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Research Article

Performance Comparison of Wavelet and Multiwavelet

Denoising Methods for an Electrocardiogram Signal

Balambigai Subramanian,1Asokan Ramasamy,2and Kamalakannan Rangasamy1

1Department of Electronics and Communication Engineering, Kongu Engineering College, Perundurai, Erode District,

TamilNadu638052,India

2Kongunadu College of Engineering and Technology, ottiyam, Trichy District, Tamil Nadu 621215, India

Correspondence should be addressed to Balambigai Subramanian; bharathian@yahoo.com

Received January ; Revised April ; Accepted April ; Published May

Academic Editor: Feng Gao

Copyright © Balambigai Subramanian et al. is is an open access article distributed under the Creative Commons

Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is

properly cited.

e increase in the occurrence of cardiovascular diseases in the world has made electrocardiogram an important tool to diagnose

the various arrhythmias of the heart. But the recorded electrocardiogram oen contains artefacts like power line noise, baseline

noise, and muscle artefacts. Hence denoising of electrocardiogram signals is very important for accurate diagnosis of heart diseases.

e properties of wavelets and multiwavelets have better denoising capability compared to conventional ltering techniques. e

electrocardiogram signals have been taken from the MIT-BIH arrhythmia database. e simulation results prove that there is a

.% increase in the performance of multiwavelets over the performance of wavelets in terms of signal to noise ratio (SNR).

1. Introduction

In modern medicine, there are many methods to diagnose

heart disease such as electrocardiogram (ECG), ultrasound,

magnetic resonance imaging (MRI), and computer tomog-

raphy (CT). Among these methods, diagnosis using elec-

trocardiogram has the advantages of convenience and low

cost so that it can be used in a wide area. However, certain

arrhythmia (a fast, slow, or irregular heartbeat) which can

cause abnormal symptoms may occur only sporadically or

may occur only under certain conditions such as stress.

Arrhythmia of this type is dicult to obtain on an electro-

cardiogram tracing that runs only for a few minutes. e

electrocardiogram is the record of variation of bioelectric

potential with respect to time as the human heart beats. Due

toitseaseofuseandnoninvasiveness,electrocardiogram

plays an important role in patient monitoring and diagnosis.

e change in solar activity including electrocardio-

graphicdatawithvariationsingalacticcosmicrays,geomag-

netic activity, and atmospheric pressure suggests the possi-

bility of links among these physical environmental variations

and health risks, such as myocardial infarctions and ischemic

strokes. An increase in the incidence of myocardial infarction

in association with magnetic storms has been reported by

Corn´

elissen et al. [].

Magnetic storms are found to decrease heart rate variabil-

ity (HRV) indicating a possible mechanism since a reduced

HRV is an important factor for coronary artery disease and

myocardial infarction. An increase of % in mortality during

years of maximal solar activity is found when compared with

years of minimal solar activity. ese chronodiagnostics are

particularly important for those venturing into regions away

from hospitals.

Goudarzi et al. []madeaneorttondtheoptimum

multiwavelet for compression of ECG signals to be used

along with SPIHT codec. is work examined dierent

multiwavelets on sets of ECG data with entirely dierent

characteristics selected from MIT-BIH database and assessed

the functionality of the dierent multiwavelets in compress-

ing electrocardiogram signals and their simulation results

showed the cardinal balanced multiwavelet (cardbal) by the

means of identity (Id) preltering method to be the best

eective transformation and the most ecient multiwavelet

was applied for SPIHT coding algorithm on the transformed

signal by this multiwavelet.

Hindawi Publishing Corporation

Journal of Applied Mathematics

Volume 2014, Article ID 241540, 8 pages

http://dx.doi.org/10.1155/2014/241540

Journal of Applied Mathematics

Kania et al. [] studied the application of wavelet denois-

ing in noise reduction of multichannel high resolution ECG

signals. e inuence of the selection of wavelet function

and the choice of decomposition level on eciency of

denoising process was considered and whole procedures of

noise reduction were implemented in MATLAB environment

using the fast wavelet transform. e denoising method was

foundtobeadvantageoussincenoiselevelwasdecreased

in ECG signals, in which noise reduction by averaging had

limited application, that is, in case of arrhythmia.

Helenprabha and Natarajan []proposedatechnique

used for measuring electrical signals generated by foetal heart

as measured from multichannel potential recordings on the

mother’s body surface. ey proposed a new class of adaptive

lter that combines the attractive properties of nite impulse

response (FIR) lter with innite impulse response (IIR)

lter. e maternal ECG and foetal signals were simulated

using MATLAB. e gamma lter design was implemented

in FPGA Spartan E which was programmed using VHDL.

eirresultshavesolvedthecomplexsituationsmorereliably

than normal adaptive methods used earlier for recovering

foetal signals.

Chang et al. [] proposed measures to make the optimal

lter design under dierent constraints possible for ECG

signal processing. Experiments have been conducted by them

with articially and practically corrupted ECG signals for

PLI adaptive ltering technique. e assessments included

the convergence time, the frequency tracking eciency,

theexecutiontime,andtherelativestatisticsintimeand

frequency domain. e results demonstrated that there is no

universal optimum approach for this application thus far.

Alfaouri and Daqrouq [] performed wavelet transform

thresholding technique for ECG signal denoising. ey

decomposed the signal into ve levels of wavelet transform

using the Daubechies wavelet (db) and determined a thresh-

oldthroughalooptondthevaluewhereminimumerror

was achieved between the detailed coecients of threshold

noisy signal and the original signal. e threshold value was

accomplished experimentally aer using a loop of calculating

a minimum error between the denoised wavelet subsignals

and the original free of noise subsignals. e experimental

application of the threshold result was better than Donoho’s

threshold particularly in ECG signal denoising.

Zhidong and Chan []proposedanovelmethodforthe

removal of power line frequency from ECG signals based

on empirical mode decomposition (EMD) and adaptive

lter. A data-driven adaptive technique called EMD was

used to decompose ECG signal into a series of intrinsic

mode functions (IMFs). e adaptive power line cancellation

lter was designed to remove the power line interference,

the reference signal of which was produced by selective

reconstruction of IMFs. Clinic ECG signals were used to

evaluate the performance of the lter. Results indicated that

the power line interference of ECG was removed eectively

by the new method.

Kaur and Singh [] proposed a combination method

for power line interference reduction in ECG. e methods

were moving average method and using the IIR notch

characteristics. eir results showed reduction in the power

line noise in the ECG signal using the proposed lter that has

fewer coecients and hence lesser computation time for real

time processing.

Haque et al. [] used wavelet method to detect the small

variations of ECG features. ey simulated standard ECG

signals as well as the simulated noise corrupted signal using

FFT and wavelet for proper feature extraction. ey found

wavelettobesuperiortotheconventionalFFTmethodin

nding the small abnormalities in electrocardiogram signals.

Tan and L ei [ ] used wavelet transform to lter out

noise interferences of electrocardiogram signals for the l-

tering of the myoelectric interference, the power frequency

interference, and the baseline dri. Firstly Coif wavelet was

adapted to decompose electrocardiogram signals containing

noises.Secondly,thesoandhardthresholdvaluequantied

high-frequency coecients of every scale and nally the

electrocardiogram were reconstructed using high-frequency

coecients of every scale which were quantied by the

threshold value. Experiments showed that wavelet transform

had good real time ltering eect and it had more advantages

than traditional methods.

2. Materials and Methods

2.1. Wavelet Method. Awaveletissimplyasmallwavewhich

has energy concentrated in time. It is compactly supported

andhasniteenergyfunction.Itcansatisfyadmissibil-

ity condition and could be amendable for multiresolution

analysis. e wavelet transform is a mathematical tool for

decomposing a signal into a set of orthogonal waveforms

localized both in time and frequency domains. e wavelet

transform is a suitable tool to analyse the electrocardiogram

signal, which is characterized by a cyclic occurrence of

patterns with dierent frequency content (Pwave, QRS

complex, and Twave). It is a decomposition of the signal

as a combination of a set of basic functions, obtained by

means of dilation (a)andtranslation(b) of a single prototype

wavelet; there are several wavelet functions (mother wavelet

with dierent properties) like the Morlet or Mexican Hat

wavelets or complex frequency Bspline wavelets that are used

in study.

Wavelet analysis is done by the breaking up of a signal

into a shied and scaled version of the original wavelet. A

continuouswavelettransformcanbedenedasthesumof

overall time of the signal multiplied by a scaled and shied

version of the wavelet function. e greater the scale factor

“a” is, the wider the basis function is and, consequently,

the corresponding coecient gives information about lower

frequency components of the signal and vice versa.

e wavelet transform is designed to address the problem

of nonstationary signals such as electrocardiogram signals.

It involves representing a time function in terms of simple,

xed building blocks, and termed wavelets. e next step

is the selection of number of decomposition levels of signal

𝑖();seeFigure . First decomposition level is obtained by

using two complementary high- and low-pass lters and

then half of the samples are eliminated. e lters cut

frequency is equal to half of the bandwidth of analysed signal.

Journal of Applied Mathematics

lter

lter

2

2

Low-pass

Low-pass

Low-pass

lter

High-pass

High-pass

High-pass

lter

2

2

lter

lter

2

2

Level 1 Level 2 Level 3

Approximation

Detail

x(n)

cD1

cD2

cD3

cA1

cA2

cA3

F : Diagram of multiresolution analysis of signal 𝑖().

Such algorithm, which is amplication of discrete wavelet

transform, is known as fast wavelet transform.

For analysis the following mother wavelet was used:

Ψ𝑚,𝑛 ()=2−𝑚/2Ψ2−𝑚−, ()

where is coecient of time translation and is coecient

of scale (compression).

In the rst step threshold values for detail coecients at

every level of decomposition are determined according to the

following relationship:

THR𝐽=2log

𝑗

.()

e next step is the modication of values of the jth level

detail coecients basis of appointed threshold. is method

is called so thresholding procedure as follows:

𝑗()=sgn 𝑗()||−THR𝑗; 𝑗()>THR𝑗,

0; 𝑗()≤THR𝑗.()

e nal step of the analysis is reconstruction of signal

𝑖()based of approximation coecients chosen th level of

decomposition (𝑖) and modied detail co ecients from th

(𝑖)aswellashigherlevelsofdecomposition

𝑖()=

𝑛𝑚,𝑛Φ𝑘2−𝑚−

+𝑚𝑘

𝑚=𝑚0

𝑛𝑚,𝑛Ψ𝑚,𝑛 2−𝑚−, ()

where Φ𝑘()is scaling function from kth level of decompo-

sition and Ψ𝑚,𝑛()are wavelet functions for =

0,...,𝑘

levels of decomposition.

e advantages of wavelet methods are possibility of

receiving good quality signal for beat to beat analysis and

possibility of having high quality signal while averaging

technique is impossible, as causing morphology distortion

of electrocardiogram signals, it provides a way for analysing

waveforms bounded in both frequency and duration, it allows

signals to be stored more eciently than by the Fourier

transform,itcanleadtobetterapproximatereal-worldsignals

anditiswell-suitedforapproximatingdatawithsharp

discontinuities. e disadvantage of wavelet method is that

the wavelet transforms ignore polynomial components of the

signal up to the approximation order of the basis.

2.2. Equation for Continuous Wavelet Transform. e wavelet

transform equation is given by

CWTΨ

𝑥(,)=Ψ(,)=1

||𝑡()Ψ∗−

, ()

where () = given signal, =translation parameter, =

scaling parameter =1/,andΨ()=mother wavelet.

2.3. Multiwavelet Method. Multiwavelets constitute a new

chapter which has been added to wavelet theory in recent

years. Recently, much interest has been generated in the study

of the multiwavelets where more than one scaling functions

and mother wavelet are used to represent a given signal. e

rst construction for polynomial multiwavelets was given by

Albert, who used them as a basis for the representation of

certain operators. Later, Geronimo, Hardin, and Massopust

constructed a multiscaling function with components using

fractal interpolation.

In spite of many theoretical results on multiwavelet,

their successful applications to various problems in signal

processing are still limited. Unlike scalar wavelets in which

Mallet’s pyramid algorithm have provided a solution for good

signal decomposition and reconstruction, a good framework

for the application of the multiwavelet is still not available.

Nevertheless, several researchers have proposed method of

Journal of Applied Mathematics

how to apply a given multiwavelet lter to signal and image

decomposition.

2.4. Multiscaling Functions and Multiwavelets. e concept

of multiresolution analysis can be extended from the scalar

case to general dimension N. A vector valued function

=[

12,...,𝑟]𝑇belonging to 2()𝑟and Niscalleda

multiscaling function if the sequence of closed spaces

𝑗=span 2𝑗/2𝑖2𝑗−:1≤≤,∈.()

∈constitute a multiresolution analysis (MRA) of

multiplicity for 2(). e multiscaling function must

satisfy the two-scale dilation equation

()=2

𝑘𝑘(2−).()

Now let 𝑗denote a complementary space of 𝑗in 𝑗+1.e

vector valued function Ψ=[Ψ

1Ψ2,...,Ψ𝑟]𝑇such that

𝑗=span 2𝑗/2𝑖2𝑗−:1≤≤,∈.()

∈is called a multiwavelet. e multiscaling function must

satisfy the two-scale equation

Ψ()=2

𝑘𝑘(2−).()

𝑘∈

2()𝑟×𝑟 is an ×matrix of coecients. e two-

scale equations ()and()canberealizedasamultilterbank

operating on input data streams and ltering them in two

routput data streams, each of which is downsampled by a

factor of two. If ()isthegivensignalanditisassumedthat

()∈ 0,then

()=2

𝑘𝑇

0,𝑘(−).()

And the scaling coecient 𝑇

1,𝑘 of the rst level can be consid-

ered as a result of low-pass multiltering and downsampling

as follows:

1,𝑘 =

𝑚𝑚−2𝑘0,𝑚.()

Analogously, the rst level multiwavelet coecients 1,𝑘 are

obtained using high-pass multiltering and downsampling as

follows:

1,𝑘 =

𝑚𝑚−2𝑘0,𝑚.()

Full multiwavelet decomposition of the signal () can be

found by iterative ltering of the scaling coecient as follows:

𝑗,𝑘 =

𝑚𝑚−2𝑘𝑗−1,𝑚,

𝑗,𝑘 =

𝑚𝑚−2𝑘𝑗−1,𝑚.()

Note that 𝑗,𝑘 and 𝑗,𝑘 are ×1column vectors.

2.5. Advantages of Wavelets and Multiwavelets Compared to

Conventional Filtering Techniques

(i) e Fourier transform fails to analyze the nonsta-

tionary signal, whereas wavelet transform allows the

components of a nonstationary signal to be analyzed.

(ii) Wavelet transform holds the property of multires-

olution to give both time and frequency domain

information in a simultaneous manner.

(iii) A set of wavelets which are complementary can

decompose the given data without gaps or overlap so

that the decomposition process becomes mathemati-

cally reversible.

2.6. Comparison between Wavelet and Multiwavelet. Multi-

wavelets contain multiple scaling functions, whereas scalar

wavelets contain one scaling function and one wavelet.

is leads to more degrees of freedom in constructing

wavelets. erefore, opposed to scalar wavelets, properties

such as compact support, orthogonality, symmetry, vanishing

moments, and short support can be gathered simultaneously

in multiwavelets which are fundamental in signal processing.

e increase in degree of freedom in multiwavelets is

obtained at the expense of replacing scalars with matrices,

scalar functions with vector functions, and single matrices

with block of matrices. However, preltering is an essential

task which should be performed for any use of multiwavelet

in signal processing.

3. Results and Discussions

3.1. Data Collection

3.1.1. MIT-BIH Arrhythmia Database. MIT-BIH arrhythmia

database consists of -half-hour electrocardiogram record-

ings. e recordings were digitized at Hz (samples per

secondperchannel)with-bitresolutionovermV.e

simulations were carried out in MATLAB environment

Rb. Various benchmark records from the MIT-BIH

database were considered for this study.

(A) Performance Analysis of Wavelet Based Denoising Method

for Electrocardiogram

Wav e l e t D e n o i s i n g Usin g B i o r t h o g o n a l 1 D Wavelet. Figure

shows the wavelet denoising for the record m in which

level approximation coecient 1for Biorthogonal wavelet

shows that there is maximum noise in it. Hence reconstruc-

tion of the original signal to obtain the denoised electrocar-

diogram from 1coecients will also contain the maximum

noise. e level decomposition contains the least noise and

hence reconstruction is done using 4.

Original and Denoised Signals Using Biorthogonal Wavelet.

Figure shows the comparison of the original signal and

the denoised signal using Biorthogonal wavelet at level

decomposition for the record m. In this the signal to

noise ratio obtained is . dB and the power line noise

Journal of Applied Mathematics

500 1000 1500 2000 2500 3000 3500

0

100

950

1000

1050

1100

1150

1000

s

a4

d4

d

2

−4

500

1

00

0

1500

2

000

2

500

3000

3500

0

100

95

0

1

000

1

05

0

11

00

11

5

0

1

000

4

4

2

−

4

F : Wavelet denoising for ECG record no m using Biorthogonal D wavelet.

500 1000 1500 2000 2500 3000 3500

900

1050

1100

1150

1200

1250

1300

Original and denoised signals

Original ECG signal

Denoised ECG signal

5

0

0

1

000

1

50

0

200

0

250

0

3

000

3

500

90

0

1050

1

1

0

0

1

1

50

1

2

00

1250

1300

O

ri

g

inal and denoised si

g

nal

s

F : Original and denoised signals for ECG record no m using Biorthogonal wavelet.

is reduced for this record. Figure shows the approximation

and coecient details aer the signal in record m has

been subjected to the Biorthogonal wavelet transform and

Figure shows the original and denoised electrocardiogram

in the record m. e signal to noise ratio obtained is

.dB. is shows that the noise has to be removed further

to enhance the quality of the obtained electrocardiogram.

(B) Performance Analysis of Multiwavelet Based Denoising

Method for Electrocardiogram

Biothogonal Based Multiwavelet Denoising. e multiwavelet

denoising for the record m shown in Figure yields

a signal to noise ratio of . dB in which the power

line noise gets removed. Figure shows the multiwavelet

denoising for the record m and the signal to noise ratio

obtained is . dB because of the removalof power line

noise.

3.2. Performance Comparison of Wavelet and Multiwavelet

Methods. Comparison of signal to noise ratio for wavelet

and multiwavelet based denoising techniques for various

electrocardiogram records.

4. Conclusion

e inference from Tables ,,,andis that the output signal

tonoiseratiovalueofmultiwaveletdenoisingfunctionsis

Journal of Applied Mathematics

3500

−5

0

5

−20

0

20

−100

−50

0

50

−100

0

100

200

1000

1100

1200

1300

1000

1200

1400

s

.

a4

d4

d3

d2

d1

Decomposition at level 4:s=a

4+d

4+d

3+d

2+d

1

3

5

00

−

5

0

5

−2

0

0

2

0

−1

00

−

50

0

50

−1

00

0

1

00

2

00

1

000

11

00

12

00

1

300

1

00

0

12

0

0

140

0

s

a

4

d

4

d

3

d

2

d

1

F : Wavelet denoising for ECG record no m using Biorthogonal D wavelet.

500 1000 1500 2000 2500 3000 3500

1000

1050

1100

1150

1200

1250

1300

1350

1400

1450

Denoised signal

500

1000

1500

2

000

2

500

3000

3500

100

0

105

0

1

1

00

1

1

50

1

2

00

1

2

50

1300

1350

1

4

0

0

1

4

5

0

D

enoised si

g

nal

Original ECG signal

Denoised ECG signal

F : Original and denoised signals for ECG record no m using Biorthogonal wavelet.

T : Performance comparison of wavelet and multiwavelet for

record m.

Wav e l e t f a m i l y

SNR (dB)

Record no m

Wavelet Multiwavelet

Bio . . .

Db . .

Db . .

Coif . .

Sym . .

greater than the signal to noise value of wavelet functions. e

table also indicates that the Daubechies wavelet has better

denoising capability than when compared to corresponding

values of the wavelet denoising as the shape of this wavelet

T : Performance comparison of wavelet and multiwavelet for

record m.

Wav e l e t f a m i l y

SNR (dB)

Record no m

Wavelet Multiwavelet

Bio . . .

Db . .

Db . .

Coif . .

Sym . .

is more close to the shape of electrocardiogram. e increase

in signal to noise ratio value indicates that there is no loss in

the information contained in the original electrocardiogram

signal and multiwavelet has better denoising capability to

Journal of Applied Mathematics

500 10001500 2000 2500 3000 3500

900

950

1000

1050

1100

1150

1200

1250

1300

1

Signals

500 10001500 2000 2500 3000 3500

D1 D2 D3 D4 A4

500 10001500 2000 2500 3000 3500

850

900

950

1000

1050

1100

1150

1200

1250

1300

1350 Denoised signals

Coecients

F : Multiwavelet denoising for ECG record no m using Biorthogonal D wavelet.

1000

1050

1100

1150

1200

1250

1300

1350

1400

1450

1

D1 D2 D3 D4 A4

500 10001500 2000 2500 3000 3500500 10001500 2000 2500 3000 3500500 10001500 2000 2500 3000 3500 900

1000

1100

1200

1300

1400

1500

Signals Denoised signals

Coecients

F : Multiwavelet denoising for ECG record no m using Biorthogonal D wavelet.

T : Performance comparison of wavelet and multiwavelet for

record m.

Wav e l e t f a m i l y

SNR (dB)

Record no m

Wavelet Multiwavelet

Bio . . .

Db . .

Db . .

Coif . .

Sym . .

T : Performance comparison of wavelet and multiwavelet for

record m.

Wav e l e t f a m i l y

SNR (dB)

Record no m

Wavelet Multiwavelet

Bio . . .

Db . .

Db . .

Coif . .

Sym . .

Journal of Applied Mathematics

remove the power line noise in the various electrocardiogram

records.

Conflict of Interests

e authors declare that they have no conict of interests

regarding the publication of this paper.

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Hindawi Publishing Corporation

http://www.hindawi.com Volume 2014

Decision Sciences

Advances in

Discrete Mathematics

Journal of

Hindawi Publishing Corporation

http://www.hindawi.com

Volume 2014

Hindawi Publishing Corporation

http://www.hindawi.com Volume 2014

Stochastic Analysis

International Journal of