoFromEEGdependencymultichannel matching pursuit to sparse topographic EEGdecompositionrdquo Journal of Neuroscience Methods vol 153 no2 pp 261ndash275 2006

[31] J-L Starck M Elad and D Donoho ldquoRedundant multiscaletransforms and their application for morphological componentseparationrdquo Advances in Imaging and Electron Physics vol 132pp 287ndash348 2004

[32] P J Franaszczuk G K Bergey P J Durka andHM EisenbergldquoTime-frequency analysis using thematching pursuit algorithmapplied to seizures originating from the mesial temporal loberdquoElectroencephalography and Clinical Neurophysiology vol 106no 6 pp 513ndash521 1998

[33] P J Durka A Matysiak E M Montes P V Sosa and K JBlinowska ldquoMultichannel matching pursuit and EEG inversesolutionsrdquo Journal of Neuroscience Methods vol 148 no 1 pp49ndash59 2005

[34] J Bobin J-L Starck J Fadili and Y Moudden ldquoSparsityand morphological diversity in blind source separationrdquo IEEETransactions on Image Processing vol 16 no 11 pp 2662ndash26742007

[35] P J Durka D Ircha and K J Blinowska ldquoStochastic time-frequency dictionaries formatching pursuitrdquo IEEE Transactionson Signal Processing vol 49 no 3 pp 507ndash510 2001

[36] X Yong R K Ward and G E Birch ldquoGeneralized morpholog-ical component analysis for EEG source separation and artifactremovalrdquo in Proceedings of the 4th International IEEEEMBSConference on Neural Engineering (NER rsquo09) pp 343ndash346Antalya Turkey May 2009

[37] B Singh G Ai and H Wagatsuma ldquoAn electrooculographyanalysis in the time-frequency domain using morphologicalcomponent analysis toward the development of mobile BCIsystemsrdquo in Universal Access in Human-Computer InteractionAccess to Interaction 9th International Conference UAHCI 2015Held as Part of HCI International 2015 Los Angeles CA USAAugust 2ndash7 2015 Proceedings Part II vol 9176 of Lecture Notesin Computer Science pp 528ndash537 Springer Berlin Germany2015

[38] S S Chen D L Donoho and M A Saunders ldquoAtomicdecomposition by basis pursuitrdquo SIAM Review vol 43 no 1pp 129ndash159 2001

[39] D L Donoho and X Huo ldquoUncertainty principles and idealatomic decompositionrdquo IEEE Transactions on InformationThe-ory vol 47 no 7 pp 2845ndash2862 2001

[40] F Miwakeichi E Martınez-Montes P A Valdes-Sosa NNishiyama H Mizuhara and Y Yamaguchi ldquoDecomposingEEG data into spacendashtimendashfrequency components using par-allel factor analysisrdquo NeuroImage vol 22 no 3 pp 1035ndash10452004

[41] K J Friston C D Frith P F Liddle and R S J FrackowiakldquoFunctional connectivity the principal-component analysis oflarge (PET) data setsrdquo Journal of Cerebral Blood Flow andMetabolism vol 13 no 1 pp 5ndash14 1993

[42] S Makeig T-P Jung A J Bell D Ghahremani and T JSejnowski ldquoBlind separation of auditory event-related brainresponses into independent componentsrdquo Proceedings of theNational Academy of Sciences of the United States of Americavol 94 no 20 pp 10979ndash10984 1997

[43] Biomedical Signal httpwwwmedicinemcgillcaphysiovlabbiomed signalseeg nhtm

[44] S E G Nilsson and B E Andersson ldquoCorneal DC recordingsof slow ocular potential changes such as the ERG c-wave and thelight peak in clinical workmdashequipment and examples of resultsrdquoDocumenta Ophthalmologica vol 68 no 3-4 pp 313ndash325 1988

[45] OG Lins TW Picton P Berg andM Scherg ldquoOcular artifactsin EEG and event-related potentials I scalp topographyrdquo BrainTopography vol 6 no 1 pp 51ndash63 1993

[46] T W Picton P Van Roon M L Armilio P Berg N Ille andM Scherg ldquoThe correction of ocular artifacts a topographicperspectiverdquo Clinical Neurophysiology vol 111 no 1 pp 53ndash652000

[47] A S Keren S Yuval-Greenberg and L Y Deouell ldquoSaccadicspike potentials in gamma-band EEG characterization detec-tion and suppressionrdquo NeuroImage vol 49 no 3 pp 2248ndash2263 2010

[48] M Plochl J P Ossandon and P Konig ldquoCombining EEG andeye tracking identification characterization and correctionof eye movement artifacts in electroencephalographic datardquoFrontiers in Human Neuroscience vol 6 article 278 2012

[49] S Dandekar C Privitera T Carney and S A Klein ldquoNeuralsaccadic response estimation during natural viewingrdquo Journalof Neurophysiology vol 107 no 6 pp 1776ndash1790 2012

[50] G Ai N Sato B Singh and H Wagatsuma ldquoDirection andviewing area-sensitive influence of EOGartifacts revealed in theEEG topographic pattern analysisrdquo Cognitive Neurodynamicsvol 10 no 4 pp 301ndash314 2016

[51] P Berg and M Scherg ldquoDipole models of eye movements andblinksrdquo Electroencephalography and Clinical Neurophysiologyvol 79 no 1 pp 36ndash44 1991

[52] R J Croft and R J Barry ldquoRemoval of ocular artifact from theEEG a reviewrdquo Neurophysiologie Clinique vol 30 no 1 pp 5ndash19 2000

[53] I J Rampil ldquoA primer for EEG signal processing in anesthesiardquoAnesthesiology vol 89 no 4 pp 980ndash1002 1998

[54] J L Starck Y Moudden J Bobin M Elad and D DonoholdquoMorphological component analysisrdquo in Optics amp Photonics2005 p 59140Q International Society forOptics and Photonics2005

[55] S Sardy A Bruce and P Tseng ldquoBlock coordinate relaxationmethods for nonparametric signal denoising with waveletdictionariesrdquo Journal of Computational and Graphical Statisticsvol 9 pp 361ndash379 2000

[56] M Puschel and J M F Moura ldquoThe algebraic approach to thediscrete cosine and sine transforms and their fast algorithmsrdquoSIAM Journal on Computing vol 32 no 5 pp 1280ndash1316 2003

[57] X Shao and S G Johnson ldquoType-IV DCT DST and MDCTalgorithms with reduced numbers of arithmetic operationsrdquoSignal Processing vol 88 no 6 pp 1313ndash1326 2008

[58] R G Andrzejak K Lehnertz F Mormann C Rieke P Davidand C E Elger ldquoIndications of nonlinear deterministic and

Computational and Mathematical Methods in Medicine 13

0

50

0

20

UDWT

DCT

DIRAC

0

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus30

(a)

UDWT

DST

DIRAC

0

0

20

0

50

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus50

minus20

minus20

(b)

0

0

50

100

0

UDWT

LDCT

DIRAC

Pote

ntia

l (V

)Po

tent

ial (V

)Po

tent

ial (V

)

Samples20000 1000

minus20

minus40

minus80

(c)

Figure 11 Component separated fromEEG (Fp1 electrode) signal by explicit dictionaries (a)UDWT-DCT-DIRAC (b)UDWT-DST-DIRACand (c) UDWT-LDCT-DIRAC respectively

This study revealed the nature of EEG signals in the senseof morphologies contained in the original signal by usingMCA The UDWT was used to decompose the slow andbump morphology The DCT DST and LDCT transformwere used to decompose the EEG signal Spike typemorphol-ogy was decomposed by DIRAC Redundant transforms ofDCT and DST have a similar capability in representing themorphology of oscillatory activities Therefore we used theDCT LDCT and DST dictionaries for validations of EEGsignal The detailed significant differences in morphology ofDCT and DST were given in past studies [56 57] while inour analysis there were no significant differences The rightcombination of redundant transforms to form overcompletedictionary revealed the desired decomposition in principle

In Section 42 ldquoBlocksrdquo ldquoBumpsrdquo similar to simulatedEOG signal defined in past studies [59ndash61] as shown in

Figure 4 and EEG data [58] were used to validate ourpurposed method The ldquoBlocksrdquo with abrupt changes weresimilar to the horizontal and vertical eye movements sim-ply as described by past studies [25 51] For the sake ofsimplicity in the present study ldquoBumpsrdquo were used as arepresentative signal form as eye blinks that happens inunexpected timings as illustrated in Figure 5 The separationof components by given dictionary works well in this evalu-ation but the further analysis is necessary for the evaluationof the signal decomposition with complex eye movementswhich requires presumably various redundant dictionariesIn the verification of the component discrimination as shownin Figures 6 and 7 the accuracy of the averaged EOGcomponent decomposition was above 90 which suggests aplausible performance even in the complex eye movementsThe combined DST and DIRAC dictionaries had better

14 Computational and Mathematical Methods in Medicine

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

Samples20000 1000

V1u

H1

(a) UDWT components separated by UDWT-DST-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(b) UDWT components separated by UDWT-DCT-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(c) UDWT components separated by UDWT-LDCT-DIRAC

Figure 12 UDWT component taken from Fp1 Fp2 Cz O1 and O2 separated by UDWT-DCT-DIRAC UDWT-DST-DIRAC and UDWT-LDCT-DIRAC respectively

decomposition performance than others while DST andDCT theoretically have no meaningful difference The usageof iEEG as the true EEG signal had a large benefit whichcan be used for the performance test for past proposedmethods like ICA and PCA consistently Our proposedmethod successfully demonstrated the performance in cc andthe frequency profile especially in Section 42 while in theserious discussion of the real EEG and EOG signals the DSTor DCT component exhibited a baseline fluctuation of thesignal which denotes the persistence of the EOG componentor other slow frequency artifacts noises and the factor willbe improved by the fine-tuned design of the DST or DCTdictionary with a band pass filter function In addition thethreshold problem exits in the optimization algorithm andnumber of iterations [37]

The EEG decomposition had not mark with a combi-nation of a second and a third component of EEG signal

decomposed by ldquoDST DCT and LDCTrdquo andDIRAC respec-tively based on the morphology Therefore the accuratecombination in the further perspective will be considerableEven the combination of all components and the mixedsignal or real EEG signal had cc above 97 for all redundanttransforms as is analyzed in the frequency spectrum thesignal morphology has further meaning in the viewpointof the signal transmission The MCA method has such anextended and flexible availability for signal analyses

6 Conclusion

Morphological Component Analysis methodology wasapplied to the simulated semisimulated and real EOGand EEG signal The successful decomposition of the EOGand EEG signal into their morphological component wasdemonstrated It seems to be that the EEG signals and

Computational and Mathematical Methods in Medicine 15

artifacts in EEG have been represented by different explicitdictionaries We analyzed the EEG signals involved with theEOG artifacts which were influenced by task conditionsTheDIRAC explicit dictionary decomposed the EEG signal intospike-like activities which may be related to the transientproperty of EEG UDWT explicit dictionary representsslow movement or bumps DCT DST and LDCT explicitdictionaries represent dominant signal that represents EEGsor pure tones signals as monomorphic and polymorphicactivities These results suggested that the effectivenessof MCA in ocular artifacts removal from the EEG rawsignal was derived from signal morphology characterizedas slow and smooth change of EOG time series In thefurther analysis the MCA is required to compare withother competing methods for the EEG and EOG signaldecomposition

Competing Interests

The authors have declared that no competing interests exist

Acknowledgments

This work was partly supported by JSPS KAKENHI 16H01616and 26240032 and theNewEnergy and Industrial TechnologyDevelopment Organization (NEDO) ldquoNext-Generation Arti-ficial Intelligence (3) Base Technology for Next-GenerationAIrdquo (Automated Driving Task) and the collaborative researchproject with Fujitsu Ten Limited

References

[1] J P Donoghue J N Sanes N G Hatsopoulos and G GaalldquoNeural discharge and local field potential oscillations in pri-mate motor cortex during voluntary movementsrdquo Journal ofNeurophysiology vol 79 no 1 pp 159ndash173 1998

[2] J A Uriguen and B Garcia-Zapirain ldquoEEG artifact removalmdashstate-of-the-art and guidelinesrdquo Journal of Neural Engineeringvol 12 no 3 Article ID 031001 2015

[3] C Kamarajan and B Porjesz ldquoAdvances in electrophysiologicalresearchrdquoAlcohol Research Current Reviews vol 37 no 1 article53 2015

[4] L F Nicolas-Alonso and J Gomez-Gil ldquoBrain computer inter-faces a reviewrdquo Sensors vol 12 no 2 pp 1211ndash1279 2012

[5] L Mayaud M Congedo A Van Laghenhove et al ldquoA compar-ison of recording modalities of P300 event-related potentials(ERP) for brain-computer interface (BCI) paradigmrdquo Neuro-physiologie CliniqueClinical Neurophysiology vol 43 no 4 pp217ndash227 2013

[6] X-Y Wang J Jin Y Zhang and B Wang ldquoBrain controlhuman-computer integration control based on brain-computerinterfacerdquo Acta Automatica Sinica vol 39 no 3 pp 208ndash2212013

[7] G Al-Hudhud ldquoAffective command-based control system inte-grating brain signals in commands control systemsrdquo Computersin Human Behavior vol 30 pp 535ndash541 2014

[8] J L Sirvent Blasco E Ianez A Ubeda and JM Azorın ldquoVisualevoked potential-based brain-machine interface applications toassist disabled peoplerdquo Expert Systems with Applications vol 39no 9 pp 7908ndash7918 2012

[9] H Cecotti ldquoSpelling with non-invasive Brain-Computer Inter-facesmdashcurrent and future trendsrdquo Journal of Physiology Parisvol 105 no 1ndash3 pp 106ndash114 2011

[10] I S Kotchetkov B Y Hwang G Appelboom C P Kellnerand E S Connolly Jr ldquoBrain-computer interfaces militaryneurosurgical and ethical perspectiverdquo Neurosurgical Focusvol 28 no 5 article no E25 2010

[11] R N Vigario ldquoExtraction of ocular artefacts from EEG usingindependent component analysisrdquo Electroencephalography andClinical Neurophysiology vol 103 no 3 pp 395ndash404 1997

[12] W Zhou and J Gotman ldquoAutomatic removal of eye movementartifacts from the EEG using ICA and the dipole modelrdquoProgress in Natural Science vol 19 no 9 pp 1165ndash1170 2009

[13] R Sameni andCGouy-Pailler ldquoAn iterative subspace denoisingalgorithm for removing electroencephalogram ocular artifactsrdquoJournal of Neuroscience Methods vol 225 pp 97ndash105 2014

[14] M Breakspear and J R Terry ldquoDetection and description ofnon-linear interdependence in normal multichannel humanEEG datardquo Clinical Neurophysiology vol 113 no 5 pp 735ndash7532002

[15] U R Acharya O Faust N Kannathal T Chua and S Laxmin-arayan ldquoNon-linear analysis of EEG signals at various sleepstagesrdquo Computer Methods and Programs in Biomedicine vol80 no 1 pp 37ndash45 2005

[16] L I Aftanas and S A Golocheikine ldquoNon-linear dynamiccomplexity of the human EEGduringmeditationrdquoNeuroscienceLetters vol 330 no 2 pp 143ndash146 2002

[17] M J Fadili J-L Starck J Bobin and Y Moudden ldquoImagedecomposition and separation using sparse representations anoverviewrdquo Proceedings of the IEEE vol 98 no 6 pp 983ndash9942010

[18] K J Blinowska and P J Durka ldquoUnbiased high resolutionmethod of EEG analysis in time-frequency spacerdquo Acta Neuro-biologiae Experimentalis vol 61 no 3 pp 157ndash174 2001

[19] E Imani H-R Pourreza and T Banaee ldquoFully automateddiabetic retinopathy screening usingmorphological componentanalysisrdquo Computerized Medical Imaging and Graphics vol 43pp 78ndash88 2015

[20] E Imani M Javidi and H-R Pourreza ldquoImprovement ofretinal blood vessel detection using morphological componentanalysisrdquo Computer Methods and Programs in Biomedicine vol118 no 3 pp 263ndash279 2016

[21] A S Al-Fahoum and A A Al-Fraihat ldquoMethods of EEG signalfeatures extraction using linear analysis in frequency and time-frequency domainsrdquo ISRN Neuroscience vol 2014 Article ID730218 7 pages 2014

[22] M Zibulevsky and B A Pearlmutter ldquoBlind source separationby sparse decomposition in a signal dictionaryrdquoNeural Compu-tation vol 13 no 4 pp 863ndash882 2001

[23] N P Castellanos andVAMakarov ldquoRecovering EEGbrain sig-nals artifact suppression with wavelet enhanced independentcomponent analysisrdquo Journal of Neuroscience Methods vol 158no 2 pp 300ndash312 2006

[24] J Hou K Morgan D M Tucker et al ldquoAn improved artifactsremoval method for high dimensional EEGrdquo Journal of Neuro-science Methods vol 268 pp 31ndash42 2016

[25] P Berg and M Scherg ldquoA multiple source approach to thecorrection of eye artifactsrdquo Electroencephalography and ClinicalNeurophysiology vol 90 no 3 pp 229ndash241 1994

[26] P K Sadasivan and D Narayana Dutt ldquoSVD based techniquefor noise reduction in electroencephalographic signalsrdquo SignalProcessing vol 55 no 2 pp 179ndash189 1996

16 Computational and Mathematical Methods in Medicine

[27] C A Joyce I F Gorodnitsky andMKutas ldquoAutomatic removalof eye movement and blink artifacts from EEG data using blindcomponent separationrdquo Psychophysiology vol 41 no 2 pp 313ndash325 2004

[28] G L Wallstrom R E Kass A Miller J F Cohn and N A FoxldquoAutomatic correction of ocular artifacts in the EEG a com-parison of regression-based and component-based methodsrdquoInternational Journal of Psychophysiology vol 53 no 2 pp 105ndash119 2004

[29] S M Gordon V Lawhern A D Passaro and K McDowellldquoInformed decomposition of electroencephalographic datardquoJournal of Neuroscience Methods vol 256 pp 41ndash55 2015

[30] D StuderUHoffmann andTKoenig ldquoFromEEGdependencymultichannel matching pursuit to sparse topographic EEGdecompositionrdquo Journal of Neuroscience Methods vol 153 no2 pp 261ndash275 2006

[31] J-L Starck M Elad and D Donoho ldquoRedundant multiscaletransforms and their application for morphological componentseparationrdquo Advances in Imaging and Electron Physics vol 132pp 287ndash348 2004

[32] P J Franaszczuk G K Bergey P J Durka andHM EisenbergldquoTime-frequency analysis using thematching pursuit algorithmapplied to seizures originating from the mesial temporal loberdquoElectroencephalography and Clinical Neurophysiology vol 106no 6 pp 513ndash521 1998

[33] P J Durka A Matysiak E M Montes P V Sosa and K JBlinowska ldquoMultichannel matching pursuit and EEG inversesolutionsrdquo Journal of Neuroscience Methods vol 148 no 1 pp49ndash59 2005

[34] J Bobin J-L Starck J Fadili and Y Moudden ldquoSparsityand morphological diversity in blind source separationrdquo IEEETransactions on Image Processing vol 16 no 11 pp 2662ndash26742007

[35] P J Durka D Ircha and K J Blinowska ldquoStochastic time-frequency dictionaries formatching pursuitrdquo IEEE Transactionson Signal Processing vol 49 no 3 pp 507ndash510 2001

[36] X Yong R K Ward and G E Birch ldquoGeneralized morpholog-ical component analysis for EEG source separation and artifactremovalrdquo in Proceedings of the 4th International IEEEEMBSConference on Neural Engineering (NER rsquo09) pp 343ndash346Antalya Turkey May 2009

[37] B Singh G Ai and H Wagatsuma ldquoAn electrooculographyanalysis in the time-frequency domain using morphologicalcomponent analysis toward the development of mobile BCIsystemsrdquo in Universal Access in Human-Computer InteractionAccess to Interaction 9th International Conference UAHCI 2015Held as Part of HCI International 2015 Los Angeles CA USAAugust 2ndash7 2015 Proceedings Part II vol 9176 of Lecture Notesin Computer Science pp 528ndash537 Springer Berlin Germany2015

[38] S S Chen D L Donoho and M A Saunders ldquoAtomicdecomposition by basis pursuitrdquo SIAM Review vol 43 no 1pp 129ndash159 2001

[39] D L Donoho and X Huo ldquoUncertainty principles and idealatomic decompositionrdquo IEEE Transactions on InformationThe-ory vol 47 no 7 pp 2845ndash2862 2001

[40] F Miwakeichi E Martınez-Montes P A Valdes-Sosa NNishiyama H Mizuhara and Y Yamaguchi ldquoDecomposingEEG data into spacendashtimendashfrequency components using par-allel factor analysisrdquo NeuroImage vol 22 no 3 pp 1035ndash10452004

[41] K J Friston C D Frith P F Liddle and R S J FrackowiakldquoFunctional connectivity the principal-component analysis oflarge (PET) data setsrdquo Journal of Cerebral Blood Flow andMetabolism vol 13 no 1 pp 5ndash14 1993

[42] S Makeig T-P Jung A J Bell D Ghahremani and T JSejnowski ldquoBlind separation of auditory event-related brainresponses into independent componentsrdquo Proceedings of theNational Academy of Sciences of the United States of Americavol 94 no 20 pp 10979ndash10984 1997

[43] Biomedical Signal httpwwwmedicinemcgillcaphysiovlabbiomed signalseeg nhtm

[44] S E G Nilsson and B E Andersson ldquoCorneal DC recordingsof slow ocular potential changes such as the ERG c-wave and thelight peak in clinical workmdashequipment and examples of resultsrdquoDocumenta Ophthalmologica vol 68 no 3-4 pp 313ndash325 1988

[45] OG Lins TW Picton P Berg andM Scherg ldquoOcular artifactsin EEG and event-related potentials I scalp topographyrdquo BrainTopography vol 6 no 1 pp 51ndash63 1993

[46] T W Picton P Van Roon M L Armilio P Berg N Ille andM Scherg ldquoThe correction of ocular artifacts a topographicperspectiverdquo Clinical Neurophysiology vol 111 no 1 pp 53ndash652000

[47] A S Keren S Yuval-Greenberg and L Y Deouell ldquoSaccadicspike potentials in gamma-band EEG characterization detec-tion and suppressionrdquo NeuroImage vol 49 no 3 pp 2248ndash2263 2010

[48] M Plochl J P Ossandon and P Konig ldquoCombining EEG andeye tracking identification characterization and correctionof eye movement artifacts in electroencephalographic datardquoFrontiers in Human Neuroscience vol 6 article 278 2012

[49] S Dandekar C Privitera T Carney and S A Klein ldquoNeuralsaccadic response estimation during natural viewingrdquo Journalof Neurophysiology vol 107 no 6 pp 1776ndash1790 2012

[50] G Ai N Sato B Singh and H Wagatsuma ldquoDirection andviewing area-sensitive influence of EOGartifacts revealed in theEEG topographic pattern analysisrdquo Cognitive Neurodynamicsvol 10 no 4 pp 301ndash314 2016

[51] P Berg and M Scherg ldquoDipole models of eye movements andblinksrdquo Electroencephalography and Clinical Neurophysiologyvol 79 no 1 pp 36ndash44 1991

[52] R J Croft and R J Barry ldquoRemoval of ocular artifact from theEEG a reviewrdquo Neurophysiologie Clinique vol 30 no 1 pp 5ndash19 2000

[53] I J Rampil ldquoA primer for EEG signal processing in anesthesiardquoAnesthesiology vol 89 no 4 pp 980ndash1002 1998

[54] J L Starck Y Moudden J Bobin M Elad and D DonoholdquoMorphological component analysisrdquo in Optics amp Photonics2005 p 59140Q International Society forOptics and Photonics2005

[55] S Sardy A Bruce and P Tseng ldquoBlock coordinate relaxationmethods for nonparametric signal denoising with waveletdictionariesrdquo Journal of Computational and Graphical Statisticsvol 9 pp 361ndash379 2000

[56] M Puschel and J M F Moura ldquoThe algebraic approach to thediscrete cosine and sine transforms and their fast algorithmsrdquoSIAM Journal on Computing vol 32 no 5 pp 1280ndash1316 2003

[57] X Shao and S G Johnson ldquoType-IV DCT DST and MDCTalgorithms with reduced numbers of arithmetic operationsrdquoSignal Processing vol 88 no 6 pp 1313ndash1326 2008

[58] R G Andrzejak K Lehnertz F Mormann C Rieke P Davidand C E Elger ldquoIndications of nonlinear deterministic and

14 Computational and Mathematical Methods in Medicine

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

Samples20000 1000

V1u

H1

(a) UDWT components separated by UDWT-DST-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(b) UDWT components separated by UDWT-DCT-DIRAC

Samples20000 1000

Fp1

Fp2

Cz

O1

O2

Pote

ntia

l (V

)

V1u

H1

(c) UDWT components separated by UDWT-LDCT-DIRAC

Figure 12 UDWT component taken from Fp1 Fp2 Cz O1 and O2 separated by UDWT-DCT-DIRAC UDWT-DST-DIRAC and UDWT-LDCT-DIRAC respectively

decomposition performance than others while DST andDCT theoretically have no meaningful difference The usageof iEEG as the true EEG signal had a large benefit whichcan be used for the performance test for past proposedmethods like ICA and PCA consistently Our proposedmethod successfully demonstrated the performance in cc andthe frequency profile especially in Section 42 while in theserious discussion of the real EEG and EOG signals the DSTor DCT component exhibited a baseline fluctuation of thesignal which denotes the persistence of the EOG componentor other slow frequency artifacts noises and the factor willbe improved by the fine-tuned design of the DST or DCTdictionary with a band pass filter function In addition thethreshold problem exits in the optimization algorithm andnumber of iterations [37]

The EEG decomposition had not mark with a combi-nation of a second and a third component of EEG signal

decomposed by ldquoDST DCT and LDCTrdquo andDIRAC respec-tively based on the morphology Therefore the accuratecombination in the further perspective will be considerableEven the combination of all components and the mixedsignal or real EEG signal had cc above 97 for all redundanttransforms as is analyzed in the frequency spectrum thesignal morphology has further meaning in the viewpointof the signal transmission The MCA method has such anextended and flexible availability for signal analyses

6 Conclusion

Morphological Component Analysis methodology wasapplied to the simulated semisimulated and real EOGand EEG signal The successful decomposition of the EOGand EEG signal into their morphological component wasdemonstrated It seems to be that the EEG signals and

Computational and Mathematical Methods in Medicine 15

artifacts in EEG have been represented by different explicitdictionaries We analyzed the EEG signals involved with theEOG artifacts which were influenced by task conditionsTheDIRAC explicit dictionary decomposed the EEG signal intospike-like activities which may be related to the transientproperty of EEG UDWT explicit dictionary representsslow movement or bumps DCT DST and LDCT explicitdictionaries represent dominant signal that represents EEGsor pure tones signals as monomorphic and polymorphicactivities These results suggested that the effectivenessof MCA in ocular artifacts removal from the EEG rawsignal was derived from signal morphology characterizedas slow and smooth change of EOG time series In thefurther analysis the MCA is required to compare withother competing methods for the EEG and EOG signaldecomposition

Competing Interests

The authors have declared that no competing interests exist

Acknowledgments

This work was partly supported by JSPS KAKENHI 16H01616and 26240032 and theNewEnergy and Industrial TechnologyDevelopment Organization (NEDO) ldquoNext-Generation Arti-ficial Intelligence (3) Base Technology for Next-GenerationAIrdquo (Automated Driving Task) and the collaborative researchproject with Fujitsu Ten Limited

References

[1] J P Donoghue J N Sanes N G Hatsopoulos and G GaalldquoNeural discharge and local field potential oscillations in pri-mate motor cortex during voluntary movementsrdquo Journal ofNeurophysiology vol 79 no 1 pp 159ndash173 1998

[2] J A Uriguen and B Garcia-Zapirain ldquoEEG artifact removalmdashstate-of-the-art and guidelinesrdquo Journal of Neural Engineeringvol 12 no 3 Article ID 031001 2015

[3] C Kamarajan and B Porjesz ldquoAdvances in electrophysiologicalresearchrdquoAlcohol Research Current Reviews vol 37 no 1 article53 2015

[4] L F Nicolas-Alonso and J Gomez-Gil ldquoBrain computer inter-faces a reviewrdquo Sensors vol 12 no 2 pp 1211ndash1279 2012

[5] L Mayaud M Congedo A Van Laghenhove et al ldquoA compar-ison of recording modalities of P300 event-related potentials(ERP) for brain-computer interface (BCI) paradigmrdquo Neuro-physiologie CliniqueClinical Neurophysiology vol 43 no 4 pp217ndash227 2013

[6] X-Y Wang J Jin Y Zhang and B Wang ldquoBrain controlhuman-computer integration control based on brain-computerinterfacerdquo Acta Automatica Sinica vol 39 no 3 pp 208ndash2212013

[7] G Al-Hudhud ldquoAffective command-based control system inte-grating brain signals in commands control systemsrdquo Computersin Human Behavior vol 30 pp 535ndash541 2014

[8] J L Sirvent Blasco E Ianez A Ubeda and JM Azorın ldquoVisualevoked potential-based brain-machine interface applications toassist disabled peoplerdquo Expert Systems with Applications vol 39no 9 pp 7908ndash7918 2012

[9] H Cecotti ldquoSpelling with non-invasive Brain-Computer Inter-facesmdashcurrent and future trendsrdquo Journal of Physiology Parisvol 105 no 1ndash3 pp 106ndash114 2011

[10] I S Kotchetkov B Y Hwang G Appelboom C P Kellnerand E S Connolly Jr ldquoBrain-computer interfaces militaryneurosurgical and ethical perspectiverdquo Neurosurgical Focusvol 28 no 5 article no E25 2010

[11] R N Vigario ldquoExtraction of ocular artefacts from EEG usingindependent component analysisrdquo Electroencephalography andClinical Neurophysiology vol 103 no 3 pp 395ndash404 1997

[12] W Zhou and J Gotman ldquoAutomatic removal of eye movementartifacts from the EEG using ICA and the dipole modelrdquoProgress in Natural Science vol 19 no 9 pp 1165ndash1170 2009

[13] R Sameni andCGouy-Pailler ldquoAn iterative subspace denoisingalgorithm for removing electroencephalogram ocular artifactsrdquoJournal of Neuroscience Methods vol 225 pp 97ndash105 2014

[14] M Breakspear and J R Terry ldquoDetection and description ofnon-linear interdependence in normal multichannel humanEEG datardquo Clinical Neurophysiology vol 113 no 5 pp 735ndash7532002

[15] U R Acharya O Faust N Kannathal T Chua and S Laxmin-arayan ldquoNon-linear analysis of EEG signals at various sleepstagesrdquo Computer Methods and Programs in Biomedicine vol80 no 1 pp 37ndash45 2005

[16] L I Aftanas and S A Golocheikine ldquoNon-linear dynamiccomplexity of the human EEGduringmeditationrdquoNeuroscienceLetters vol 330 no 2 pp 143ndash146 2002

[17] M J Fadili J-L Starck J Bobin and Y Moudden ldquoImagedecomposition and separation using sparse representations anoverviewrdquo Proceedings of the IEEE vol 98 no 6 pp 983ndash9942010

[18] K J Blinowska and P J Durka ldquoUnbiased high resolutionmethod of EEG analysis in time-frequency spacerdquo Acta Neuro-biologiae Experimentalis vol 61 no 3 pp 157ndash174 2001

[19] E Imani H-R Pourreza and T Banaee ldquoFully automateddiabetic retinopathy screening usingmorphological componentanalysisrdquo Computerized Medical Imaging and Graphics vol 43pp 78ndash88 2015

[20] E Imani M Javidi and H-R Pourreza ldquoImprovement ofretinal blood vessel detection using morphological componentanalysisrdquo Computer Methods and Programs in Biomedicine vol118 no 3 pp 263ndash279 2016

[21] A S Al-Fahoum and A A Al-Fraihat ldquoMethods of EEG signalfeatures extraction using linear analysis in frequency and time-frequency domainsrdquo ISRN Neuroscience vol 2014 Article ID730218 7 pages 2014

[22] M Zibulevsky and B A Pearlmutter ldquoBlind source separationby sparse decomposition in a signal dictionaryrdquoNeural Compu-tation vol 13 no 4 pp 863ndash882 2001

[23] N P Castellanos andVAMakarov ldquoRecovering EEGbrain sig-nals artifact suppression with wavelet enhanced independentcomponent analysisrdquo Journal of Neuroscience Methods vol 158no 2 pp 300ndash312 2006

[24] J Hou K Morgan D M Tucker et al ldquoAn improved artifactsremoval method for high dimensional EEGrdquo Journal of Neuro-science Methods vol 268 pp 31ndash42 2016

[25] P Berg and M Scherg ldquoA multiple source approach to thecorrection of eye artifactsrdquo Electroencephalography and ClinicalNeurophysiology vol 90 no 3 pp 229ndash241 1994

[26] P K Sadasivan and D Narayana Dutt ldquoSVD based techniquefor noise reduction in electroencephalographic signalsrdquo SignalProcessing vol 55 no 2 pp 179ndash189 1996

16 Computational and Mathematical Methods in Medicine

[27] C A Joyce I F Gorodnitsky andMKutas ldquoAutomatic removalof eye movement and blink artifacts from EEG data using blindcomponent separationrdquo Psychophysiology vol 41 no 2 pp 313ndash325 2004

[28] G L Wallstrom R E Kass A Miller J F Cohn and N A FoxldquoAutomatic correction of ocular artifacts in the EEG a com-parison of regression-based and component-based methodsrdquoInternational Journal of Psychophysiology vol 53 no 2 pp 105ndash119 2004

[29] S M Gordon V Lawhern A D Passaro and K McDowellldquoInformed decomposition of electroencephalographic datardquoJournal of Neuroscience Methods vol 256 pp 41ndash55 2015

[30] D StuderUHoffmann andTKoenig ldquoFromEEGdependencymultichannel matching pursuit to sparse topographic EEGdecompositionrdquo Journal of Neuroscience Methods vol 153 no2 pp 261ndash275 2006

[31] J-L Starck M Elad and D Donoho ldquoRedundant multiscaletransforms and their application for morphological componentseparationrdquo Advances in Imaging and Electron Physics vol 132pp 287ndash348 2004

[32] P J Franaszczuk G K Bergey P J Durka andHM EisenbergldquoTime-frequency analysis using thematching pursuit algorithmapplied to seizures originating from the mesial temporal loberdquoElectroencephalography and Clinical Neurophysiology vol 106no 6 pp 513ndash521 1998

[33] P J Durka A Matysiak E M Montes P V Sosa and K JBlinowska ldquoMultichannel matching pursuit and EEG inversesolutionsrdquo Journal of Neuroscience Methods vol 148 no 1 pp49ndash59 2005

[34] J Bobin J-L Starck J Fadili and Y Moudden ldquoSparsityand morphological diversity in blind source separationrdquo IEEETransactions on Image Processing vol 16 no 11 pp 2662ndash26742007

[35] P J Durka D Ircha and K J Blinowska ldquoStochastic time-frequency dictionaries formatching pursuitrdquo IEEE Transactionson Signal Processing vol 49 no 3 pp 507ndash510 2001

[36] X Yong R K Ward and G E Birch ldquoGeneralized morpholog-ical component analysis for EEG source separation and artifactremovalrdquo in Proceedings of the 4th International IEEEEMBSConference on Neural Engineering (NER rsquo09) pp 343ndash346Antalya Turkey May 2009

[37] B Singh G Ai and H Wagatsuma ldquoAn electrooculographyanalysis in the time-frequency domain using morphologicalcomponent analysis toward the development of mobile BCIsystemsrdquo in Universal Access in Human-Computer InteractionAccess to Interaction 9th International Conference UAHCI 2015Held as Part of HCI International 2015 Los Angeles CA USAAugust 2ndash7 2015 Proceedings Part II vol 9176 of Lecture Notesin Computer Science pp 528ndash537 Springer Berlin Germany2015

[38] S S Chen D L Donoho and M A Saunders ldquoAtomicdecomposition by basis pursuitrdquo SIAM Review vol 43 no 1pp 129ndash159 2001

[39] D L Donoho and X Huo ldquoUncertainty principles and idealatomic decompositionrdquo IEEE Transactions on InformationThe-ory vol 47 no 7 pp 2845ndash2862 2001

[40] F Miwakeichi E Martınez-Montes P A Valdes-Sosa NNishiyama H Mizuhara and Y Yamaguchi ldquoDecomposingEEG data into spacendashtimendashfrequency components using par-allel factor analysisrdquo NeuroImage vol 22 no 3 pp 1035ndash10452004

[41] K J Friston C D Frith P F Liddle and R S J FrackowiakldquoFunctional connectivity the principal-component analysis oflarge (PET) data setsrdquo Journal of Cerebral Blood Flow andMetabolism vol 13 no 1 pp 5ndash14 1993

[42] S Makeig T-P Jung A J Bell D Ghahremani and T JSejnowski ldquoBlind separation of auditory event-related brainresponses into independent componentsrdquo Proceedings of theNational Academy of Sciences of the United States of Americavol 94 no 20 pp 10979ndash10984 1997

[43] Biomedical Signal httpwwwmedicinemcgillcaphysiovlabbiomed signalseeg nhtm

[44] S E G Nilsson and B E Andersson ldquoCorneal DC recordingsof slow ocular potential changes such as the ERG c-wave and thelight peak in clinical workmdashequipment and examples of resultsrdquoDocumenta Ophthalmologica vol 68 no 3-4 pp 313ndash325 1988

[45] OG Lins TW Picton P Berg andM Scherg ldquoOcular artifactsin EEG and event-related potentials I scalp topographyrdquo BrainTopography vol 6 no 1 pp 51ndash63 1993

[46] T W Picton P Van Roon M L Armilio P Berg N Ille andM Scherg ldquoThe correction of ocular artifacts a topographicperspectiverdquo Clinical Neurophysiology vol 111 no 1 pp 53ndash652000

[47] A S Keren S Yuval-Greenberg and L Y Deouell ldquoSaccadicspike potentials in gamma-band EEG characterization detec-tion and suppressionrdquo NeuroImage vol 49 no 3 pp 2248ndash2263 2010

[48] M Plochl J P Ossandon and P Konig ldquoCombining EEG andeye tracking identification characterization and correctionof eye movement artifacts in electroencephalographic datardquoFrontiers in Human Neuroscience vol 6 article 278 2012

[49] S Dandekar C Privitera T Carney and S A Klein ldquoNeuralsaccadic response estimation during natural viewingrdquo Journalof Neurophysiology vol 107 no 6 pp 1776ndash1790 2012

[50] G Ai N Sato B Singh and H Wagatsuma ldquoDirection andviewing area-sensitive influence of EOGartifacts revealed in theEEG topographic pattern analysisrdquo Cognitive Neurodynamicsvol 10 no 4 pp 301ndash314 2016

[51] P Berg and M Scherg ldquoDipole models of eye movements andblinksrdquo Electroencephalography and Clinical Neurophysiologyvol 79 no 1 pp 36ndash44 1991

[52] R J Croft and R J Barry ldquoRemoval of ocular artifact from theEEG a reviewrdquo Neurophysiologie Clinique vol 30 no 1 pp 5ndash19 2000

[53] I J Rampil ldquoA primer for EEG signal processing in anesthesiardquoAnesthesiology vol 89 no 4 pp 980ndash1002 1998

[54] J L Starck Y Moudden J Bobin M Elad and D DonoholdquoMorphological component analysisrdquo in Optics amp Photonics2005 p 59140Q International Society forOptics and Photonics2005

[55] S Sardy A Bruce and P Tseng ldquoBlock coordinate relaxationmethods for nonparametric signal denoising with waveletdictionariesrdquo Journal of Computational and Graphical Statisticsvol 9 pp 361ndash379 2000

[56] M Puschel and J M F Moura ldquoThe algebraic approach to thediscrete cosine and sine transforms and their fast algorithmsrdquoSIAM Journal on Computing vol 32 no 5 pp 1280ndash1316 2003

[57] X Shao and S G Johnson ldquoType-IV DCT DST and MDCTalgorithms with reduced numbers of arithmetic operationsrdquoSignal Processing vol 88 no 6 pp 1313ndash1326 2008

[58] R G Andrzejak K Lehnertz F Mormann C Rieke P Davidand C E Elger ldquoIndications of nonlinear deterministic and

Computational and Mathematical Methods in Medicine 15

artifacts in EEG have been represented by different explicitdictionaries We analyzed the EEG signals involved with theEOG artifacts which were influenced by task conditionsTheDIRAC explicit dictionary decomposed the EEG signal intospike-like activities which may be related to the transientproperty of EEG UDWT explicit dictionary representsslow movement or bumps DCT DST and LDCT explicitdictionaries represent dominant signal that represents EEGsor pure tones signals as monomorphic and polymorphicactivities These results suggested that the effectivenessof MCA in ocular artifacts removal from the EEG rawsignal was derived from signal morphology characterizedas slow and smooth change of EOG time series In thefurther analysis the MCA is required to compare withother competing methods for the EEG and EOG signaldecomposition

Competing Interests

The authors have declared that no competing interests exist

Acknowledgments

This work was partly supported by JSPS KAKENHI 16H01616and 26240032 and theNewEnergy and Industrial TechnologyDevelopment Organization (NEDO) ldquoNext-Generation Arti-ficial Intelligence (3) Base Technology for Next-GenerationAIrdquo (Automated Driving Task) and the collaborative researchproject with Fujitsu Ten Limited

References

[1] J P Donoghue J N Sanes N G Hatsopoulos and G GaalldquoNeural discharge and local field potential oscillations in pri-mate motor cortex during voluntary movementsrdquo Journal ofNeurophysiology vol 79 no 1 pp 159ndash173 1998

[2] J A Uriguen and B Garcia-Zapirain ldquoEEG artifact removalmdashstate-of-the-art and guidelinesrdquo Journal of Neural Engineeringvol 12 no 3 Article ID 031001 2015

[3] C Kamarajan and B Porjesz ldquoAdvances in electrophysiologicalresearchrdquoAlcohol Research Current Reviews vol 37 no 1 article53 2015

[4] L F Nicolas-Alonso and J Gomez-Gil ldquoBrain computer inter-faces a reviewrdquo Sensors vol 12 no 2 pp 1211ndash1279 2012

[5] L Mayaud M Congedo A Van Laghenhove et al ldquoA compar-ison of recording modalities of P300 event-related potentials(ERP) for brain-computer interface (BCI) paradigmrdquo Neuro-physiologie CliniqueClinical Neurophysiology vol 43 no 4 pp217ndash227 2013

[6] X-Y Wang J Jin Y Zhang and B Wang ldquoBrain controlhuman-computer integration control based on brain-computerinterfacerdquo Acta Automatica Sinica vol 39 no 3 pp 208ndash2212013

[7] G Al-Hudhud ldquoAffective command-based control system inte-grating brain signals in commands control systemsrdquo Computersin Human Behavior vol 30 pp 535ndash541 2014

[8] J L Sirvent Blasco E Ianez A Ubeda and JM Azorın ldquoVisualevoked potential-based brain-machine interface applications toassist disabled peoplerdquo Expert Systems with Applications vol 39no 9 pp 7908ndash7918 2012

[9] H Cecotti ldquoSpelling with non-invasive Brain-Computer Inter-facesmdashcurrent and future trendsrdquo Journal of Physiology Parisvol 105 no 1ndash3 pp 106ndash114 2011

[10] I S Kotchetkov B Y Hwang G Appelboom C P Kellnerand E S Connolly Jr ldquoBrain-computer interfaces militaryneurosurgical and ethical perspectiverdquo Neurosurgical Focusvol 28 no 5 article no E25 2010

[11] R N Vigario ldquoExtraction of ocular artefacts from EEG usingindependent component analysisrdquo Electroencephalography andClinical Neurophysiology vol 103 no 3 pp 395ndash404 1997

[12] W Zhou and J Gotman ldquoAutomatic removal of eye movementartifacts from the EEG using ICA and the dipole modelrdquoProgress in Natural Science vol 19 no 9 pp 1165ndash1170 2009

[13] R Sameni andCGouy-Pailler ldquoAn iterative subspace denoisingalgorithm for removing electroencephalogram ocular artifactsrdquoJournal of Neuroscience Methods vol 225 pp 97ndash105 2014

[14] M Breakspear and J R Terry ldquoDetection and description ofnon-linear interdependence in normal multichannel humanEEG datardquo Clinical Neurophysiology vol 113 no 5 pp 735ndash7532002

[15] U R Acharya O Faust N Kannathal T Chua and S Laxmin-arayan ldquoNon-linear analysis of EEG signals at various sleepstagesrdquo Computer Methods and Programs in Biomedicine vol80 no 1 pp 37ndash45 2005

[16] L I Aftanas and S A Golocheikine ldquoNon-linear dynamiccomplexity of the human EEGduringmeditationrdquoNeuroscienceLetters vol 330 no 2 pp 143ndash146 2002

[17] M J Fadili J-L Starck J Bobin and Y Moudden ldquoImagedecomposition and separation using sparse representations anoverviewrdquo Proceedings of the IEEE vol 98 no 6 pp 983ndash9942010

[18] K J Blinowska and P J Durka ldquoUnbiased high resolutionmethod of EEG analysis in time-frequency spacerdquo Acta Neuro-biologiae Experimentalis vol 61 no 3 pp 157ndash174 2001

[19] E Imani H-R Pourreza and T Banaee ldquoFully automateddiabetic retinopathy screening usingmorphological componentanalysisrdquo Computerized Medical Imaging and Graphics vol 43pp 78ndash88 2015

[20] E Imani M Javidi and H-R Pourreza ldquoImprovement ofretinal blood vessel detection using morphological componentanalysisrdquo Computer Methods and Programs in Biomedicine vol118 no 3 pp 263ndash279 2016

[21] A S Al-Fahoum and A A Al-Fraihat ldquoMethods of EEG signalfeatures extraction using linear analysis in frequency and time-frequency domainsrdquo ISRN Neuroscience vol 2014 Article ID730218 7 pages 2014

[22] M Zibulevsky and B A Pearlmutter ldquoBlind source separationby sparse decomposition in a signal dictionaryrdquoNeural Compu-tation vol 13 no 4 pp 863ndash882 2001

[23] N P Castellanos andVAMakarov ldquoRecovering EEGbrain sig-nals artifact suppression with wavelet enhanced independentcomponent analysisrdquo Journal of Neuroscience Methods vol 158no 2 pp 300ndash312 2006

[24] J Hou K Morgan D M Tucker et al ldquoAn improved artifactsremoval method for high dimensional EEGrdquo Journal of Neuro-science Methods vol 268 pp 31ndash42 2016

[25] P Berg and M Scherg ldquoA multiple source approach to thecorrection of eye artifactsrdquo Electroencephalography and ClinicalNeurophysiology vol 90 no 3 pp 229ndash241 1994

[26] P K Sadasivan and D Narayana Dutt ldquoSVD based techniquefor noise reduction in electroencephalographic signalsrdquo SignalProcessing vol 55 no 2 pp 179ndash189 1996

16 Computational and Mathematical Methods in Medicine

[27] C A Joyce I F Gorodnitsky andMKutas ldquoAutomatic removalof eye movement and blink artifacts from EEG data using blindcomponent separationrdquo Psychophysiology vol 41 no 2 pp 313ndash325 2004

[28] G L Wallstrom R E Kass A Miller J F Cohn and N A FoxldquoAutomatic correction of ocular artifacts in the EEG a com-parison of regression-based and component-based methodsrdquoInternational Journal of Psychophysiology vol 53 no 2 pp 105ndash119 2004

[29] S M Gordon V Lawhern A D Passaro and K McDowellldquoInformed decomposition of electroencephalographic datardquoJournal of Neuroscience Methods vol 256 pp 41ndash55 2015

[30] D StuderUHoffmann andTKoenig ldquoFromEEGdependencymultichannel matching pursuit to sparse topographic EEGdecompositionrdquo Journal of Neuroscience Methods vol 153 no2 pp 261ndash275 2006

[31] J-L Starck M Elad and D Donoho ldquoRedundant multiscaletransforms and their application for morphological componentseparationrdquo Advances in Imaging and Electron Physics vol 132pp 287ndash348 2004

[32] P J Franaszczuk G K Bergey P J Durka andHM EisenbergldquoTime-frequency analysis using thematching pursuit algorithmapplied to seizures originating from the mesial temporal loberdquoElectroencephalography and Clinical Neurophysiology vol 106no 6 pp 513ndash521 1998

[33] P J Durka A Matysiak E M Montes P V Sosa and K JBlinowska ldquoMultichannel matching pursuit and EEG inversesolutionsrdquo Journal of Neuroscience Methods vol 148 no 1 pp49ndash59 2005

[34] J Bobin J-L Starck J Fadili and Y Moudden ldquoSparsityand morphological diversity in blind source separationrdquo IEEETransactions on Image Processing vol 16 no 11 pp 2662ndash26742007

[35] P J Durka D Ircha and K J Blinowska ldquoStochastic time-frequency dictionaries formatching pursuitrdquo IEEE Transactionson Signal Processing vol 49 no 3 pp 507ndash510 2001

[36] X Yong R K Ward and G E Birch ldquoGeneralized morpholog-ical component analysis for EEG source separation and artifactremovalrdquo in Proceedings of the 4th International IEEEEMBSConference on Neural Engineering (NER rsquo09) pp 343ndash346Antalya Turkey May 2009

[37] B Singh G Ai and H Wagatsuma ldquoAn electrooculographyanalysis in the time-frequency domain using morphologicalcomponent analysis toward the development of mobile BCIsystemsrdquo in Universal Access in Human-Computer InteractionAccess to Interaction 9th International Conference UAHCI 2015Held as Part of HCI International 2015 Los Angeles CA USAAugust 2ndash7 2015 Proceedings Part II vol 9176 of Lecture Notesin Computer Science pp 528ndash537 Springer Berlin Germany2015

[38] S S Chen D L Donoho and M A Saunders ldquoAtomicdecomposition by basis pursuitrdquo SIAM Review vol 43 no 1pp 129ndash159 2001

[39] D L Donoho and X Huo ldquoUncertainty principles and idealatomic decompositionrdquo IEEE Transactions on InformationThe-ory vol 47 no 7 pp 2845ndash2862 2001

[40] F Miwakeichi E Martınez-Montes P A Valdes-Sosa NNishiyama H Mizuhara and Y Yamaguchi ldquoDecomposingEEG data into spacendashtimendashfrequency components using par-allel factor analysisrdquo NeuroImage vol 22 no 3 pp 1035ndash10452004

[41] K J Friston C D Frith P F Liddle and R S J FrackowiakldquoFunctional connectivity the principal-component analysis oflarge (PET) data setsrdquo Journal of Cerebral Blood Flow andMetabolism vol 13 no 1 pp 5ndash14 1993

[42] S Makeig T-P Jung A J Bell D Ghahremani and T JSejnowski ldquoBlind separation of auditory event-related brainresponses into independent componentsrdquo Proceedings of theNational Academy of Sciences of the United States of Americavol 94 no 20 pp 10979ndash10984 1997

[43] Biomedical Signal httpwwwmedicinemcgillcaphysiovlabbiomed signalseeg nhtm

[44] S E G Nilsson and B E Andersson ldquoCorneal DC recordingsof slow ocular potential changes such as the ERG c-wave and thelight peak in clinical workmdashequipment and examples of resultsrdquoDocumenta Ophthalmologica vol 68 no 3-4 pp 313ndash325 1988

[45] OG Lins TW Picton P Berg andM Scherg ldquoOcular artifactsin EEG and event-related potentials I scalp topographyrdquo BrainTopography vol 6 no 1 pp 51ndash63 1993

[46] T W Picton P Van Roon M L Armilio P Berg N Ille andM Scherg ldquoThe correction of ocular artifacts a topographicperspectiverdquo Clinical Neurophysiology vol 111 no 1 pp 53ndash652000

[47] A S Keren S Yuval-Greenberg and L Y Deouell ldquoSaccadicspike potentials in gamma-band EEG characterization detec-tion and suppressionrdquo NeuroImage vol 49 no 3 pp 2248ndash2263 2010

[48] M Plochl J P Ossandon and P Konig ldquoCombining EEG andeye tracking identification characterization and correctionof eye movement artifacts in electroencephalographic datardquoFrontiers in Human Neuroscience vol 6 article 278 2012

[49] S Dandekar C Privitera T Carney and S A Klein ldquoNeuralsaccadic response estimation during natural viewingrdquo Journalof Neurophysiology vol 107 no 6 pp 1776ndash1790 2012

[50] G Ai N Sato B Singh and H Wagatsuma ldquoDirection andviewing area-sensitive influence of EOGartifacts revealed in theEEG topographic pattern analysisrdquo Cognitive Neurodynamicsvol 10 no 4 pp 301ndash314 2016

[51] P Berg and M Scherg ldquoDipole models of eye movements andblinksrdquo Electroencephalography and Clinical Neurophysiologyvol 79 no 1 pp 36ndash44 1991

[52] R J Croft and R J Barry ldquoRemoval of ocular artifact from theEEG a reviewrdquo Neurophysiologie Clinique vol 30 no 1 pp 5ndash19 2000

[53] I J Rampil ldquoA primer for EEG signal processing in anesthesiardquoAnesthesiology vol 89 no 4 pp 980ndash1002 1998

[54] J L Starck Y Moudden J Bobin M Elad and D DonoholdquoMorphological component analysisrdquo in Optics amp Photonics2005 p 59140Q International Society forOptics and Photonics2005

[55] S Sardy A Bruce and P Tseng ldquoBlock coordinate relaxationmethods for nonparametric signal denoising with waveletdictionariesrdquo Journal of Computational and Graphical Statisticsvol 9 pp 361ndash379 2000

[56] M Puschel and J M F Moura ldquoThe algebraic approach to thediscrete cosine and sine transforms and their fast algorithmsrdquoSIAM Journal on Computing vol 32 no 5 pp 1280ndash1316 2003

[57] X Shao and S G Johnson ldquoType-IV DCT DST and MDCTalgorithms with reduced numbers of arithmetic operationsrdquoSignal Processing vol 88 no 6 pp 1313ndash1326 2008

[58] R G Andrzejak K Lehnertz F Mormann C Rieke P Davidand C E Elger ldquoIndications of nonlinear deterministic and

16 Computational and Mathematical Methods in Medicine

[27] C A Joyce I F Gorodnitsky andMKutas ldquoAutomatic removalof eye movement and blink artifacts from EEG data using blindcomponent separationrdquo Psychophysiology vol 41 no 2 pp 313ndash325 2004

[28] G L Wallstrom R E Kass A Miller J F Cohn and N A FoxldquoAutomatic correction of ocular artifacts in the EEG a com-parison of regression-based and component-based methodsrdquoInternational Journal of Psychophysiology vol 53 no 2 pp 105ndash119 2004

[29] S M Gordon V Lawhern A D Passaro and K McDowellldquoInformed decomposition of electroencephalographic datardquoJournal of Neuroscience Methods vol 256 pp 41ndash55 2015

[30] D StuderUHoffmann andTKoenig ldquoFromEEGdependencymultichannel matching pursuit to sparse topographic EEGdecompositionrdquo Journal of Neuroscience Methods vol 153 no2 pp 261ndash275 2006

[31] J-L Starck M Elad and D Donoho ldquoRedundant multiscaletransforms and their application for morphological componentseparationrdquo Advances in Imaging and Electron Physics vol 132pp 287ndash348 2004

[32] P J Franaszczuk G K Bergey P J Durka andHM EisenbergldquoTime-frequency analysis using thematching pursuit algorithmapplied to seizures originating from the mesial temporal loberdquoElectroencephalography and Clinical Neurophysiology vol 106no 6 pp 513ndash521 1998

[33] P J Durka A Matysiak E M Montes P V Sosa and K JBlinowska ldquoMultichannel matching pursuit and EEG inversesolutionsrdquo Journal of Neuroscience Methods vol 148 no 1 pp49ndash59 2005

[34] J Bobin J-L Starck J Fadili and Y Moudden ldquoSparsityand morphological diversity in blind source separationrdquo IEEETransactions on Image Processing vol 16 no 11 pp 2662ndash26742007

[35] P J Durka D Ircha and K J Blinowska ldquoStochastic time-frequency dictionaries formatching pursuitrdquo IEEE Transactionson Signal Processing vol 49 no 3 pp 507ndash510 2001

[36] X Yong R K Ward and G E Birch ldquoGeneralized morpholog-ical component analysis for EEG source separation and artifactremovalrdquo in Proceedings of the 4th International IEEEEMBSConference on Neural Engineering (NER rsquo09) pp 343ndash346Antalya Turkey May 2009

[37] B Singh G Ai and H Wagatsuma ldquoAn electrooculographyanalysis in the time-frequency domain using morphologicalcomponent analysis toward the development of mobile BCIsystemsrdquo in Universal Access in Human-Computer InteractionAccess to Interaction 9th International Conference UAHCI 2015Held as Part of HCI International 2015 Los Angeles CA USAAugust 2ndash7 2015 Proceedings Part II vol 9176 of Lecture Notesin Computer Science pp 528ndash537 Springer Berlin Germany2015

[38] S S Chen D L Donoho and M A Saunders ldquoAtomicdecomposition by basis pursuitrdquo SIAM Review vol 43 no 1pp 129ndash159 2001

[39] D L Donoho and X Huo ldquoUncertainty principles and idealatomic decompositionrdquo IEEE Transactions on InformationThe-ory vol 47 no 7 pp 2845ndash2862 2001

[40] F Miwakeichi E Martınez-Montes P A Valdes-Sosa NNishiyama H Mizuhara and Y Yamaguchi ldquoDecomposingEEG data into spacendashtimendashfrequency components using par-allel factor analysisrdquo NeuroImage vol 22 no 3 pp 1035ndash10452004

[41] K J Friston C D Frith P F Liddle and R S J FrackowiakldquoFunctional connectivity the principal-component analysis oflarge (PET) data setsrdquo Journal of Cerebral Blood Flow andMetabolism vol 13 no 1 pp 5ndash14 1993

[42] S Makeig T-P Jung A J Bell D Ghahremani and T JSejnowski ldquoBlind separation of auditory event-related brainresponses into independent componentsrdquo Proceedings of theNational Academy of Sciences of the United States of Americavol 94 no 20 pp 10979ndash10984 1997

[43] Biomedical Signal httpwwwmedicinemcgillcaphysiovlabbiomed signalseeg nhtm

[44] S E G Nilsson and B E Andersson ldquoCorneal DC recordingsof slow ocular potential changes such as the ERG c-wave and thelight peak in clinical workmdashequipment and examples of resultsrdquoDocumenta Ophthalmologica vol 68 no 3-4 pp 313ndash325 1988

[45] OG Lins TW Picton P Berg andM Scherg ldquoOcular artifactsin EEG and event-related potentials I scalp topographyrdquo BrainTopography vol 6 no 1 pp 51ndash63 1993

[46] T W Picton P Van Roon M L Armilio P Berg N Ille andM Scherg ldquoThe correction of ocular artifacts a topographicperspectiverdquo Clinical Neurophysiology vol 111 no 1 pp 53ndash652000

[47] A S Keren S Yuval-Greenberg and L Y Deouell ldquoSaccadicspike potentials in gamma-band EEG characterization detec-tion and suppressionrdquo NeuroImage vol 49 no 3 pp 2248ndash2263 2010

[48] M Plochl J P Ossandon and P Konig ldquoCombining EEG andeye tracking identification characterization and correctionof eye movement artifacts in electroencephalographic datardquoFrontiers in Human Neuroscience vol 6 article 278 2012

[49] S Dandekar C Privitera T Carney and S A Klein ldquoNeuralsaccadic response estimation during natural viewingrdquo Journalof Neurophysiology vol 107 no 6 pp 1776ndash1790 2012

[50] G Ai N Sato B Singh and H Wagatsuma ldquoDirection andviewing area-sensitive influence of EOGartifacts revealed in theEEG topographic pattern analysisrdquo Cognitive Neurodynamicsvol 10 no 4 pp 301ndash314 2016

[51] P Berg and M Scherg ldquoDipole models of eye movements andblinksrdquo Electroencephalography and Clinical Neurophysiologyvol 79 no 1 pp 36ndash44 1991

[52] R J Croft and R J Barry ldquoRemoval of ocular artifact from theEEG a reviewrdquo Neurophysiologie Clinique vol 30 no 1 pp 5ndash19 2000

[53] I J Rampil ldquoA primer for EEG signal processing in anesthesiardquoAnesthesiology vol 89 no 4 pp 980ndash1002 1998

[54] J L Starck Y Moudden J Bobin M Elad and D DonoholdquoMorphological component analysisrdquo in Optics amp Photonics2005 p 59140Q International Society forOptics and Photonics2005

[55] S Sardy A Bruce and P Tseng ldquoBlock coordinate relaxationmethods for nonparametric signal denoising with waveletdictionariesrdquo Journal of Computational and Graphical Statisticsvol 9 pp 361ndash379 2000

[56] M Puschel and J M F Moura ldquoThe algebraic approach to thediscrete cosine and sine transforms and their fast algorithmsrdquoSIAM Journal on Computing vol 32 no 5 pp 1280ndash1316 2003

[57] X Shao and S G Johnson ldquoType-IV DCT DST and MDCTalgorithms with reduced numbers of arithmetic operationsrdquoSignal Processing vol 88 no 6 pp 1313ndash1326 2008

[58] R G Andrzejak K Lehnertz F Mormann C Rieke P Davidand C E Elger ldquoIndications of nonlinear deterministic and

Computational and Mathematical Methods in Medicine 17

finite-dimensional structures in time series of brain electricalactivity dependence on recording region and brain staterdquoPhysical Review E vol 64 no 6 Article ID 061907 2001

[59] R R Coifman and D L Donoho ldquoTranslationInvariant de-noisingrdquo in Wavelets and Statistics vol 103 of Lecture Notes inStatistics pp 125ndash150 Springer Berlin Germany 1995

[60] M Lang H Guo J E Odegard C S Burrus and R O WellsJr ldquoNoise reduction using an undecimated discrete wavelettransformrdquo IEEE Signal Processing Letters vol 3 no 1 pp 10ndash121996

[61] J-L Starck J Fadili and FMurtagh ldquoThe undecimated waveletdecomposition and its reconstructionrdquo IEEE Transactions onImage Processing vol 16 no 2 pp 297ndash309 2007

Submit your manuscripts athttpswwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

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Diabetes ResearchJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

Submit your manuscripts athttpswwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

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Behavioural Neurology

EndocrinologyInternational Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

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BioMed Research International

OncologyJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

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PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

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Diabetes ResearchJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

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Gastroenterology Research and Practice

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Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

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