Comparison of Wavelet Types and Thresholding Methods on Wavelet Based Denoising of Heart Sounds

doi:10.4236/jsip.2013.43B029

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Journal of Signal and Information Processing, 2013, 4, 164-167

doi:10.4236/jsip.2013.43B029 Published Online August 2013 (http://www.scirp.org/journal/jsip)

Comparison of Wavelet Types and Thresholding Methods

on Wavelet Based Denoising of Heart Sounds

Burhan Ergen

Department of Computer Engineering, Firat University, Elazig, Turkey.

Email: [email protected]

Received April, 2013.

ABSTRACT

This paper focuses on the denoising of phonocardiogram (PCG) signals by means of discrete wavelet transform (DWT)

using different wavelets and noise level estimation methods. The signal obtained by denoising from PCG signal con-

taminated white noise and the original PCG signal is compared to determine the appropriate parameters for denoising.

The comparison is evaluated in terms of signal to noise ratio (SNR) before and after denoising . The results showed that

the decomposition lev el is the most important parameter determining the denoising quality.

Keywords: Discrete Wavelet Transform; Denoising; PCG

1. Introduction

The structural defects of the heart are often reflected on

the acoustical vibrations produced as a result of the me-

chanical action of the heart. The proper analysis of heart

sound allows non-invasive detection of coronary artery

stenosis, and valve disorders causing the heart murmurs

[1]. It is possible a computer aided detection of the ab-

normalities by means of processing and analyzing of the

acoustical vibration [2]. A record of the acoustical vibra-

tions acquired by means of microphones, called phono-

cardiogram (PCG), consist of the heart sounds and the

murmurs. While the heart sounds are produced opening

and closing of the heart valves, the murmurs are pro-

duced by the turbulence of blood flow.

The heart sounds have low frequency components, and

the murmurs are high frequency signals occurring gener-

ally between heart sounds. The murmurs can be com-

monly heard in abnormal cardiovascular cases. The fre-

quency components of a PCG signal may achieve around

1 KHz, which seen particularly in abnormal patient due

to the murmurs. On contrary healthy person, the fre-

quency components can exist above 300 Hz in diseased

patients. In normal patients, the spectral energy exists in

the interval of 100 and 200Hz, and rarely reaches up

300Hz [3].

This noise decreases the performance of visual and

computerized analysis. The respiration sounds by lung

mechanical actions, patient movement, and improper

contacts of microphone to the skin, and external noises

from the environments are also added as noise signal into

PCG records. The traditional method to remove the noise

from a PCG signal is to use a low or band pass filter with

cut off frequencies. However the filtering techniques are

able to remove a relevant of the noise, they are incapable

if the noise in the band of the signal to be analyzed.

In the present study, we performed the discrete wave-

let transform (DWT) to overcome the limitations of the

traditional methods. The denoising based on DWT is

consist of three steps; decomposition of the signal, thre-

sholding and reconstruction of the signal. Hard and soft

thresholding approaches are usually applied to eliminate

of small coefficient in denoi sing process.

In the hard thresholding, the wavelet coefficient below

a give value are stetted to zero, while in soft thresholding

the wavelet coefficient are reduced be a quantity to the

thresh value. The thresh old value is the estimation of th e

noise level, which is generally calculated from the stan-

dard derivation of the detail coefficient. The given signal

is decomposed on to a set of orthonormal wavelet func-

tion that constitutes a wavelet basis. The most known

wavelets providing the ortogonality properties are Du-

bechies, Symlets, Coiflets and Discrete Meyer to provide

reconstruction using the fast algorithms.

The result of the DWT is a multilevel decomposition,

in which the signal is decomposed in ‘approximation’

and ‘detail’ coefficients at each level. This is made

through a process that is equivalent to low-pass and high

passes filtering, respectively [4]. DWT decomposition

leads to a tree structure as shown in Figure 1, where ap-

proximation and detail coefficients are presented.

Here, it is studied on the effects of wavelet types, de-

Comparison of Wavelet Types and Thresholding Methods on Wavelet Based Denoising of Heart Sounds 165

composition levels, thresholding techniques and noise

estimation method s.

AAx

AAAx DAAx

DAx

N/2

N/4

N/8

Figure 1. The approximation and the detailed coefficients in

the tree structure of the DWT.

2. Methods

2.1. Discrete Wavelet Transform

The wavelet transform is first introduced for the time-

frequency analysis of transient continuous signal, and

then extended to the theory of multi-resolution wavelet

transform using FIR filter approximation. The discrete

wavelets used in multi- res-

olution analysis constituting an orthonormal basis for

[5,6].

)2(2)( 2/

,ntt mm

nm  



)(

2L)(txis decomposed an different scale,

 









 













mk k

kLLkmm tkAtkDtx

1,, )()()()()(



(1)

where )(



is discrete analysis wavelet, and )(



is discrete scaling, is the detailed signal at scale

, and is the approximated signal at scale.

and is obtained using the scaling and

wavelet filters [4,8].

)(kDm

2(Dm

)(kALAL

)k)k(

)1(

)2(),(2)(

2/1

nh(-1)

nttng

nttnh

n









(2)

The wavelet coefficient can be computed by means of

a pyramid transfer algorithm. The algorithms refer to a

FIR filter bank with low-pass filter h, high-pass filter g,

and down sampling by a factor at each stage of the

filter bank [6]. Figure 1 shows the tree structure of DWT

decomposition for three levels.

2.2. Threshold Estimation

The main idea of the wavelet denoising to obtain the

ideal components of the signal from the noisy signal re-

quires the estimation of the noise level. There are many

possible approaches to the estimation of the noise level,

and a systematic investigation about their performance [8,

9]. In this work, four different threshold options were

applied to assess their effectiveness.

Rigresure is adoptive threshold selection using the

Stein’s unbiase d ri sk estimation criteria;

)loglog(2 2NNThValue



 (3)

where is the length of the signal, and



is the stan-

dard deviation of the noise. The latter is estimated from

the detail coefficient at the first level of signal decompo-

sition; 674.0/)(Dxmedian



Sqtwolog is defined as the universal threshold;

)(log2 NThValue e



 (4)

Heursure is the heuristic version that uses a mixture of

the previous rules.

Minimaxi is a threshold selection using the minmax

principle. A fixed threshold is selected to get the min-

mum of the maximum mean square error, obtained the

worst function in given set, when compared against a

ideal procedure.

2.3. Assessments for Comparison

The studies were made on a heart sounds contaminated at

a desired SNR level by white Gaussian noise. Measuring

the performance of the denoising method by calculation

of the residual SNR (SNR) gi ven as;



 



10 12

10log logn

SNR xnx n

















 (5)

where is the original sign al, is the denoised

signal. The comparison between the initial SNR and the

result SNR may be used as the performance indicator.

][nx ][nxdn

3. Experiments and Results

The assessments were made of the behavior of different

mother wavelets and four different threshold estimation

techniques in order to find the most reliable parameters

for DWT denoising of heart so unds. These hav e drowned

from the most used wavelet families, Daubechies, Sym-

lets, Coiflets, and Discrete Meyer.

The PCG signal was contaminated at SNR=5dB in or-

der to test the performance of the wavelets and the thre-

shold estimation techniques. A normal PCG signal gen-

erally contains only two heart sounds, first and second

heart sounds. Figure 2 illustrates a sample PCG signal,

the noisy signal, a denoised sample using DWT, and the

error between the original and the denoised PCG signals.

The frequency components of a normal PCG signals

can be rise up 200 Hz, and the energy of the most sig-

nificant components concentrates around the frequency

band 100 - 150 Hz. The frequency ban ds of the signal are

important in point of the denoising technique using DWT

approaches. Because the DWT approaches decomposes

Comparison of Wavelet Types and Thresholding Methods on Wavelet Based Denoising of Heart Sounds

166

the signal into frequency bands to eliminate the detail

components assumed as noise, the decomposition level

reflects directly on the frequency components that cause

the smoothed version of the signal.

(a) (b)

Figure 2. Wavelet denoising of a PCG signal, a) Original

signal, b) Noisy signal, c) Denoised signal, d) Error between

the original and the denoised signal.

The effected components are related to not only de-

composition level but also sampling frequency. The de-

composition level, l, influences the frequency bands by

dividing the sampling frequency respect to 2l. In our ex-

periments, choosing l=5 causes the proceeding of the

denoising process down to 150 Hz due to the sampling

frequency is 11.5 Hz.

Therefore, the most important factor determining the

SNR level is the depth of the decomposition. Table 1

presents the SNR results respect to the decomposition

level with by using symlet8 and rigresure estimation for

hard and soft tresholding. For the both tresholding tech-

niques, it is seen that the highest SNR values obtained

when the composition level is 5 due to the reason ex-

pressed above.

Table 1. SNR level respect to the depth of decomposition.

Level Hard Soft

1 8.1209 7.8843

2 11.1471 10.9218

3 14.3251 14.0031

4 17.2973 16.9275

5 20.1305 19.4396

6 13.2248 13.2472

7 12.1531 9.8726

8 10.8010 8.3255

9 10.4986 8.1632

10 10.4912 8.1593

The other parameters to obtain best SNR level are the

kind of the wavelet and the thresholding rule. Table 2

presents the SNR leve ls using different wavelet when the

decomposition level is 5. In Table 2, there is no signifi-

cant difference in SNR in terms of wavelet type s. Never-

theless, it is attracting that the mother wavelets having

high oscillation number produces better SNR results.

Table 2. SNR values respect to wavelet types (Rigrsure,

level = 5).

Wavelet Type Hard Soft

Daubechies2 16.5378 16.5057

Daubechies3 18.9391 18.8353

Daubechies4 19.8138 19.8002

Daubechies5 19.8747 19.7425

Symlet2 16.3487 16.4181

Symlet3 18.5401 18.7874

Symlet4 19.5732 19.8002

Symlet5 19.4795 19.5458

Coiflet1 16.7746 16.7658

Coiflet2 19.4866 19.4501

Coiflet 3 19.7812 19.6252

Discrete Meyer 19.9018 19.7154

It is attracting that the wavelets having higher oscilla-

tion frequency gives better SNR results. For example, the

symlet wavelet having eight oscillations in its mother

wavelet produces better SNR level than the lower ones.

The very lower oscillation frequency causes the lower

SNR results.

The estimation techniques show the same performance

for the level 5 respects to the initial SNR level. For the

comparison, the initial SNR level before denoising is

increased from 1dB to 30dB, and the result SNR level

after denoising is calculated using Equation (5). Figure 3

presents a comparison of the four noise estimation me-

thods for level 5 and 8 by using Symlet8.

We have observed no distinguishing evidence among

the noise level estimation methods until level 6. After

this level, rigresure method has produced better SNR

values. And it is observed that rigresure preserve the

second heart sound in PCG signals while the other me-

thods destroying. This situation is clearly seen in Figure

The signal part belonging to second heart sound taking

place at around 0.7 s in Figure 4 (a) cannot be seen in

the other figures. This also proves that the rigresure pre-

serve the main characteristic of the signal. Therefore, we

can conclude that the rigresure is the best noise estima-

tion method.

Comparison of Wavelet Types and Thresholding Methods on Wavelet Based Denoising of Heart Sounds

167

(a)

(b)

Figure 3. The SNR values after denoising before denoising

for level 5 and 8.

(a) (b)

Figure 4. The denoised signal using four different threshold

rules at eighth level.

4. Conclusions

The wavelet denoising techniques were studied on a

noised PCG signal in this work. The performances of

several variations of denoising including thresholding

rules and the type of wavelet were compared to produce

the best denoising results of the methods.

We conclude that reasonable decomposition level is

bsolutely depending on the sampling frequency and the

frequency band of the signal. Just in this study, the de-

composition level of 5 produced reasonable results be-

cause the frequency band of a normal PCG signal is

around 150 - 200 Hz and the sampling frequency is 11.5

KHz. Since the noise level method is one of the impor-

tant parameter in wavelet denoising, it is examined for

different levels. We have not seen any noteworthy dif-

ferences in the methods from level 1 to level 6. After this

level, rigresure method has showed superiority to the

other methods in terms of SNR level. Consequently, it is

determined that the wavelet type is not very important if

the oscillation number is not very low, th e decomposition

level is absolutely depends on the frequency band of the

PCG signal and its sampling frequency, and rigresure

method is best of the noise estimation techniques.

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