0 500 1000 1500 2000 2500 3000
−1 0 1
(a) Original signal ( Lead−II ECG, CSE multilead measurement library, M01−003 )
0 500 1000 1500 2000 2500 3000
−1 0 1
(c) Wavelet filtered signal after hard thresholding using proposed method−M2
Sample
0 500 1000 1500 2000 2500 3000
−1 0 1
(b) Wavelet filtered signal after hard thresholding using proposed method−M1
Amplitude
Figure 3.17: Wavelet filtered lead-II ECG signal using proposed methods (a) original signal, (b) wavelet filtered signal using proposed denoising method-M1 and (c) wavelet filtered signal using proposed denoising method- M2. CSE multilead measurement library, data set-M01-003 with six wavelet decomposition levels
.
3.4 Summary
ity measure in term of Kurtosis instead of conventional statistical approach. Lower order subbands are expected to have relatively higher noise energy compared to the signal energy. The proposed method gives higher threshold values for lower order subbands. It is the combination of three in- dividual factors, αj, βj and γj. Combined denoising factor gives improved results. The method is tested with spatially nonhomogeneous functions, Blocks, Bumps, HeaviSine and Doppler with noise.
The performance of the proposed thresholding method evaluated using synthetic ECG signal after adding noise and the recorded signal from database. Also, it is compared with the existing classical thresholding method such as soft thresholding, hard threshoding and SURE. Results show that the performance of the proposed method is better compared to the existing methods. The proposed de- noising method not only filters ECG signal effectively but also can help retain the clinical information in the signal.
4
Multiscale Principal Component Analysis for Multichannel ECG Compression
Contents
4.1 PCA for Multichannel Electrocardiogram . . . 83 4.2 Proposed Multiscale Principal Component Analysis . . . 85 4.3 Proposed MSPCA based Compression Method . . . 96 4.4 Results and Discussion . . . 98 4.5 Summary . . . 114
In this Chapter, we introduce Multiscale Principal Component Analysis (MSPCA) for multichannel electrocardiogram (MECG) signals. In wavelet domain, principal components analysis (PCA) of mul- tiscale multivariate matrices of multichannel signals may help reduce dimension and remove redun- dant information present in signals. Principal Component Analysis (PCA) is widely used for multivari- ate data analysis [124], [155]. Since last two decades, PCA is evolving with different extensions or modifications such as multiway PCA (MPCA) [125], multiblock PCA [156], non-linear PCA [126, 132], probabilistic principal component analysis [130] and weighted PCA [157]. PCA reduces data dimen- sion by retaining an optimum number of Principal Components (PC). The data set is transformed to a new dimension with a reduced set of variables [124]. PCA transforms the data matrix in a statis- tically optimal manner by diagonalizing the covariance matrix. The first few significant components capture the correlations between the variables. Elimination of insignificant components reduces the redundant information in the data set [124].
The information at different wavelet scales can be effectively analyzed using PCA. MSPCA based analysis of multichannel ECG signals are not addressed in literature. Literature reviews in Chapter 2, show the classical PCA based applications in ECG signal processing. For physiological signals like ECG and EEG, conventional PCA has been applied for data reduction, noise elimination, beat detec- tion, classification, signal separation and feature extraction [12], [119], [13]. PCA is used as a tool for separation of respiratory and non-respiratory segments in an ECG signal [14]. During processing of an ECG signal, it may not be advisable to distort the diagnostic information in the signal [102], [138].
Conventional PCA based methods have not considered the distortion of clinically important diagnos- tic features. Significant energies of cardiac signal-components or diagnostic components are present at different frequency bands in an ECG spectrum. Wavelet transform of an ECG signal reproduces them at different scales or subbands [102]. This grossly translates or segments ‘PQRST’ morpholo- gies into different subbands. In wavelet subbands, the correlation between multichannel ECG signal components can be effectively captured. Correlation of multichannel ECG data in wavelet subbands may help implementation of PCA without affecting the clinical information. This motivates us to im- plement Multiscale Principal Component Analysis (MSPCA) at wavelet scales and coding the PCA coefficients to achieve multichannel compression.
The related review of literatures in Chapter 2, show that MSPCA based processing of multichan-
4.1 PCA for Multichannel Electrocardiogram
nel ECG and compression of these signals are not addressed. It is seen that MSPCA has higher potential to represent clinical signal components in few PCA coefficients. So, in this Chapter, we propose a compression scheme for multichannel electrocardiogram (MECG) data, using Multiscale PCA (MSPCA) and Huffman coding. In Section 4.1, conventional PCA for multichannel ECG signals is discussed. Section 4.2, presents the proposed multiscale PCA for Multichannel ECG. Section 4.3 contain proposed MSPCA based compression of MECG signals. Results are discussed in Section 4.4.
4.1 PCA for Multichannel Electrocardiogram
PCA is used for ECG signal processing using cut and align or lead piling process on the single channel signal [12] to form the multivariate data. This method uses the redundancies between ECG beats. For multichannel ECG signals, conventional PCA can be applied with appropriate multivariate matrix formation. The multichannel ECG signal,S, can be represented as
S=
s11 s12 . . s1n s21 s22 . . s2n
. . . . .
sN1 sN2 . . sN n
(4.1)
wherespq is the pth sample of theqth channel signal. There are n number of channels withN number of samples in each channel. In this, individual channel data are represented in separate columns.
To explore the correlations between the data in different channels or leads of MECG signals, scatter plots and correlation coefficients can be evaluated. The scatter plot provides a graphical display of correlation between variables in a cartesian co-ordinate system [158]. Fig.4.1 shows the scatter plots and the correlation values for a 12 channel ECG data. The scatter plots between data in different ECG leads are shown in lower half triangular plot matrix and the correlation values are shown at the upper half triangular table. The diagonal elements show correlation with same channel signal. Looking at the plots, the correlations and the redundancies between pairs of channels can be intuitively imagined. If dots of scatter plot are clustered from lower left to upper right it suggests
−2 0 2 V5
−2 0 2 V4
−2 0 2 V3
−2 0 2 V2
−1 0 1 V1
−1 0 1 aVF
−10 0 10 aVL
−1 0 1 aVR
−1 0 1 III
−10 0 10 II
−5 0 5
−1 0 1
Lead−I
V6
−2 0 2
V5
−2 0 2
V4
−2 0 2
V3
−2 0 2
V2
−1 0 1
V1
−1 0 1
aVF
−10 0 10
aVL
−1 0 1
aVR
−1 0 1
III
−10 0 10
II
Correlations between leads of a 12 channel ECG
V6
Lead−I
0.8148 0.8070
0.6823
0.4480 0.4913
−0.6037
−0.1921 0.7541
−0.0135 −0.0628
0.6470 0.3706 0.3782
0.9367
0.9934
0.9555
−0.8743
−0.9849
−0.5960
−0.8256
0.9451 0.9811
−0.7009 0.9905
−0.9517
−0.1206
−0.2853
0.0277
−0.1101
−0.1080
0.0732
0.1061
−0.1112
0.8163 0.2987 0.6170
−0.5170
−0.5986 0.5797 0.6503
−0.7953 0.6958 0.8121
−0.8253
−0.5820
0.7472
0.3389
0.9175
0.9948 0.9774 0.8887 0.3053
−0.1138 0.7293
−0.5496
−0.8486 0.6576
−0.8147 0.4286 0.6322
−0.1263 0.5200
−0.3019
0.9425 0.9211 0.8453
Scatter plots between leads of a 12 channel ECG
1 1
1 1
1 1
1 1
1 1
1 1
Figure 4.1: Scatter matrix plot for original signals. Signals in different ECG leads are scatter plotted. Database used is CSE multilead measurement library, data set M01-033.
.
positive correlation. Similarly dots from upper left to lower right indicate a negative correlation. If the data points are closer to form a straight line, it indicates higher correlation between the two variables.
Between lead-I and lead-II the correlation value is high which is0.9451. Lead-I signal is the potential difference between left arm (LA) and right arm (RA) and lead-II signal is the potential difference between left leg (LL) and right arm (RA). In both the cases, right arm is the common limb and this is the reason for high correlation value between Lead-I and Lead-II data. Likewise higher correlations are found between lead-II and lead-aVR (−.9849), between lead-II and lead-aVL (0.9905), between