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Biomedical Signal Processing and Control 38 (2017) 388–399

Contents lists available at ScienceDirect

Biomedical Signal Processing and Control

jo ur nal homep age: www.elsev ier .com/ locate /bspc

n adaptive thresholding method for the wavelet based denoising ofhonocardiogram signal

uneet Kumar Jaina,∗, Anil Kumar Tiwarib

Center for Information and Communication Technology, Indian Institute of Technology Jodhpur, Rajasthan 342011, IndiaDepartment of Electrical Engineering, Indian Institute of Technology Jodhpur, Rajasthan 342011, India

r t i c l e i n f o

rticle history:eceived 9 February 2017ccepted 11 July 2017vailable online 30 July 2017

eywords:eart sound signalhonocardiographyiscrete wavelet transformavelet denoising

hresholding

a b s t r a c t

Segmentation of the phonocardiography (PCG) signal into cardiac cycles is a primary task for the diag-nosis of cardiovascular diseases. However, PCG is highly susceptible to noise, and extra sound calledmurmur may also be present in the PCG signal due to pathology. These components cause difficultiesin the segmentation and therefore, segmentation is often preceded by the denoising of the PCG signalto emphasize the fundamental heart sounds S1 and S2, by removing these unwanted components. Forthe denoising of the PCG signal, discrete wavelet transform (DWT) based algorithms have shown goodperformance because such algorithms suppress in-band noise besides the out-of-band noise. Selectionof threshold value and threshold function significantly affects the performance of these algorithms. Inthis paper, for threshold value estimation, an adaptive method based on statistical parameters of thegiven PCG signal is proposed. The statistical parameters are found to be highly effective for this purpose.We also propose a new threshold function, non-linear mid function, to address the issues of SNR and

transients in the existing threshold functions, soft and hard. The proposed method is applied on a largenumber of PCG signals with additive white Gaussian noise, red noise, and pink noise. The Performance ofthe proposed method is also evaluated on the PCG signals recorded in real-life noisy scenarios and signalswith murmur sound. The obtained results show that the proposed method is significantly superior to thecompetitive algorithms.

© 2017 Elsevier Ltd. All rights reserved.

. Introduction

Heart valvular diseases are manifested into heart sound signaluch earlier than they cause serious damage to the heart [1]. It is

ecause the genesis of the heart sound components is related to theovement of the heart valves [2]. Phonocardiography is the mostidely used technique for the heart sound signal analysis because

f its user-friendly features such as easy to use, timeless set-up pro-ess, and cost effectiveness [3–5]. It uses a sensor called electronictethoscope, which acquires the heart sound signal and convertst into an electrical form using a microphone. Thus, analysis of theCG signal is of paramount importance to diagnose heart valvu-ar diseases at an early stage. However, availability of only a small

umber of experts in this field motivated researchers to developlgorithms for automatic analysis of the PCG signal.

∗ Corresponding author at: 1106, Academic Block-1, IIT Jodhpur, Old Residencyoad, Ratanada, Jodhpur, Rajsthan 342011, India.

E-mail addresses: puneetjain@iitj.ac.in (P.K. Jain), akt@iitj.ac.in (A.K. Tiwari).

ttp://dx.doi.org/10.1016/j.bspc.2017.07.002746-8094/© 2017 Elsevier Ltd. All rights reserved.

Automatic analysis of the PCG signal is generally performed intwo steps; segmentation and classification [6,7]. In the segmenta-tion step, fundamental heart sounds (FHS), S1 and S2, are identifiedand then the signal is segmented into systole and diastole periods[7]. Systole is the time duration from S1 to S2 and the diastole is thetime duration from S2 to next S1 [6]. In the classification step, thePCG signal is classified as normal or abnormal having a particulardisease. Thus, the primary task in the PCG signal analysis is its seg-mentation [7]. However, PCG signal is highly susceptible to variousnoises generated due to the motion of subject, subject’s own speechand other’s speech, movement of the stethoscope used to acquirethe PCG signal, lung sounds, and ambient sources [4,7,8]. Further-more, pathologies may cause the presence of extra sound in thePCG signal, called as murmur [6]. The presence of these componentsmakes the segmentation task difficult. Therefore, to emphasize theS1 and S2, segmentation is often preceded by denoising to minimizethe contamination level of noise and to remove the murmurs from

the signal [9,10]. However, the presence of murmurs in systole ordiastole period and their time-frequency characteristics leads to adiagnosis of heart valvular diseases [11,12]. For example, murmurdue to aortic stenosis, mitral regurgitation and pulmonary stenosis

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ccur in systole period and aortic regurgitation and mitral stenosisccur in diastolic period [6]. The features related to the murmursan be extracted from the segmented cardiac cycles more efficientlys compared to the signal without segmented cardiac cycles [10].herefore, once the PCG signal is segmented into cardiac cycles,athological features, if present, are extracted from these cycles10].

Various denoising algorithms for the PCG signal in time domainnd frequency domain have been proposed [3]. In the time domain,enoising algorithms have been proposed based on conventionallters such as Chebyshev IIR filter [13], adaptive noise cancellerANC), and autocorrelation method [14]. The conventional filtersre limited to suppress the noise which is out of the frequencyand of the signal components. On the other hand, ANC basedlgorithms such as least mean square (LMS) [15,16], suppress theoise in an adaptive manner and, hence, suppress in-band noises well. The major drawback of the ANC algorithms is that theyeed reference (noise source) signal, which is not available in mostases of the real-life scenarios. Manikandan and Soman [14], pro-osed a computationally efficient denoising algorithm based on

ag-1 autocorrelation method [14]. However, performance of theselgorithms significantly degrades as the level of noise increases.

In the frequency domain based denoising algorithms, the timeomain signal is first transformed into the frequency domain using

specific transform function such as Fourier transform and waveletransform (WT), and then the transformed signal is processed. Anal-sis of the PCG signal in frequency domain provides the informationbout spectral characteristics of the components presented in theignal and, hence, more efficiency in noise removal can be obtaineds compared to the time domain. Sanei et. al. proposed an approacho separate the murmurs from the PCG signal using singular spec-rum analysis [11]. In another approach, murmurs were removedrom the PCG signal using constrained tunable-Q wavelet transform17]. However, both the algorithms require high computationalime.

The most widely used method for the denoising of the PCG sig-al is based on the DWT [8,18,19] due to the fact that the DWToefficients of the PCG signal components will be large and theyill be confined to specific frequency band, while the coefficients

or the noise components will have small amplitude and scatteredn different frequency bands [20]. Thus, denoising can be achievedy suppressing the small coefficients. However, the performancef the DWT based denoising algorithm significantly depends onhe choice of the parameters: (1) Mother wavelet, (2) Number ofecomposition levels and the levels to be processed, (3) Thresholdalue, and (4) Threshold function [8].

For the denoising, mother wavelet should be orthogonal, whichllows perfect reconstruction of the signal [5]. For the PCG sig-al denoising, various orthogonal wavelets have been suggesteduch as Coiflet [18,21], Symlet [12] and Daubechies [2,22]. In [4],hourasia et al. developed a new wavelet for PCG signal of a foetus.

The second parameter is the number of decomposition levels.he number of decomposition levels should be selected preciselyuch that the useful signal components and unwanted componentsie in different levels. The frequency range of each level depends onhe sampling frequency of the signal. As the sampling frequencyncreases the frequency range of particular level increases [23].herefore, different choices for a number of decomposition lev-ls are reported in the literature [5,8]. After the decomposition,evels to be processed should be chosen appropriately. In litera-ure, most of the algorithms processed all the decomposed levels5,8,21,24], which requires unnecessary high computation. In other

pproaches, the signal is reconstructed using coefficients at a fewelected levels, while discarding others [2,12,22]. These approachesemove only out-of-band noise. To suppress the in-band noise, theevels associated with the signal components should also be pro-

essing and Control 38 (2017) 388–399 389

cessed [18]. Researchers have also proposed algorithms for theappropriate selection of the levels based on the energy and fre-quency range of the PCG signal [25,26].

The third parameter, threshold value, plays a crucial role in DWTbased denoising. A large value of threshold affects the useful sig-nal components, while a low threshold value will be ineffective tosuppress the unwanted signal components [9]. For the PCG signal,mostly used threshold estimation methods are ‘rigrsure’ [4,18,27],‘heursure’ [5,8], ‘sqtwolog’ [24], and ‘minimaxi’ [8,21]. The ‘sqt-wolog’ is a fixed form method and does not take into account thecontent of the signal, but only depends on the length of the sig-nal [4]. It provides a threshold value larger than other methods andhence it may result into over thresholding. ‘minimaxi’ is also a fixedform threshold method, in which the threshold value is estimatedsuch that the maximum risk of estimation error is minimized [5].‘rigrsure’ method determines a threshold value to minimize theSteins unbiased risk estimation (SURE). ‘rigrsure’ and ‘minimaxi’methods estimates threshold value to minimize the risk estimationand results into low threshold value [28]. ‘heursure’ method selectsone of the methods from the ‘sqtwolog’ and ‘rigrsure’ methods,based on the comparison between the SURE estimation and SNR[5]. Naseri and Homaeinezhad [22] devised a threshold estimationmethod based on the weighted variance of the noise while Kumarand Saha [29] calculated the threshold as the 20% of the weightedmaximum energy of the coefficient vector. However, values ofparameters used in these methods were obtained heuristically.

The fourth parameter is the threshold function, which definesthe way to treat the wavelet coefficients using the estimatedthreshold value. Soft and hard are two existing threshold func-tions used extensively for the denoising of PCG signals [4,18,21].In soft threshold function, the coefficients lower than the thresh-old are replaced by zeros while other coefficients get shrank bythe threshold value [4]. In hard threshold function, the coefficientslower than the threshold are replaced by zeros, as in soft thresh-old, while larger coefficients remain unchanged. Hard thresholdfunction may cause discontinuities in the reconstructed signal andmake it oscillating [5]. In soft threshold function, shrinkage of thewavelet coefficients by threshold reduces the effect of singulari-ties and transients that cannot be addressed by the hard thresholdfunction [30]. However, hard threshold function produces largerSNR value than the soft threshold function. Zhao [27] proposeda generalized threshold function although it needs a selection ofparameter, which controls the performance of the algorithm.

To address the issues discussed above related to threshold esti-mation and threshold function, we propose a new DWT baseddenoising algorithm for the PCG signals. We used ‘Coif-5’ waveletas mother wavelet and performed five levels of decomposition ofthe PCG signal sampled at 2 kHz. When a signal with 2 kHz sam-pling frequency is decomposed, the 4th and 5th levels cover thefrequency range 31–125 Hz, approximately [31], and hence covermost of the frequency range of the S1 and S2, which is 25–120 Hz[31]. Therefore, in the proposed algorithm, only these two levelsare processed. Removal of the coefficients of lower detailed levelsalso removes the out-of-band noise. To further improve the per-formance of the denoising, we propose a novel adaptive thresholdestimation method using statistical properties of the DWT coef-ficients. The proposed method uses the domain knowledge thatthe sum of the length of the S1 and S2 remains less than 25% ofthe length of a cardiac cycle [32,33]. Therefore, a new parameter,med75 is calculated instead of traditional median value. The med75represents the 75th percentile value in the sorted absolute valuesof a coefficient vector in ascending order. Further, to address the

issue of threshold function, we also propose a new method calledas ‘non-linear mid’ function for the PCG signal. Furthermore, itsparameters are optimized using the genetic algorithm, to improve

390 P.K. Jain, A.K. Tiwari / Biomedical Signal Processing and Control 38 (2017) 388–399

DWT based denoising algorithm.

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ts performance for the PCG signals. Thus, the proposed algorithmdaptively shrinks the wavelet coefficients of the PCG signal.

Rest of the paper is organised as follow; The proposed denois-ng algorithm is described in Section 2. The obtained results of theroposed method and its comparison with state-of-the-art meth-ds are discussed in Section 3. Section 4 concludes the result of theaper.

. Methodology

The proposed algorithm calculates a threshold value adaptivelynd the same is applied to the wavelet coefficients of selected levels.he proposed algorithm performs in three steps as described below.

.1. Decomposition of the signal

The first step in DWT based denoising is the decompositionf the signal into approximation (A) and detailed (D) coefficients.hese coefficients can be obtained by applying analysis filters: lowass filter (H) and high pass filter (G). To obtain the coefficients atext level, the output of the lowpass filter, called as approxima-ion coefficients, and output of highpass filter, called as detailedoefficients, are decimated by a factor of two and then both thenalysis filters are applied to the decimated approximation coeffi-ients. These two steps are applied recursively to obtain coefficientst higher levels, as shown in Fig. 1. This decomposition algorithms called as Mallat algorithm and the constructed tree is called as

allat decomposition tree [34].In the proposed algorithm, ‘Coif-5’ wavelet is chosen as mother

avelet because it gives better performance for the denoising ofCG signal as compared to other wavelets [8,5,21]. Using the ‘Coif-5’avelet, the signal is decomposed up to five levels. Decomposi-

ion of the signal with 2 kHz sampling frequency will result intove detailed levels (500–1000, 250–500, 125–250, 62–125, and1–62 Hz) and one approximation level (0–31 Hz) [31]. Thus, theth and 5th detailed levels cover most of the frequency range ofHS, which is typically 25–120 Hz [31] and hence FHS are promi-ently present in these two levels, as shown in Fig. 2. Therefore,nly these two levels are processed further while other detailedevel coefficients and approximation coefficients are discarded.on-inclusion of lower level detailed coefficients also suppress theurmurs from the signal because frequency range of most of theurmurs is higher than the frequency range of S1 and S2 [35]. The

uppression of the murmurs is required to emphasize the S1 and

2. However, the characteristic features of the murmur are neededor the diagnosis of the heart valve diseases. Hence, these featuresill be required and same can be extracted after the PCG signal is

egmented into cardiac cycles.

Fig. 2. Reconstructed signal at various detailed levels and approximation level.

2.2. Thresholding of the coefficients

The second step is thresholding of the wavelet coefficients, inwhich the coefficients are modified based on a threshold value.Generally, thresholding of the coefficients is performed in threesteps [8], described in following subsections.

2.2.1. Estimation of the thresholdAs stated in the introduction section, the existing methods are

either not adaptive to the SNR of the signal or try to minimize therisk for the worst case. The threshold value should be a function ofthe SNR of the signal so that the noise can be suppressed efficientlywithout, or minimally, affecting the useful signal components. Inview of this requirement, a novel method of threshold estimationbased on characteristics of the PCG signal is proposed and given asfollows.

In this method, a new parameter is obtained to estimate thenoise level based on the time domain information of the heartsound signal. A detailed time-domain analysis of multiple PCG sig-nals is provided in [31]. According to it, the sum of time durationof S1 and S2 remains less than 25% of the time duration of a cardiac

cycle. Same observations are also reported in [32,33] for normaland various pathological cases. Thus, 75th percentile value of theabsolute values of the signal, sorted in ascending order, indicatesthe level of noise present in the signal, as shown in Fig. 3(a). Fur-

P.K. Jain, A.K. Tiwari / Biomedical Signal Processing and Control 38 (2017) 388–399 391

Fig. 3. Statistical parameters for the signal with added white Gaussian noise: (a) med75 at two different SNR values and (b) med75 and median values at various SNR values.

F in three different cases (a) Low level of noise, (b) Moderate level of noise, and (c) Highlyn

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ig. 4. Statistical parameter analysis for the wavelet coefficients (detailed level-4)

oisy.

hermore, the 75th percentile value gives effective indication of theoise level as compared to the 50th percentile value (median), ashown in Fig. 3(b). Therefore, we propose a new variable med75,hich represents 75th percentile value of the sorted absolute

alues of coefficient vector in ascending order, and used for thestimation of the threshold value.

Fig. 4 provides the analysis of the med75 parameter andtatistical parameters, mean (m = mean(|Dj|)) and variance (v =ariance(|Dj|)), of the absolute of the coefficient vector (Dj) con-aminated with noise at three different levels, low, moderate, andigh. As shown in the figure, in the first case, when the med75 is

ower than the variance (v) and mean (m), the noise level is veryow and therefore the threshold value should be low. In this case,he difference between the med75 and variance (v) is proportionalo SNR of the signal, as shown in Fig. 5. The second case, when theed75 is larger than the variance (v) and smaller than the mean (m),

epresents a signal contaminated with a moderate level of noise. Inhe third case, where noise level is very high, the med75 is largerhan the mean (m) and variance (v) both. Therefore, the thresholdalue should be high. In this case, as shown in Fig. 5, difference

etween the med75 and mean (m) increases with decrease in SNR.ased on these observations of relationship between three param-

Fig. 5. Statistical parameters (mean, Med75, and variance) of the wavelet coefficients(detailed level-4) of signal contaminated with white Gaussian noise at various levels.

eters, mean (m), med75, and variance (v), the threshold estimationis proposed as follows:⎧⎪⎪⎪⎨med75 × [1 − (v − med75)] if (med75 < v) Case : 1

T =⎪⎪⎪⎩med75

if ((med75 > v)

&&(med75 < m))Case : 2

med75 + (med75 − m) if (med75 > m) Case : 3

(1)

392 P.K. Jain, A.K. Tiwari / Biomedical Signal Processing and Control 38 (2017) 388–399

, mid,

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Fig. 6. Output response of the soft, hard

In the first case, the threshold is obtained by multiplying med75nd (1 − (v − med75)), as given in Eq. (1), to obtain a small valuef threshold. In this case, the multiplying factor (1 − (v − med75))ill increase with decrease in SNR and consequentially the thresh-

ld value will increase. As the value of med75 reaches close tohe variance (v), the multiplying factor tends to be one and hencehreshold becomes close to med75 value. In the second case, thehreshold value is set equal to the med75. As the level of noisencreases further, the med75 will also increase (shown in Fig. 5)nd consequentially the threshold value will increase. In the thirdase where threshold value should be high, difference between theed75 and mean (m) increases with decrease in SNR, as discussed

bove. Therefore, the threshold is obtained by summing the med75nd the difference of the med75 and mean (m), as given in Eq. (1).

.2.2. Threshold rescalingAfter the estimation of the threshold value, it is rescaled accord-

ng to the level of noise present in the signal. The Multiple-scaleependent (mln) [36] rescaling approach is used to rescale the esti-ated threshold value T. According to it, the variance of noise is

stimated for each level and the threshold value is rescaled i.e. mul-iplied by the variance of the noise. Since the noise variance (�) isnknown in most cases, it is estimated as follow [4]:

ˆ = MAD{Dj[n]}0.6745

(2)

here MAD{Dj} represents median of absolute value of detail coef-cients at level j.

.2.3. Applying threshold to the coefficientsThe third step is to apply the scaled threshold value to the

avelet coefficients using a threshold function. Mostly used thresh-ld functions for the PCG signal are ‘soft’ and ‘hard’ functions [30].s discussed in Section 1, the hard function produces larger SNRalue than the soft function. However, the hard function may causeiscontinuities in the denoised signal. To overcome these short-omings, another threshold function, called as mid function [37] isxplored to use for the PCG signals. As shown in Fig. 6, it uses twohreshold values, T1 and T2, given as follow:

1 = × T (3)

2 = × T (4)

he wavelet coefficients are treated in three partitions: (1) retainhe coefficients with large values unchanged, (2) coefficients with

and non-linear mid threshold functions.

small values are set to zero, and (3) linearly shrink moderate valuecoefficients by the threshold, as follow:

DTj [k]mid

=

⎧⎪⎨⎪⎩

Dj[k] if |Dj[k]| > T2

sign(Dj[k])(|Dj[k]| − T1) if T1 ≤ |Dj[k]| ≤ T2

0 if |Dj[k]| < T1

(5)

Thus, this threshold function overcomes the issue of soft thresh-old function by retaining large coefficients without change, whilereduces the issue of discontinuities by linearly shrinking of themiddle coefficients. However, the mid function also contains dis-continuities as in case of soft and hard functions. To resolve thisissue of the ‘mid’ function, the linear behaviour of the function inthe range of T1 to T2 is transformed into the non-linear behaviourto form a ‘non-linear mid’ function as follows:

DTj [k] =

non−linear mid

⎧⎪⎨⎪⎩

Dj[k] if |Dj[k]| > T2

Dj[k]3/T22 if T1 ≤ |Dj[k]| ≤ T2

0 if |Dj[k]| < T1

(6)

2.2.4. Optimisation of parameters and ˇIn [37], value of was set to one and value of was set to two.

In this work, the values of and parameters are optimised toimprove the performance of the ‘non-linear mid’ threshold functionfor the PCG signal. For the optimization, the genetic algorithm (GA)is used because it is found to be more effective in global optimiza-tion [38]. The GA is an adaptive heuristic search algorithm basedon the evolutionary ideas of natural selection in which strongerindividuals are likely be the winners in a competing environment[39]. The algorithm repeatedly modifies a population of individualsolutions and, over successive generations, the population evolvestoward an optimal solution [39]. The algorithm is implementedwith the help of Matlab® (MathWorks) global optimization tool-box. The objective function is to minimize the mean square errorbetween the coefficients of clean signal and the thresholded coef-ficients, as follow:

E = 1N

N∑n=1

[Dclean

j (n) − DTj (n)]2

(7)

where N is the length of vector, Dcleanj

is a coefficient vector of jth

level of the clean signal, and DTj

is thresholded coefficient vectorof jth level of the noisy signal. In addition to optimization usingGA, experiments were performed on the signal contaminated withvarious types of simulated noise including white Gaussian, red, and

pink noise models. Based on the obtained results of optimisationby the Genetic algorithm and experiments, the value of is foundto be one for all noise levels. This was an expected value as thecoefficients having an amplitude smaller than the threshold value

l Processing and Control 38 (2017) 388–399 393

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P.K. Jain, A.K. Tiwari / Biomedical Signa

T) should be zero and this will happen with = 1, as this can beeen from (2). On the other hand, the value of is obtained to be aunction of noise level. This is given as follows:

={

1.3 med75 ≤ v

1.4 med75 > v(8)

n case of low noise (med75 ≤ v), the value of should be low. Wexpected the value of to be large for high noise case. However,ince the value of estimated threshold (T) itself is large, the opti-um value of the second threshold (T2 = × T) is obtained at aoderate value of (in this case 1.4), as against 2 given in [37].

.3. Reconstruction of the signal

After thresholding of the coefficients, the signal is reconstructedrom the thresholded coefficients. To reconstruct, the highest leveletailed and approximation coefficients are up-sampled by twond passed through the high pass filter (G) and low pass filter (H),espectively [34]. The summation of the outputs of these two filtersesults into approximation coefficients for the next level recon-truction, as shown in Fig. 1. G and H are called as synthesis filtersnd they are orthogonal to the analysis filters. The synthesis filtersave relation with the analysis filters such that all four filters, twonalysis filters and two synthesis filters, form quadrature mirrorlters [4].

In the proposed method, detailed coefficients at level 4thnd 5th are thresholded according to the proposed thresholdingethod, as discussed previously. The coefficients at detailed levels

st, 2nd, and 3rd and the approximation coefficients are made zero.hus, the reconstructed signal contains the signal corresponding tohe thresholded coefficients at 4th and 5th levels.

. Results and discussion

Experiments are performed on the PCG signal contaminatedith simulated white Gaussian noise, and presented in Section 3.1.

or the noise simulation, pink and red noise models are also con-idered because Gradolewski and Redlarski [8] observed that theharacteristics of real-life noise are similar to pink and red noises.btained results for these noises are presented in Section 3.2. Fur-

hermore, the performance of the proposed method is also analysedn the PCG signal acquired in real-life noisy scenarios, and pre-ented in Section 3.3. To show the efficacy of the method to removehe murmur sounds, it is applied to various pathological signalsbtained from publicly available database [40].

Performance evaluation indices: For the quantitative evalua-ion of the methods, following three parameters are used.

(A) Signal-to-noise ratio (SNR): SNR is most commonly usedarameter to evaluate the performance of denoising algorithms.he expression for SNR is given as follows [8]:

NRdB = 10 × log10

(Signal power

Noise power

)(9)

(B) Fit coefficient: Fit coefficient, proposed in [8] for the perfor-ance evaluation of denoising algorithm for PCG signals, shows if

he information about subject’s health is preserved. It is obtaineds follows:

fit = 100 ×

(1 −

∑N

i=1[f2(i) − f 1(i)]2

∑N

i=1

[f1(i) − (1/N)

∑N

j=1f1(j)]2)

(10)

here f1 is clean signal and f2 is the denoised signal. This coeffi-ient indicates the difference in morphology of the denoised signal2 with respect to the clean signal f1. Basically, it is a normalizedoefficient of determination in the range of 0% to 100% [41]. It is

Fig. 7. Peak detection and identification: (a) PCG signal, and (b) envelope of thesignal with identified components.

used in the statistical model analysis to assess goodness of fit ofa model. The value of fit will be 0% when signals are mismatchedand the information is lost, and 100% when there is a perfect matchbetween the signals.

(C) Detection rate of S1 and S2: To show the diagnostic signif-icance of the method, the detection rate of the FHS, S1 and S2,are obtained. The detection rate shows the percentage of correctlydetected components in the denoised signal using a particularmethod. Detection of components is achieved by a threshold-basedpeak finding algorithm presented in [42]. Fig. 7 shows the PCGsignal, its envelope extracted using normalized average Shannonenergy, and the components detected by the algorithm [42].

A number of false detected components are also obtained. Asmall number of false components with high detection rates of S1and S2 show that the method is efficient to suppress the noise. If thenumber of false components is low and detection rate of the com-ponents is also low, it means the threshold value is high and thusresulted into over thresholding. On the other hand, a large num-ber of false points show the inefficacy of the threshold method tosuppress the noise.

Database used for experiments: The experimental results areobtained using two datasets of PCG signals. First is taken fromthe eGeneralMedical [40], which includes PCG signal for normaland various pathological cases. This dataset does not include thePCG signals contaminated with real life noise. Therefore, a seconddataset is created by acquiring PCG signals from ten subjects in clin-ical and noisy environments, each for 20 seconds duration. For boththe datasets, the sampling frequency is set to 2 kHz. The samplingrate of 2 kHz is sufficient for the PCG signal because its fundamentalcomponents and pathological sounds, murmurs, lie below 800 Hzfrequency [7,8].

The proposed threshold estimation method uses med75, as dis-cussed in previous section, to measure the level of noise in thesignal. To be effective of med75, the signal under considerationshould cover at least one cardiac cycle. Therefore, in the proposedmethod, the signal is segmented into non-overlapping windowsand the length of the window is set to 2 seconds. This length willcover the one cardiac cycle until the heart rate does not go less than30 beats per minute.

State-of-the-art methods: Performance of the proposedmethod is compared with the performance of DWT based denois-ing methods reported in literature [5,8,21]. Messer et al. [5], andGradolewski and Redlarski [8] performed experiments to deter-mine the optimum parameters of DWT for denoising of the PCGsignals. Based on the experimentally determined optimum param-eters, for the comparison, we used ‘Coif-5’ as mother wavelet, ‘mln’as rescaling method and following two combinations of thresholdestimation methods and threshold function.

DWT-A: ‘rigrsure’ threshold with soft threshold function.DWT-B: ‘minimaxi’ threshold with hard threshold function.

394 P.K. Jain, A.K. Tiwari / Biomedical Signal Processing and Control 38 (2017) 388–399

F with

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ig. 8. Denoising results for soft, hard, mid, and non-linear mid threshold functionsheursure’, (d) ‘minimaxi’, (e) and (f) proposed threshold estimation method.

Approximation coefficients were discarded because they areut-of-frequency band of FHS, as observed in Fig. 2.

.1. Results for the PCG signal with added white Gaussian noise

Although white Gaussian noise characteristics were notbserved in real-life noise [8], the proposed method is applied to theCG signal with Additive White Gaussian Noise (AWGN) to analysets efficacy to suppress it. Experiments were performed on the PCGignals acquired from 10 subjects. These signals were acquired in

clinical scenario and then multiple instances of white Gaussianoise were added at various input SNR. The obtained qualitativeesults using various methods, at −4.63 dB SNR, are shown in Fig. 8.his SNR value is obtained when the white Gaussian noise is addedith 10 dB SNR per sample to the signal using MATLAB® (Math-orks). The obtained quantitative results are provided in terms of

NR and fit values in Table 1 as mean ± standard deviation, and inerms of detection rates in Fig. 9, for all subjects at various levels ofNR.

Results of the proposed threshold estimation method withhreshold functions including soft, hard, mid and proposed mid arenalysed and compared with all four threshold estimation methods‘sqtwolog’, ‘rigrsure’, ‘heursure’, and ‘minimaxi’), separately.

Soft threshold function: The proposed threshold estimationethod and all the four methods with soft threshold function are

pplied to the PCG signal with AWGN. From Fig. 8(a)–(e), it can bebserved that the proposed threshold estimation method is out-erforming all popular methods. ‘rigrsure’ and ‘heursure’ are alsoroviding satisfactory results with soft threshold function, while

sqtwolog’ method results into over thresholding.From Table 1, it can be observed that the SNR values are higher

f the denoised signal using the proposed threshold estimationethod compared to other methods. The same result can also be

bserved for the fit coefficient. At a low level of noise (SNR >0.38 dB),heursure’ method is giving similar performances as that of the pro-osed method. On the other hand, at a high level of noise (SNR0.38 dB), ‘rigrsure’ method is producing higher SNR and fit valueshan the ‘heursure’ method.

Hard threshold function: Similarly, experiments are per-ormed with hard threshold function. From Fig. 8(a)–(e), it cane observed that the proposed threshold estimation method out-erforms competitive methods. However, the denoised signal has

various thresholds estimated by different methods: (a) ‘sqtwolog’, (b) ‘rigrsure’, (c)

discontinuities, which is expected in the case of hard thresholdfunction. Fig. 8(a), in particular, shows that ‘sqtwolog’ suppressedthe noise significantly. However, it results into over thresholdingand consequentially, PCG signal’s useful components also got sup-pressed.

As shown in Table 1, at a high level of noise (SNR <5.42 dB) theproposed method is producing highest SNR values when comparedto state-of-the-art methods. However, at low level of noise (up to5.42 dB), ‘sqtwolog’ method is producing highest SNR values amongall methods. But, ‘sqtwolog’ may suppress the heart sound compo-nents and it may lead to wrong diagnosis [8]. Higher fit values forthe proposed threshold estimation method also demonstrates thesuperiority of it over the compared methods.

In the comparison of soft and hard threshold functions, the hardfunction produces higher SNR and fit values than the soft function.However, the result of the hard function contains few noise compo-nents. These results are in line with the reported works in literature[30].

Mid and proposed non-linear mid threshold functions: Theresults are obtained using the proposed threshold estimationmethod with mid and proposed non-linear mid threshold func-tions separately, and plotted in Fig. 8(f). From the figure, it can beobserved that the threshold value obtained by the proposed thresh-old estimation method with the mid function suppresses the noiseeffectively. The quantitative effectiveness of the proposed thresh-old estimation method in terms of SNR and Fit values can be foundin Table 1. From the table, it can be observed that the proposedthreshold estimation method with mid function produces higherSNR and fit values when compared to the values obtained using thesoft and hard functions. These observations show that the mid func-tion overcomes the issues related to both soft and hard thresholdfunctions. The proposed threshold estimation method also ensuresthat there is no significant loss in PCG signal components and hencediagnostic information present in the signal are preserved. How-ever, there is some loss of information due to the use of the midfunction [37], as can be seen in Fig. 8(f) at time instant 2.7 sec, S2component is suppressed. This loss of S2 is because the value of

(two as in [37]) is high and consequentially the upper limit (T2)

of coefficient shrinking is also high. This issue is addressed in theproposed non-linear mid threshold function by tuning the param-eter ˇ, hence the results are improved as shown in Fig. 8(f), secondcolumn.

P.K. Jain, A.K. Tiwari / Biomedical Signal Processing and Control 38 (2017) 388–399 395

Table 1Obtained SNR (in dB) of the denoised PCG signals (average of 10 instance ± standard deviation) contaminated with simulated white Gaussian noise.

SNR due to addition of AWGN SNR after denoising (dB) Fit coefficient (%)

10.38 ± 0.04 5.42 ± 0.05 0.38 ± 0.04 −4.63 ± 0.04 10.38 ± 0.04 5.42 ± 0.05 0.38 ± 0.04 −4.63 ± 0.04

Soft threshold functionsqtwolog 12.74 ± 0.16 8.30 ± 0.25 3.97 ± 0.20 0.76 ± 0.11 99.76 ± 0.02 97.96 ± 0.09 84.83 ± 0.13 31.56 ± 0.26rigrsure 16.35 ± 0.27 11.91 ± 0.17 7.26 ± 0.25 2.78 ± 0.43 99.96 ± 0.01 99.75 ± 0.03 97.73 ± 0.04 78.55 ± 0.31heursure 16.44 ± 0.26 12.08 ± 0.26 7.53 ± 0.20 2.59 ± 0.23 99.97 ± 0.01 99.76 ± 0.01 97.49 ± 0.03 73.30 ± 0.26minimaxi 14.41 ± 0.17 10.02 ± 0.27 5.61 ± 0.21 1.85 ± 0.14 99.89 ± 0.01 99.11 ± 0.01 92.94 ± 0.05 60.17 ± 0.25Proposed 16.54 ± 0.24 12.18 ± 0.26 7.59 ± 0.18 3.07 ± 0.21 99.97 ± 0.01 99.75 ± 0.01 97.66 ± 0.06 82.59 ± 0.23

Hard threshold functionsqtwolog 19.13 ± 0.18 14.80 ± 0.26 8.11 ± 0.33 2.33 ± 0.35 99.98 ± 0.00 99.88 ± 0.01 97.37 ± 0.02 62.11 ± 0.41rigrsure 14.79 ± 0.45 9.84 ± 0.46 4.99 ± 0.43 1.14 ± 0.75 99.95 ± 0.01 99.51 ± 0.03 95.19 ± 0.15 54.65 ± 0.21heursure 15.34 ± 0.46 10.61 ± 0.28 5.99 ± 0.55 1.95 ± 0.50 99.96 ± 0.01 99.69 ± 0.02 96.86 ± 0.10 65.18 ± 0.19minimaxi 17.72 ± 0.32 13.09 ± 0.25 7.96 ± 0.40 2.48 ± 0.40 99.97 ± 0.01 99.74 ± 0.07 97.15 ± 0.18 67.13 ± 0.22Proposed 18.54 ± 0.37 14.47 ± 0.37 8.86 ± 0.43 3.43 ± 0.25 99.98 ± 0.01 99.88 ± 0.01 98.14 ± 0.03 82.77 ± 0.13

Mid threshold functionProposed 19.05 ± 0.19 14.86 ± 0.21 8.98 ± 0.18 3.52 ± 0.27 99.98 ± 0.01 99.89 ± 0.01 98.32 ± 0.08 83.09 ± 0.24

Proposed non-linear mid threshold functionProposed 19.18 ± 0.21 14.89 ± 0.25 9.51 ± 0.37 4.03 ± 0.15 99.98 ± 0.01 99.89 ± 0.02 98.61 ± 0.09 85.09 ± 0.21

Bold values indicates the maximum value in the respective column. The boldness is used to highlight the maximum values obtained using the proposed method.

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Fig. 9. Results for PCG signals of different subjects with AWGN: (a) D

The figure depicts that the proposed method (proposed thresh-ld estimation method with proposed non-linear mid function) isble to suppress the noise from the PCG signal with AWGN at lowNR −4.63 dB. The SNR and fit values obtained using the proposedethod given in Table 1, are highest among all the methods. There

s a significant improvement in SNR and fit values for the proposedethod at higher level of noise.Same results are also observed for the detection rate of S1 and

2 using the proposed method, as shown in Fig. 9(a and b). Detectedumber of false points is also lowest among all methods (as shown

n Fig. 9). These results show the diagnostic superiority of the pro-osed method over state-of-the-art methods.

.2. Results in case of pink and red noise

The proposed method is also applied to the PCG signals con-aminated with simulated pink noise and red noise, generatedhrough MATLAB® code created by Hristo Zhivomirov [43]. Thebtained denoised signals are given in Fig. 10. The figure showshe superiority of the proposed method over state-of-art meth-ds. To quantify the results, in addition to the waveforms givenn Fig. 10, we obtained SNR and fit values of the denoised signal atarious noise levels as shown in Fig. 11. The figure elucidates thathe proposed method significantly improves the SNR values of theenoised signal and produces higher fit values. Furthermore, as inhe case of AWGN, our methods gives higher detection rates of S1

nd S2, as shown in Fig. 12, and at the same time, gives lower num-er of false points. It shows that the proposed method is efficient touppress the pink and red noises, which have similar characteristicso real-life noise.

on rate of S1, (b) Detection rate of S2, and (c) Number of false points.

3.3. Results for the PCG signal recorded in noisy scenarios

As discussed in Section 1, the PCG signal is vulnerable to variousnoises generated in real-life scenarios. Therefore, it is of paramountimportance to analyse the efficacy of the proposed method undersuch scenarios. For this purpose, PCG signals are recorded fromdifferent subjects when they were moving and speaking, whileworking in an office where there were other sources of noise suchas noise due to other person’s talking. Fig. 13 shows qualitative,and Table 2 gives quantitative performance evaluation of results ofthe proposed method as compared to the state-of-art methods. Thefigure shows the performance superiority of the proposed methodover the compared methods. The detection rate of S1 and S2, andnumber of false points are presented in Table 2. The numbersquantify the efficacy of the proposed method over state-of-the-artmethods.

3.4. Results for PCG signal with murmur sound

In order to evaluate the efficacy of the proposed method’s abil-ity to emphasize the S1 and S2 in the presence of murmurs, dataset[40] comprising of variety of murmur cases was used in the experi-ments. Fig. 14 shows the obtained results of denoising using variousmethods for few cases of murmurs. From the figure, it can beobserved that the proposed method suppressed the murmurs sig-nificantly in all cases. As expected, this improved the accuracy of thesegmentation as shown in Table 3. However, in the case of aorticstenosis, mitral valve prolapse, pulmonary stenosis and tricuspid

regurgitation, few components were undetected and hence falsepoints are observed. This is because the murmurs significantly over-lap the frequency range of the FHS. In these cases, the signal needsto be decomposed into narrow frequency bands.

396 P.K. Jain, A.K. Tiwari / Biomedical Signal Processing and Control 38 (2017) 388–399

Fig. 10. Obtained denoising results for the PCG signal contaminated with pink and red noise: (a) Clean signal, (b) Noisy signal, (c) DWT-A, (d) DWT-B, and (e) Proposedmethod.

Fig. 11. SNR and fit values for the denoised PCG signal contaminated with pink and red noise.

Fig. 12. Detection rate of S1 and S2 and number of false points in the denoised PCG signal contaminated with pink and red noise.

P.K. Jain, A.K. Tiwari / Biomedical Signal Processing and Control 38 (2017) 388–399 397

Fig. 13. Denoising results for the recorded PCG signal (a) in noise scenario using various methods: (b) DWT-A, (c) DWT-B, and (d) Proposed method.

Table 2Result for the PCG signals contaminated with noise generated in real-life scenarios.

S. No. Heart rate % Of S1 detection % Of S2 detection False points

DWT-A DWT-B Proposed DWT-A DWT-B Proposed DWT-A DWT-B Proposed

1 68 100 100 100 100 90.9 100 1 0 02 69 90.9 90.9 100 81.8 72.7 90.9 4 6 13 71 100 100 100 91.6 100 100 2 0 04 74 91.6 91.6 100 75 83.3 91.6 4 4 25 74 100 100 100 91.6 83.3 100 1 4 16 76 92.3 92.3 100 76.9 84.6 92.3 4 3 07 78 100 100 100 92.3 84.6 100 3 5 18 81 100 100 100 100 92.8 100 0 1 09 84 93.3 93.3 100 80 73.3 100 4 7 010 88 93.3 93.3 93.3 66.6 73.3 86.6 7 5 2

Fig. 14. Results of various methods to remove murmurs from the PCG signal; (a) murmur signal, (b) DWT-A method, (c) DWT-B method, and (d) Proposed method.

398 P.K. Jain, A.K. Tiwari / Biomedical Signal Processing and Control 38 (2017) 388–399

Table 3Result for PCG signal with murmur.

Murmur Number of cases (cycles) % Of S1 detection % Of S2 detection False points

DWT A DWT B Proposed DWT A DWT B Proposed DWT A DWT-B Proposed

Aortic stenosis 6 (45) 100 100 100 88.8 88.8 100 28 28 4Aortic insufficiency 1 (6) 100 100 100 100 100 100 1 2 0Mitral stenosis 1 (8) 100 100 100 100 100 100 0 0 0Aortic regurgitation 1 (6) 100 100 100 100 100 100 4 4 0Physiology split S2 1 (4) 100 100 100 100 100 100 0 0 0Pulmonary regurgitation 1 (7) 100 100 100 100 100 100 7 7 0tricuspid stenosis 1 (4) 100 100 100 100 100 100 0 0 0Wide split S2 3 (15) 100 100 100 100 100 100 0 0 0Ejection click 3 (18) 100 100 100 100 100 100 0 0 0Opening snap 1 (6) 100 100 100 100 100 100 3 3 0Mitral valve prolapse 5 (29) 55.1 55.1 100 82.7 82.7 96.5 28 26 14

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Mitral regurgitation 2 (19) 100 100

Pulmonary stenosis 2 (19) 68.4 68.4

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. Conclusions

In this paper, we have proposed a new threshold estimationethod for the DWT based denoising of the heart sound signal. For

he estimation of the threshold value, the proposed method useshe domain knowledge about the heart sound signal that the sum ofhe length of the S1 and S2 remains less than 25% of the length of aardiac cycle. We also proposed non-linear mid threshold functionnd optimised its parameter for the PCG signal. The performancef the proposed method is analysed for various types of simulatedoise including white Gaussian noise, pink noise, and red noise.erformance is also compared in various scenarios of real-life noise.he obtained results show that the proposed method outperformshe state-of-the-art methods. The obtained results also show thathe proposed method is able to emphasize the S1 and S2 in theresence of murmurs as well. Although, in few cases of murmurshen the murmur overlaps the FHS significantly, the proposedethod needs improvisation. Therefore, the future work includes

he decomposition of the signal into fine-tuned narrow frequencyands.

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