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 V 1 . 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.
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USING WAVELET TRANSFORM FOR CARDIAC MAPPING DE-NOISING OF HEART ANTERIOR SURFACE ISCHEMIA
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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
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.
Aouf et. al: Using Wavelet Transform For Cardiac Mapping De-Noising Of Heart Anterior Surface Ischemia
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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
Aouf et. al: Using Wavelet Transform For Cardiac Mapping De-Noising Of Heart Anterior Surface Ischemia
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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