Original Research Article

An efficient algorithm of ECG signal denoising usingthe adaptive dual threshold filter and the discretewavelet transform

Wissam Jenkal a,*, Rachid Latif a, Ahmed Toumanari a, Azzedine Dliou a,Oussama El B'charri a, Fadel M.R. Maoulainine b

a Laboratory of Systems Engineering and Information Technology (LiSTi), ENSA, Ibn Zohr University, Agadir, MoroccobTeam of Child, Healt and Development, CHU, Faculty of Medicine, Cady Ayyad University, Marrakech, Morocco

b i o c y b e r n e t i c s a n d b i o m e d i c a l e n g i n e e r i n g 3 6 ( 2 0 1 6 ) 4 9 9 – 5 0 8

a r t i c l e i n f o

Article history:

Received 20 January 2016

Received in revised form

28 March 2016

Accepted 5 April 2016

Available online 16 April 2016

Keywords:

ECG signal denoising

Wavelet coefficients

Dual threshold

Adaptive filtering

a b s t r a c t

This paper proposes an efficient method of ECG signal denoising using the adaptive dual

threshold filter (ADTF) and the discrete wavelet transform (DWT). The aim of this method is

to bring together the advantages of these methods in order to improve the filtering of the ECG

signal. The aim of the proposed method is to deal with the EMG noises, the power line

interferences and the high frequency noises that could perturb the ECG signal. This algo-

rithm is based on three steps of denoising, namely, the DWT decomposition, the ADTF step

and the highest peaks correction step. This paper presents certain applications of this

algorithm on some of the MIT-BIH Arrhythmia database's signals. The results of these

applications allow observing the high performance of the proposed method comparing to

some other techniques recently published.

# 2016 Nałęcz Institute of Biocybernetics and Biomedical Engineering of the Polish

Academy of Sciences. Published by Elsevier Sp. z o.o. All rights reserved.

Available online at www.sciencedirect.com

ScienceDirect

journal homepage: www.elsevier.com/locate/bbe

1. Introduction

The electrocardiogram (ECG) signal represents the electricalactivity of the heart. This signal presents a major factor in thediagnosis of cardiac status. It allows the evaluation ofsequences of repolarization and depolarization of the heartmuscle [1–4].

The ECG signal is a very sensitive signal to the noise. Thissensitivity is due to the low frequency-band of the ECG signal

* Corresponding author at: Laboratory of Systems Engineering and InMorocco.

E-mail address: wissamjenkal@gmail.com (W. Jenkal).http://dx.doi.org/10.1016/j.bbe.2016.04.0010208-5216/# 2016 Nałęcz Institute of Biocybernetics and Biomedical EnSp. z o.o. All rights reserved.

(0.5–150 Hz) [5–8]. This band contains different internal andexternal noises. The internal noises are the fluctuations of thehuman organs on the ECG signal, e.g. the EMG noise. This noiseis due to the interference of the ECG and the electromyogram(EMG) signal. The last one represents the electrical activity ofthe muscles and permits to identify the neuromusculardiseases. The external noises are due to the materials usedin the recording of the ECG signal, e.g. the baseline wanderingand the power line interferences. The first noise is due to theelectrodes. This noise is attested when the patient moves

formation Technology (LiSTi), ENSA, Ibn Zohr University, Agadir,

gineering of the Polish Academy of Sciences. Published by Elsevier

b i o c y b e r n e t i c s a n d b i o m e d i c a l e n g i n e e r i n g 3 6 ( 2 0 1 6 ) 4 9 9 – 5 0 8500

during the recording of the ECG signal. The second noise is dueto the influence of the power line frequency of the recordingmachines (50 or 60 Hz).

The ECG signal denoising is an essential and a preliminarytask before the analysis of this signal. Due to the different sortsof noise appearing in the ECG signal, the filtering of this signalpresents a difficult issue. This difficulty is more appeared inthe automatic processing of the ECG signal. Several techniqueshad been proposed to deal with this issue [9–17], e.g. empiricalmode decomposition (EMD), numerous methods using filterbanks, and wavelet transform. The techniques based on thefilter banks affect the waves presented in the ECG signal,especially the P and the R waves [18]. The use of the EMD filterin the ECG signal denoising presents different disadvantages,e.g. the lack of robustness to a small perturbation, the highcomputational complexity, and others [19].

One of the widely used technique of the ECG signaldenoising is the discrete wavelet transform (DWT). Thistechnique offers an important solution to deal with this issue.Several research works propose the use of different sets ofwavelet coefficients and thresholding techniques of the DWT.The wavelet coefficients propose several functions close to themorphologies of the ECG signals. The thresholding techniquespermit to analyse and to correct the different decompositionsof the ECG signal using the DWT [20].

We have proposed recently an efficient method to deal withthe ECG denoising task [21], which is inspired from an imagedenoising technique recently published using an adaptive dualthreshold median filter [22]. The method presented in [21] isbased on two algorithms. The first is an adaptive mean filteralgorithm for the baseline wander denoising, and the second isan adaptive dual threshold filter (ADTF). This filter deals withthe high frequency noises. The proposed method showspromising results. In the case of an additive noise ratio level(SNR) of 5–20 dB, the values of the percentage root-mean-squaredifference parameter (PRD) vary between 25% and 7%. For thesame additive SNR level, the obtained values of the meansquare error parameter (MSE) vary between 0.0087 and 0.00062.

In this paper, we propose an efficient method using theadaptive dual threshold filter (ADTF) and the discrete wavelettransform (DWT). This algorithm is proposed to deal with theEMG noises, the power line interferences and the highfrequency noises that could perturb the ECG signal.

This paper is organized as follows, after Section 1; Section 2presents the efficient algorithm using the ADTF and the DWT.Next, Section 3 shows the qualitative and the statistical resultsas well as the comparisons of the proposed method withrecently published works. The analysis of these results ispresented in Section 4. Finally, Section 5 concludes this paper.

2. Proposed method

2.1. The baseline wandering

As mentioned in the previous section, we recently publishedan efficient method to deal with the baseline wandering issue.This method is based on an adaptive mean filter [21]. Themean filter is a common technique in the image processing[23,24]. However, the results of this technique are a little fuzzy,

especially for larger windows. The aim of the proposed methodis based on this note. It proposes an adaptive algorithm thatpermits to extract the fuzzy representation of the ECG signal.This representation does not contain major waves of the ECGsignal, e.g. the QRS complex. Next, the baseline wanderingcorrection is assured using the following equation:

Y ¼ X�h (1)

where Y is the corrected signal, X is the original signal and h isthe fuzzy representation of the original signal. Fig. 1 presentsan example of the baseline wandering correction using thismethod.

2.2. The adaptive dual threshold filter

The basics of the adaptive dual threshold filter have beeninspired from the dual threshold median method recentlypublished [22]. This technique provides an important solutionof the image denoising. In the single threshold filters, any pixelhaving a less or a greater value than the single threshold value,this pixel is considered as a noise. This can increase thepossibility of the wrong detection of the noise. In the case ofthe dual threshold method, the noisy pixels are identified in arelatively narrow range and thus can reduce incorrectdetection probability.

In the case of the ECG signal, we have developed anadaptative dual threshold filter (ADTF). An example of theapplication of this method is illustrated in Fig. 2. The purposeof this filter is to calculate three elements for each window ofthe ECG signal. The mean of this window, the higher thresholdand the lower threshold. Where the equation of the windowmean is as follows:

g ¼ 1m

Xnþm

i¼n

CðiÞ (2)

g is the average of the selected window, m is the window sizeand C(i) is the noisy signal. The equation of the higher thresh-old is as follows:

Ht ¼ g þ ½ðMx�gÞ�b� (3)

where Ht is the higher threshold of the selected window, Mx isthe maximum value of selected window, and b is the thresh-olding coefficient, following is the lower threshold equation:

Lt ¼ g�½ðg�MiÞ�b� (4)

where Lt is the lower threshold of the selected window, Mi isthe minimum value of selected window. b is the narrow rangecoefficient with:

0 < b < 1 (5)

The b coefficient allows adapting the thresholding processin the ECG signal denoising. The coefficient varies between 0(0%) and 1 (100%). As presented in [21], the lower values of b

coefficient are required for the high concentration of thenoises. In the case of the lower concentration of the noises, alarger toleration is required, i.e. the higher values of the b

coefficient are recommended.

Fig. 2 – Example of the application of the ADTF in the case of an additive white Gaussian noise of 15 dB: (a) is the originalsignal, (b) is the noisy signal and (c) is the corrected signal.

Fig. 1 – Example of the application of the adaptive mean filter in the baseline wandering: (a) is the noisy signal, (b) is thedetected baseline wandering signal and (c) is the corrected signal.

b i o c y b e r n e t i c s a n d b i o m e d i c a l e n g i n e e r i n g 3 6 ( 2 0 1 6 ) 4 9 9 – 5 0 8 501

Fig. 3 – DWT decomposition.

Table 1 – The b parameter influence in the ADTF step.

MIT-BIH 5% 10% 15% 20%

SNRimp 101 6.82 8.69 7.54 7.16SNRimp 115 8.72 9.20 8.92 8.60

b i o c y b e r n e t i c s a n d b i o m e d i c a l e n g i n e e r i n g 3 6 ( 2 0 1 6 ) 4 9 9 – 5 0 8502

2.3. The wavelet coefficient

The discrete wavelet transform (DWT) is a mathematicaltechnique widely used in the signal processing. The aim of thistransform is to decompose a signal into different resolutionsusing high pass and low pass filters. Several high and low passcoefficients have been developed for a large choice amongdifferent scales and translations in order to obtain differentsorts of signal analysis, e.g. symlets coefficients, debauchiescoefficients, Coiflets coefficients. Regarding the equations ofthe decomposition, consider:

A½k� ¼Xn

x½n��h½2k�n� (6)

D½k� ¼Xn

x½n��g½2k�n� (7)

where h[n] is the half band low pass filter, g[n] is the half bandhigh pass filter, A[k] is the output high pass filter (the approxi-mation) and D[k] is the output low pass filter (the detail). x[n] isthe discrete form of the original ECG signal. As shown in Fig. 3.The DWT decomposes the signal at different resolutions. Eachone presents the approximation and the detail of the previousapproximation or detail from the previous resolution. The aimof the ECG signal decomposition is to extract details andapproximations needed for the denoising task.

2.4. The proposed algorithm

The proposed algorithm is based on three steps of denoising.This process permits to decrease successively the noises in theECG signal. This method has been tested in some signals of theMIT-BIH arrhythmia database of Physionet. This databasecontains 48 records with a sampling frequency of 360 Hz, i.e.each 360 samples present 1 s of the original signal.

2.4.1. Step 1: The first stage of denoising using detailsAs mention previously, the DWT decomposes the ECG signal atdifferent frequency bands. The wavelet coefficients used inthis method are the debauchies 6 coefficients (db6). Thesecoefficients show best results compared to others in thismethod. This is due to the similarity of the db6 with differentmorphologies of the ECG signal. As shown in Fig. 4, the details 1and 2 (D1 and D2) concentrate an important part of the noise inthe ECG signal [20]. In the proposed method, we propose the

elimination of these details in the first step of the proposedmethod.

2.4.2. Step 2: The application of the ADTFThe second step of the proposed method is based on theapplication of the ADTF in the corrected signal of the first step.The b parameter used for this step is equal to 10% and thewindow filtering is 10 samples of the ECG signal. Theseparameters show better results in this step. Table 1 shows anexample of the influence of the b parameter in the ADTF usingthe signal-to-noise ratio improvement parameter (SNRimp)and the white Gaussian noise level of 10 dB. The proposedalgorithm of this step is presented in Fig. 5.

2.4.3. Step 3: The highest peaks correctionThe aim of the last step of this method is to includea correcting stage of the highest peaks in the ECG signal.These peaks present some important waves of the analysedsignal, e.g. the R and the S peaks. The algorithm of this stage isas follows where Y is the result of this step:

1. i = 12. n = i + 18003. If n = the length of the corrected ECG signal (d) using the

second stepThen: the end of the step 3End If

4. j = maxima of a moving window of 5 s (1800 samples) in theabsolute value of d signal

5. a = j � 0.76. If abs(d(i)) � a

Then: Y(i � 10 : i + 10) = l(i � 10 : i + 10) ; i = i + 9Else: Y(i) = d(i)End If

7. If i � nThen: i = i + 1; go to 6Else go to 2End If

Fig. 5 – The algorithm of the first and the second steps.

Fig. 4 – First step of the proposed method: (a) is the original signal and (b) is the sum of both details 1 and 2.

b i o c y b e r n e t i c s a n d b i o m e d i c a l e n g i n e e r i n g 3 6 ( 2 0 1 6 ) 4 9 9 – 5 0 8 503

As presented in this algorithm, this step allows recoveringthe values of the highest peaks presented in the d signal, whichis the result of the ECG signal correction using the first step.The ADTF, as presented in the second step, can influence someof these peaks, especially in the cases of the high density ofnoises. The last step allows reducing these noises withoutaffecting the majority of the highest peaks.

3. Results

The simulation results have been drawn using MATLABR2014a. Three simulated noises have been tested, namely,the power line interferences, the EMG noises and the syntheticinterferences. To evaluate the performance of the proposedmethod in the case of the power line denoising, an additivefunction of these interferences is presented as follows:

NðtÞ ¼ A�sinð2�p�f�tÞ (8)

where A = 0.15 mV and f = 50 Hz. This signal is added to theoriginal ECG signal to simulate the power line interferences.The simulation of the EMG noises is drawn using the randomnoise as presented in [25]. In the case of the synthetic inter-ferences, these noises are simulated using the white Gaussiannoise (WGN) as presented in [25].

3.1. Qualitative results

The qualitative results present some figures taken from thesimulation of the proposed method. These figures allowperceiving the filtering process of the noises in order

Fig. 6 – The correction of the power line interferences: (a) the original signal, (b) the infected signal and (c) the corrected signal.

b i o c y b e r n e t i c s a n d b i o m e d i c a l e n g i n e e r i n g 3 6 ( 2 0 1 6 ) 4 9 9 – 5 0 8504

to analyse the quality of the ECG signal denoising. The ECGsignal chosen in the qualitative analyses is the signal 101 of theMIT-BIH database. Fig. 6 shows the results of the correction ofthe power line interferences based on the proposed method.Fig. 7 illustrates the results of the denoising of the EMGinterferences. These interferences are simulated using therandom noise with an amplitude of 0.15 mV. Figs. 8 and 9present the results of the denoising of the WGN, where thenoise levels are 5 and 15 dB respectively.

Fig. 7 – The denoising results of the EMG interferences: (a) the osignal.

3.2. Quantitative results

The quantitative results allow evaluating statistically theefficiency of the proposed method. The evaluation is estab-lished by using the following parameters:

- The mean square error:

MSE ¼ 1N

Xi¼N

i¼1

ðXðiÞ�YðiÞÞ2 (9)

riginal signal, (b) the infected signal and (c) the corrected

Fig. 8 – The denoising results of 5 dB of the WGN: (a) the original signal, (b) the infected signal and (c) the corrected signal.

b i o c y b e r n e t i c s a n d b i o m e d i c a l e n g i n e e r i n g 3 6 ( 2 0 1 6 ) 4 9 9 – 5 0 8 505

- The root mean square error:

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1N

Xi¼N

i¼1

ðXðiÞ�YðiÞÞ2vuut (10)

- The percent root mean square difference:

PRD ¼ 100�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPi¼N

i¼1 ðXðiÞ�YðiÞÞ2Pi¼Ni¼1 ðXðiÞÞ2

vuut (11)

Fig. 9 – The denoising results of 15 dB of the WGN: (a) the origin

- The signal-to-noise ratio output:

SNRout ¼ 10�log10Pi¼N

i¼1 ðXðiÞÞ2Pi¼Ni¼1 ðYðiÞÞ�XðiÞÞ2

!(12)

- The signal-to-noise ratio improvement:

SNRimp ¼ 10�log10Pi¼N

i¼1 ðdðiÞÞ�XðiÞÞ2Pi¼Ni¼1 ðYðiÞÞ�XðiÞÞ2

!(13)

al signal, (b) the infected signal and (c) the corrected signal.

Table 2 – The comparison of the correction results of thepower line interferences in the signal 115 of the MIT-BIHdatabase.

RL AZP FZP ADTF-DWT

SNRout 6.54 12.17 14.25 23.29MSE 0.0754 0.0206 0.0128 0.0015

Table 3 – The comparison of the correction results of theEMG interferences in the signal 115 of the MIT-BIHdatabase.

RL AZP FZP ADTF-DWT

SNRout 6.83 11.82 13.68 15.59MSE 0.0705 0.0223 0.0146 0.0069

Table 4 – The comparison of the correction results of thesynthetic interferences in the signal 115 of the MIT-BIHdatabase.

RL AZP FZP ADTF-DWT

SNRout 6.77 11.69 13.47 22.27MSE 0.0153 0.0230 0.0153 0.0019

Table 5 – The results of the synthetic interferencesdenoising (WGN of 5 dB) in some of the MIT-BIH databasesignals using the proposed method.

MIT-BIH MSE RMSE PRD SNRimp

100 0.0044 0.066 18.26 9.70101 0.0042 0.04 17.43 10.23103 0.0058 0.076 19.61 9.10113 0.0088 0.093 19.14 9.33115 0.0122 0.110 19.46 9.45117 0.0283 0.168 19.18 9.34119 0.0459 0.214 21.92 8.13122 0.0411 0.202 22.75 8.07

Table 6 – The comparison of the denoising results of theWGN (5 dB) in the signal 101 of the MIT-BIH database.

ADWT ADTF-DWT

MSE 0.005 0.0042RMSE 0.072 0.064PRD 19.65 17.43SNRimp 9.098 10.23

Table 7 – The SNRimp comparison of the denoisingresults of the WGN (5 dB) in some of the MIT-BIH databasesignals.

MIT-BIH ADWT MABWT ADTF-DWT

100 9.40 7.80 9.70101 9.09 6.90 10.23103 7.13 7.70 9.10113 7.82 7.90 9.33115 7.19 7.80 9.45117 8.62 7.90 9.34119 7.27 7.60 8.13122 7.86 6.90 8.07

Table 8 – The PRD comparison of the denoising results ofthe WGN (5 dB) in some of the MIT-BIH database signals.

MIT-BIH ADTF ADTF-DWT

100 24.55 18.26103 25.23 19.61105 24.53 20.56115 24.74 19.46

b i o c y b e r n e t i c s a n d b i o m e d i c a l e n g i n e e r i n g 3 6 ( 2 0 1 6 ) 4 9 9 – 5 0 8506

where X(i) is the original signal, d(i) is the infected signal by thenoises, Y(i) is the corrected signal and N is the length of the ECGsignal, which is the number of samples of each MIT-BIH signal.Tables 2–4 present the comparison results among severalmethods, namely, the parallel-type fractional zero-phasefiltering (FZP) [25], the Riemann–Liouville (RL) integrator [26],the zero-phase average window filter (AZP), as presented in[25], and the proposed method (ADTF-DWT). Table 2 proposesthe comparison of the power line interferences (50 Hz) wherethe amplitude is 0.15 mV as presented in [25]. In Table 3, thecomparison has been drawn in the case of the EMGinterferences. These noises have been simulated using therandom noises as presented in [25]. Table 4 presents thecomparison results in the case of synthetic interferences.These noises have been simulated using the WGN aspresented in [25] where the level of noises is 15 dB. Table 5presents the results of the filtering of the white Gaussiannoises of 5 dB in some of the MIT-BIH database signals. Theseresults have been compared with several methods, namely,the adaptive dependent wavelet thresholding technique(ADWT) and the multi-adaptive bionic wavelet transform(MABWT), as presented in [27]. This comparison is presentedin the Tables 6 and 7. For the same level of the WGN, Table 8

presents the PRD comparison of the proposed method and theADTF [21].

4. Discussion

In this paper, we shall propose an efficient method thatgathers the adaptive dual threshold filter, which is proposedrecently [21], and the DWT. The aim of this method is to bringtogether the advantages of these methods in order to improvethe filtering of the ECG signals. As shown in Fig. 6 and Table 2,the proposed method provides an important solution to dealwith the issue of the power line interferences. Fig. 6 allowsobserving the high quality of the filtering using this method.Table 2 presents the evaluation of the MSE and the SNRoutparameters in the power line denoising. As shown in this table,the proposed method provides a better performance comparedto other interesting methods recently published [25,26]. Fig. 7and Table 3 present the results of the EMG interferencesfiltering using the proposed method and others. The EMGnoises are simulated using the random noise. As shown inFig. 7, the proposed method provides a high quality ofdenoising. Table 3 permits to observe that the statisticalresults of the proposed method are better than the FZP methodand others [25,26]. Fig. 9 and Table 4 present the results of thesynthetic interferences denoising using the proposed methodand others. These interferences are simulated using the WGN.Fig. 9 shows that, in the case of 15 dB of the WGN, the proposed

b i o c y b e r n e t i c s a n d b i o m e d i c a l e n g i n e e r i n g 3 6 ( 2 0 1 6 ) 4 9 9 – 5 0 8 507

method provides an important solution to deal with thesenoises. Table 4 allows observing the better statistical results ofthe proposed method comparable to the FZP method and others[25,26]. Fig. 8 and Tables 5–7 present the statistical results of theWGN denoising, where the level of noise is 5 dB. Fig. 8 showsthat, in the case of 5 dB of the WGN, the proposed methodprovides an important solution for the high density of noises. Asshown in this figure, the proposed method permits to restore theECG waves highly infected by the high density of noises. Asshown in the Tables 5–7, the proposed method provides animportant solution to the issue of the high density of noises.Tables 6 and 7 permit to observe that the statistical results of theproposed method are better than the ADWT and the MABWTpresented in [27]. Table 8 presents the comparison of theproposed method and the ADTF, which we had proposedrecently [21]. For the higher density of noises, the proposedmethod in this paper provides better results that the ADTF. Thatis due to the high performance of the ADTF-DWT especially inthe high density of noises. The qualitative and the quantitativeresults provide a general impression of the proposed methodbehavior to deal with different kinds of noise. As shown in theseresults, the ADTF-DWT method offers high performancescompared to others method recently published [21,25–27].

5. Conclusion

In this paper, we shall propose an efficient method thatgathers the adaptive dual threshold filter, which is proposedrecently [21], and the DWT. The aim of this method is to bringtogether the advantages of these methods in order to improvethe filtering of the ECG signal. The proposed algorithm dealswith the EMG noises, the power line interferences and the highfrequency noises that could perturb the ECG signal. Thisalgorithm is based on three steps of denoising, namely, theDWT decomposition, the ADTF step and the highest peakscorrection step. This paper presents certain applications ofthis algorithm on some of the MIT-BIH Arrhythmia database'ssignals. The results presented in this paper allow observingthat the proposed method offers high performances comparedto others method recently published [21,25–27].

Financial support

We owe a debt of gratitude to the National Centre for Scientificand Technical Research of Morocco (CNRST) for their financialsupport and for their supervision (grant number: 18UIZ2015).

Acknowledgements

We gratefully acknowledge the valuable comments of thereviewers.

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