USING WAVELET TRANSFORM FOR CARDIAC MAPPING DE-NOISING OF HEART ANTERIOR SURFACE ISCHEMIA

IJICIS, Vol.14, No 3 JULY 2014

51

International Journal of Intelligent Computing and Information Science

USING WAVELET TRANSFORM FOR CARDIAC MAPPING DE-NOISING OF

HEART ANTERIOR SURFACE ISCHEMIA

M. Aouf

Higher Technological Institute,

Cairo - Egypt,

[email protected]

M. A.-M. Salem

Faculty of Computer and Information Sciences,

Aim Shams University, Egypt

[email protected]

A. Sharawy

Faculty of Engineering,

Cairo University, Egypt

[email protected]

Abstract: Anterior surface heart ischemia is one of the most prominent heart diseases. Chest cardiac

mapping using multi-electrode systems for chest leads increases the diagnostic power over the

traditional chest lead ECG. Noise is one of the most apparent problems in cardiac mapping which

decreases the fidelity of the signals. In this paper we propose a new technique for signal de-noising and

presentation of chest cardiac maps. Using the 3D wavelet transform, we apply sensitivity analysis to the

wavelets of the Daubechies (dbs) family to find out the most suitable wavelet for each chest lead at

each position. We have computed the performance measure of the signal to noise ratio (SNR) for

each chest lead at each position to measure the quality of the de-noising techniques focusing at the

most important chest lead. By applying db4, db8 and db11 at selected positions of chest leads we

are able to get optimal de-noising. The resulting cardiac maps have proven to be of diagnostic

value for the bio-potential state of the anterior surface ischemia of heart.

Keywords: Signal Processing, De-noising, Electrocardiograph, Cardiac Mapping, 3D Wavelet

Transform

1 Introduction

1.1 Multi-electrode system chest leads

Electric Imaging is one of the most advanced methods to upgrade the diagnosis of the

Electrocardiograph (ECG). Using multi-electrode system chest leads is a real step for cardiac mapping

which provides us with real electric data. The effort for acquiring potential signals from cardiac

mapping is focused on studying the current dipole distributed on chest [1, 2]. The diagnostic power of

cardiac mapping shows a real success in the area of coronary artery disease (CAD) and ischemia [3,4,5].

Chest leads have a great power for the diagnosis and classification of anterior surface ischemia of the

heart, especially V1. Figure 1 shows the overall processing performed in this paper.

1.2 QRS detection and filter bank theory

The pre-processing stage for body surface potential mapping involves peak (QRS complex) detection of

the ECG signal using a filter banks algorithm [6]. Figure 2 depicts the theory of filter banks.

Aouf et. al: Using Wavelet Transform For Cardiac Mapping De-Noising Of Heart Anterior Surface Ischemia

52

Multi electrode system

for chest leads of ECG

(30 channels)

Pre-processing filter

banks (peak detection)

Ch1 Ch2 Ch30

Converting signals into cubic

form

De-noising using dbn

Mapping

Figure 1: Processing stages for the diagnosis of ischemic heart disease by cardiac mapping using

3D wavelet transform.


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1.3

Figure 2: Filter bank design and theory [6].

The filter bank algorithm depends on non-linear processing stages and moving window integrators.

Sometimes there is a difficulty to detect the peak, so a “search back” strategy technique has to be

performed to indicate the peak (i.e., the QRS). A group of analysis and synthesis filters are used in the

design and implementation of filter banks [7][8]. Filter banks are computationally highly efficient in

time and frequency domain analysis of ECG signals.

1.4 Wavelet transform

A wavelet is simply a small wave whose energy is concentrated in time to provide a tool for the analysis

of transient, non-stationary, and time varying phenomena [9]. A wavelet transform has a great

contribution to the analysis of non-invasive medical measurements, such as the ECG. The wavelet

transform plays a great role in describing ECG waves in both the frequency and the time domain [10].

The first man who wrote about the term “wavelet” was Alfred Haar, and this was in his thesis in 1990

[11, 12]. Jean Morlet and her team have first presented the theoretical and mathematical concept. A

wavelet has a waveform of effectively limited duration and has an average value of zero. This local

property is the heart of the success of the transform. A local prototype signal, ψ(t), called a mother

wavelet or simply a wavelet has a graph lying partly above and partly below the t-axis. A set of wavelet


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functions {ψa,b(t)} can be generated by scaling and translating the mother wavelet ψ(t) by quantities a,

b, respectively as:

ψ ( )

√ ψ (

) ( )

where a>0 and b are real numbers. The wavelet transform of f(t) using the wavelets {ψa,b(t)} can be

written as follows:

∫ ( )ψ ( )

(2)

The parameters a and b are called the scale or dilation parameter and the translation or shifting

parameter, respectively. Restricting the values of a and b by integers rather than real numbers gives the

Discrete Wavelet Transform (DWT). However, an interesting type of wavelet transform is to restrict

the scaling by factors of two (binary scaling), and the translation by an integer multiple of the binary

scale factor (dyadic translation). Thus, it relates at any scale to the width of the wavelets at that scale,

i.e., a = 2j, b=k2j

, j∈Z, k∈Z, where Z & Z* represent the set of integers and positive integers,

respectively.

ψj, k

(t)=2−j/2ψ(2

−j∙t − k) (3)

Mallat[14] proposed a mathematical operator which transforms a signal into an approximation at lower

resolution, say 2j . Then he showed that the difference in information between two approximations at

resolutions 2j and 2

j+1 is extracted by the wavelet function. A scaling function φ(t) is defined such that:

Φj,k(t)=2−j/2φ(2−j∙t − k), j, k ∈ Z (4)

The signal f(t) is decomposed into two new sub-band signals using the scaling and the wavelet

functions yielding the approximation coefficient A1 and detail coefficient D1 with a lower resolution at

level j = 1, each of which has as many sample points as half of the sample points of f(t). The process is

repeated for the new approximation coefficients at level j giving the approximation and detail at level

j+1 until a level j is reached. At that level both sub-bands have only one sample point and the analysis

must stop. In fact Aj represents the global approximation of the original signal f(t)=A.

1.5 Daubechies family

Daubechies constructed the first wavelet family of scale functions that are orthogonal and have finite

vanishing moments, i.e., a compact support [13]. This property insures that the number of non-zero

coefficients in the associated filter is finite. The Haar wavelet, as shown in Fig. 3(a), is the basis of the

simplest wavelet transform. Historically, it is the first mention of what is called now “wavelet” in the

thesis by Alfred Haar in 1990. It is discontinuous and resembles a step function. The Haar wavelet

transform has the advantages of being conceptually simple, fast and memory efficient, since it can be

calculated in place without a temporary array. On the other hand, the Haar transform has limitations

because it is discontinuous, which can be a problem for some applications. It is the only symmetric

wavelet in the Daubechies family and the only one of them that has an explicit expression. The


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associated filter is of length two. This means that the resulting approximation and details are all half the

number of columns and rows of the input signal. The scale function φhaar is the simple average

function and the wavelet ψhaar is the difference. For higher order Daubechies wavelets ψdb, N denotes

the order of the wavelet and the number of vanishing moments. The regularity increases with the order

[14][13].

Figure 3: Scaling functions associated with the wavelets (a) Haar (b) Db2 (c) Db4 (d) Db8.

1.6 De-noising using the wavelet transform

Noise in the medical field, especially in ECG signal has a great powerful effect in the reduction of

signal to noise ratio (SNR). The ECG signal is always corrupted by different types of noise [15].

Wavelet transformation is one of the most popular and important techniques used in the field of de-

noising the ECG waveform [16, 17, 18, 19]. We propose a new technique using the wavelet transform

to detect and eliminate the noise of the potential signal. Equation (5) indicates that the received signal is

the sum of both the physical signal S(t) and the corrupting noise N(t).

R(t) =S(t)+N(t) (5)


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The de-noising process proposed in this paper depends upon the difference between the characteristics

of the noise and signal. The power of the wavelet technique here is detecting signal discontinuities [19].

So, we calculated the signal to noise ratio (SNR) to assess the quality of the reconstructed signal.

In this paper we present new technique using 3D wavelet transform for reconstructing and denoising of

maps representing chest leads signals at selected positions for the bio-potential state of the heart. The

rest of the paper is organized as following, The methods of map reconstruction and the 3D wavelets for

signal de-noising are represented in section 2 . The results of different db wavelets are shown and

represented statistically and graphically in section 3. Finally, the best wavelet for each lead position is

highlighted to obtain the highest diagnostic degree for heart anterior surface ischemia in the Conclusion.

2 Material and Methods

2.1 Database collection

In this research we applied our experiment to 30 patients suffering from ischemia. The range of age of

the patients was from 35 to 50, having a weight range from 80 to 100 kg and a height range from 1.6 to

1.8 meters. The equipment used in our experiment was a single channel ECG interfaced with a

computer. The experiment location was the cardiology department research at Ain-Shams Specialized

Hospital, Cairo, Egypt. In our experiment we used standard chest leads but with new electrode

placements. We chose four positions on the chest in addition to the traditional position, as shown in Fig.

4. The five positions were designated by p0, p1, p2, p3, and p4. p0 is the traditional position, while p1

and p2 are the upper positions, and p3 and p4 are the lower positions, taking into account the anatomical

structure of the chest and the chest rib locations [20].

(a)


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(b)

Figure 4: Chest leads position (a) traditional (b) map [20].

2.2 Pre-processing stage

This is the detection stage of the QRS complex using filter banks. It is applied using a processing unit to

sub-band signals, where we can evaluate the fidelity of signal reconstruction by examining the aliasing

magnitude and phase distortion. Our filter banks must be free from these distortions [21] [22]. Proper

selection of the frequency parameters is helpful for real detection. We used a filter band width of 5.6

Hz. High frequency selectivity is achieved using a filter bank with high stop band attenuation and

narrow transition bands [6].

2.3 3D Wavelet transform

The wavelet transform is well known with its time and frequency localization. Jump discontinuities or

peaks can easily be localized in the wavelet coefficients of small scales. At larger scale long time trends

of f(t) are stored in deeper layers of the coefficient hierarchy. The wavelet analysis of a signal gives two

sub-bands: the approximation and the details, generated by the scaling function (t) and the wavelet

function (t), respectively. The approximation contains the low frequency components of the signal.

The details show the high frequency, rapid changes in the signal; therefore it can be easily used to

discover the discontinuity points in the signal and for denoising [23]. The transformation may be

expressed as following:

dtttfabc ab

)()(),( ),( (6)

Where a > 0 and b are real numbers. The inverse wavelet transform using the wavelets {Ψa,b(t)} can be

written as follows:

dadbtabca

tfa b

ab )(),(1

)( ),(2 (7)


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As shown in the last equations, the signal f(t) is represented in terms of a linear combination of wavelet

coefficients c(a,b). The 3D wavelet transform is extended from the 1D wavelet transform [2][12]. It is

the product of three one-dimensional functions. The analysis is carried out along the horizontal (x), the

vertical (y), and the depth (z) dimensions of the volumetric data. The equations 8 – 15 represent the

eight wavelet and scaling functions of the 3D wavelet transform [10][24].

Φj,{k, l m}(x, y, z) = 23 j/2 Φ(x - 2- j∙k) Φ(y - 2- j∙l) Φ(z - 2- j∙m) (8)

ψ 1j,{k, l, m}(x, y, z) = 23 j/2 Ψ(x - 2- j∙k) Φ(y - 2- j∙l) Φ(z - 2- j∙m) (9)

ψ 2j,{k, l, m}(x, y, z) = 23 j/2 Φ(x - 2- j∙k) Ψ(y - 2- j∙l) Φ(z - 2- j∙m) (10)

ψ 3j,{k, l, m}(x, y, z) = 23 j/2 Ψ(x - 2- j∙k) Ψ(y - 2- j∙l) Φ(z - 2- j∙m) (11)

ψ 4j,{k, l, m}(x ,y, z) = 23 j/2 Φ(x - 2- j∙k) Φ(y - 2- j∙l) Ψ(z - 2- j∙m) (12)

ψ 5j,{k, l, m}(x ,y, z) = 23 j/2 Ψ(x - 2- j∙k) Φ(y - 2- j∙l) Ψ(z - 2- j∙m) (13)

ψ 6j,{k, l, m}(x, y, z) = 23 j/2 Φ(x - 2- j∙k) Ψ(y - 2- j∙l) Ψ(z - 2- j∙m) (14)

ψ 7j,{k, l, m}(x ,y ,z) = 23 j/2 Ψ(x - 2- j∙k) Ψ(y - 2- j∙l) Ψ(z - 2- j∙m) (15)

The different types of mother wavelets are always a subject of comparison aiming to find out which

wavelet is more suitable for which application [25][26][27]. Daubechies constructed the first wavelet

family of scale functions that are orthogonal and have finite vanishing moments, i.e., a compact support

[13]. Wavelets with fewer vanishing moments give less smoothing and remove fewer details, but

wavelets with more vanishing moments produce distortions [28][29]. The Wavelet Transform can be

applied to the approximations iteratively until a certain level. The tree formed is called „Wavelet

Decomposition Tree‟, as shown in Figure (5). The approximation and details are calculated by up-

sampling their coefficients. The signal can be reconstructed from the wavelet Approximations and

Details at any level. Figure (5) shows different ways to reconstruct the signal.

𝑆=𝐴1+𝐷1

𝑆=𝐴2+𝐷2+𝐷1

𝑆=𝐴3+𝐷3+𝐷2+𝐷1

Figure 5: Wavelet Decomposition Tree.


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2.4 De-noising using the wavelet transform

There is noise in the Details of the signal, and a simple filtering process can be made by reconstructing

the signal with a zero vector instead of the Details coefficients, but this will omit the other details of the

signal as well. A better approach is to threshold the Details then reconstruct the signal [30][31].There

are two types of threshold, hard and soft thresholds as in equations (16) and (17).

( ) { ( ) | ( )|

| ( )| (16)

( ) { ( ( )) (| ( ) |) | ( )|

| ( )| (17)

A hard threshold produces discontinuities while a soft threshold has a smoothing effect with

discontinuities. A universal thresholding rule that provides an easy, fast, and automatic thresholding is

given by:

√ (18)

Where N is the length of the coefficient vector, is the standard deviation of the noise with = 0.6745 𝑀𝐴𝐷, MAD represents the Median Absolute Deviation of the coefficients, and denotes the threshold

value. This threshold can be updated for each interval of the signal as the noise variance can vary with

time resulting in several different variance values, so there is a different noise variance for different

time intervals.

3 Results and Discussion

In this study, we have proposed an improved method for the diagnosis of anterior ischemia of the heart

using traditional ECG by plotting maps for the bio-potential state of cardiac muscle without noise.

Traditional ECG shows a spreading of the electrical signal at the ventricles of the heart from the point

of view of one position placement for the chest electrodes to obtain the six chest leads, thus V1 and V2

look at the right ventricles, V3 and V4 look at the septum between the ventricles and the anterior wall of

the left ventricle, whereas V5 and V6 look at the anterior and lateral walls of the left ventricles [32][33].

Plotting the maps with four additional positions, gives the cardiologist the facility to look more deeply

into the spreading of the electrical signals of the ventricles. The maps produce 30 channels due to the

five positions with the six chest leads. But noise is an apparent problem which decreases the fidelity of

the signals. Figure (6) shows the plots of the maps for patients suffering from anterior ischemia before

and after de-noising using the 3D wavelet transform.


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Figure 6: Denoising of maps using different Daubechies (dbs) family

Using the 3D wavelet transform, we have performed sensitivity analysis on Daubechies (db) wavelets

for de-noising. Maps were drawn at 10 msec, at 20 msec, at 30 msec, and at 40 msec from the R-

peak reference to cover the cardiac cycle. We found that maps appear differently at each instant,

which demonstrates the bio- potential propagation state at different durations for the ventricles.

Plotting maps for 30 different channels ECG makes them subjected to noise. We used the 3D

wavelet transform especially with Daubechies (db) to perform de-noising. In Figure (6) we found

that there are differences in the maps before and after de-noising. At 10 msec, maps still show

negative signal values in most of the chest leads at different positions. There is a remarkable

increase in the negative amplitude at p4 with V3, and also at p2 with V4, V5 and V6. At 20 msec,

the negative signal appearance still prevails, but with a disappearance of positive values, and

zeroes values occur at P4 with V5. At 30 msec, no significant changes occur. At 40 msec, maps still

show negative values, but signal negativity increases at p4 with V2, V3, and V4, and at P3 with V3.

Figure (7) shows the different waveforms before and after de-noising using the Daubechies (db)

family, which shows the effect of the de-noising technique upon each db separately.

Db1


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Db2

Db4

Db8


62

Db11

Figure (7): the different waveforms before and after de-noising using different Daubechies

(dbs) families

As the morphological shape of the signals before and after de-noising is different, testing the

fidelity and performance of the de-noising technique for each Daubechies (db) is very important.

To perform this, we calculated the signal to noise ratio (SNR) as in equation (19).

∑

( )

∑ ( )

…………….(19).

Where VR(n) is the reconstructed ECG signal, and SR(n) is the deformation in reconstructed ECG

signal. Table 1 to Table 5 represent the calculating process of the (SNR) for each lead at each position

for db1, db2, db4, db8 and db11, respectively.

Table-1 SNR for each chest lead at each position for each db1

V1 V2 V3 V4 V5 V6

P2 1.364025 1.394761 1.445508 1.466507 1.447167 1.378012

P1 1.39462 1.445179 1.473376 1.570089 1.536515 1.39508

P0 1.451029 1.458675 1.470105 1.515174 1.449248 1.476025

P3 1.433415 1.437018 1.453884 1.432344 1.441879 1.424003

P4 1.414367 1044015 1.439824 1.442043 1.456347 1.421737

Table-2 SNR for each chest lead at each position for db 2

V1 V2 V3 V4 V5 V6

P2 1.414134 1.440958 1.489533 1.514375 1.490382 1.426404

P1 1.440701 1.496208 1.518312 1.601702 1.574805 1.445142

P0 1.478734 1.501767 1.506195 1.541437 1.478572 1.500274


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V1 V2 V3 V4 V5 V6

P2 1.415629 1.445413 1.495063 1.520975 1.503227 1.434236

P1 1.453038 1.502442 1.524832 1.605946 1.580539 1.454775

P0 1.488108 1.515635 1.512455 1.547677 1.481741 1.506244

P3 1.485501 1.500604 1.504551 1.474098 1.497845 1.476716

P4 1.499673 1.531103 1.50262 1.505456 1.522371 1.495016


V1 V2 V3 V4 V5 V6

P2 1.419177 1.449284 1.49579 1.522194 1.50477 1.437906

P1 1.451151 1.500147 1.519459 1.603498 1.583975 1.454446

P0 1.494582 1.516509 1.515939 1.549529 1.480124 1.503581

P3 1.489877 1.498207 1.507954 1.468073 1.497801 1.473521

P4 1.497655 1.530753 1.507267 1.508975 1.524416 1.494414

P3 1.47878 1.49177 1.499949 1.469244 1.48732 1.464827

P4 1.486097 1.514505 1.497219 1.505028 1.518086 1.485658


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V1 V2 V3 V4 V5 V6

P2 1.421214 1.446092 1.496898 1.524186 1.506738 1.435229

P1 1.452366 1.501381 1.524075 1.600109 1.581572 1.452924

P0 1.491184 1.512012 1.516406 1.549593 1.479018 1.506798

P3 1.488027 1.502615 1.508345 1046987 1.493774 1.475378

P4 1.503949 1.529962 1.504762 1.507317 1.521862 1.492161

4 Conclusion

Plotting maps for patients suffering from anterior ischemia of the heart provides more details about the

propagation state of the bio-electrical signals of the ventricles of the heart, because the approach makes

use of four new positions for chest leads in addition to the traditional ECG positions. The appearance of

negative signal amplitudes in the maps reflects the bio-potential state of the ventricles, suggesting

anterior ischemia of heart.. By calculating SNR, we found that db4 is the best in case of p1 with V1,

V2, V3, V4, and V6; p0 with V5; p3 with V4, V5, and V6; and p4 with V2 and V6. On the other hand,

db8 is the best choice in case of p2 with V2 and V6; p1 with V5; p0 with V1 and V2; p3 with V1;

and p4 with V3,V4, and V5. Finally db11 is the best choice in case of p2 with V1, V3, V4, and V5;

p0 with V3, V4, and V6; p3 with V2 and V3; and p4 with V1. Therefore, the sensitivity and fidelity

of db4 for the five positions of the six chest leads is 36.33%, whereas it is 30% for db8, and

33.33% for db11.

Authors’ contribution

Eng. Mohamed Aouf is PhD student by Prof. Amr Sharawy, he has proposed the usage of the 3D wavelet

transform for the construction of the cardiac maps and signal denoising. For these purposes he has

developed the algorithms. and the implementation of the wavelet transform. Furthermore, he was

responsible for data acquisition. Dr. Mohammed Salem was responsible for the implementation of the

wavelet transform and the revision the corresponding parts of the paper. Prof. Amr Sharway guided

Eng. Aouf through the whole cycle of work. He has proved the correctness of the results and the paper.

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