55 3.4 Distributions of ECE in wavelet subbands for real ECG signal (dataset-MO1-003 from .CSE multilead measurement library) and Gaussian noise. The data set is taken from the CSE multilead measurement library and wave decomposition is used using six-level Daubechies 9/7 biorthogonal wave filters.
Electrocardiogram (ECG) and Its Clinical Components
A normal Q wave has a duration of less than 40 ms and its amplitude is 25% of the amplitude of the R wave. QRS complex: The QRS complex represents the depolarization of the cardiac muscle cells of the ven-.
Multichannel Electrocardiogram
Correlations of Electrical Activities with Multichannel ECG
The bipolar limb leads (I, II and III) and the extended limb leads (aVR, aVL and aVF) show the electrical activity of the heart from the edges of the frontal plane. The vectors at a certain angle make it easier to see the electrical activity of the heart with the weight in the direction.
ECG Signal Components in Different Leads
QRS complex is positive in leads-I and lead-V6 and negative in lead-aVR and lead-V1. The forces generated by the left ventricle dominate, and therefore a small R wave is followed in lead V1.
Processing of ECG Signals
Preprocessing
The ECG filtering techniques are used to pre-process the signal before applying other algorithms. The spectral content is in the range from 1 to 10 Hz, which overlaps with the spectrum of the PQRST complex.
Compression of ECG Signals
Time Domain Compression
Some methods use more than one variable to achieve the desired data reduction. The performance evaluation shows that there is a significant improvement in the Signal to Noise Ratio (SNR) and Root Mean Square Error (RMSE) at the same bit rate.
Frequency Domain Compression
The use of non-uniform quantizers and entropy coding improves the performance of the basic encoder. Madhukar and Murthy [60] presented a compression algorithm based on parametric modeling of single discrete cosine transformed ECG signal.
Error Measures
For the same value of polynomial expansions, the compression ratio of the Discrete Cosine Transform (DCT) is only half. It is measured at a predetermined time interval from the end of the QRS complex [15].
Wavelet Transform and ECG Signal
Chen and Itoh [73] presented a new ECG compression method based on the orthonormal wavelet transform together with an adaptive quantization strategy. 81] have proposed an ECG compression method based on the one-dimensional discrete periodized wavelet transform (NRDPWT).
Scope for the Present Work
Organization of the Thesis
Multiresolution Pyramidal Decomposition
Five-level wavelet decomposition yields an approximate subband, cA5, and five detailed subbands, cD5, cD4, cD3, cD2, and cD1. It has been reported that the lower frequency subbands contain most of the diagnostically significant information of the ECG signal [71]. In Figure 2.2, the original Lead-I signal from the CSE multilead measurement library, Dataset: MO1-041 is plotted together with its reconstructed subband signals due to six-level wavelet decomposition.
Wavelet Transform based Noise Elimination
Another noise reduction method is proposed based on energy features preserved by wavelet coefficients in conjunctive scales and their neighborhoods [112]. Xiao-Li Yang and Jing-Tian Tang [114] proposed Hilbert-Huang Transform (HHT) and wavelet transform based method to detect R wave and denoise ECG signal. Using his wavelet transform he denoised the ECG signal and then applied Empirical Mode Decomposition (EMD) to the electrocardiogram (ECG) by decomposing it into a limited number of intrinsic mode functions (IMFs).
Wavelet Transform based ECG Compression
81] have proposed an ECG compression method based on the one-dimensional nonrecursive discrete periodic wave transform (NRDPWT). 80] presented a wavelet transform-based ECG compression method with a low delay property for continuous ECG transmission, suitable for telecardiology applications over a wireless network. Two more new wavelet threshold-based ECG compression algorithms are proposed for real-time applications [102] that take into account the target distortion level (TDL) and target data rate (TDR).
Principal Component Analysis and ECG
ECG signal enhancement, a robust extension of classical PCA by analyzing shorter signal segments, is proposed [119]. PCA is used as a tool to separate respiratory and non-respiratory segments in an ECG signal [14]. The method is evaluated to a single-lead scheme considering different types of simulated and physiological noise under realistic conditions.
ECG Signal Distortion Measure
The mean square error (MSE) between the original and the processed ECG signal is used as a quality measure. The normalized mean square error (NMSE) between the original and the processed ECG signal is defined as. The root mean square error (RMSE) is another measure used to evaluate the distortion and is defined as.
Motivation for This Work
Higher order statistics at different wavelet subbands are examined for significant information about the data in time and frequency. The eigenvalues at different wave scales capture the energy of the signal and clinical information. The denoising is based on a hybrid method where Kurtosis of the signal is used in wavelet domain.
Proposed Denoising Methods
Denoising using Higher Order Statistics in Wavelet Subbands
- Proposed Threshold based on HOS and ECE
Different physiological information of the ECG signal is present in a wavelet subband, based on their frequency content. The fourth order statistics of a signal can be evaluated by estimating the Kurtosis value of the signal. Each noise elimination threshold must take into account both the Kurtosis and ECE values of the subband.
Denoising based on Kurtosis, Variance and Energy
- Proposed Thresholding Scheme
It is observed that most of the signal energy remains in the cA5, cD5 and cD4 subbands [102]. It is observed that (Figure 3.4) the lower order subbands have relatively higher noise energy compared to the signal energy. Lower order subbands are expected to have relatively higher noise energy compared to signal energy.
Evaluation of Proposed Denoising Methods
Results for Denoising using Higher Order Statistics
- Evaluation of Proposed Denoising Factors
- Evaluation of Proposed Method under Noise Conditions
The filtered signal in Figure 3.7(b) has all the fine details of the original signal while removing the noise. In Figure 3.7(d), the filtered or attenuated signal with DFj2M1 threshold shows that noise is not completely removed as marked by 1 and 2. Figure 3.9 shows the WEDD and WWPRD values when each of the three subbands are individually thresholded.
Results for Denoising based on Kurtosis, Noise Variance and Multiscale Energy 70
The Lead-III wavelet filtered signal with original signal and residual error is shown in Figure 3.15. In panel (a) original lead-II ECG signal, (b) wavelet-filtered signal using αj (factor-1), (c) wavelet-filtered signal using βj (factor-2), (d) wavelet-filtered signal using γj and (e) wavelet-filtered signal using DFdj. In Figure 3.16, the wavelet filtered signals using the above three methods are shown and compared with the proposed noise reduction method.
Summary
The performance of the proposed thresholding method was evaluated using a synthetic ECG signal after adding noise and a recorded signal from the database. The proposed denoising method not only efficiently filters the ECG signal, but also can help preserve the clinical information in the signal. Correlation of multichannel ECG data in waltz subbands can help to perform PCA without affecting clinical information.
Proposed Multiscale Principal Component Analysis
Multiscale Multivariate Energy Contribution Efficiency
The analysis of ECE for 12-lead ECG for six-level wavelet decomposition suggests the relative importance of subbands. For multiscale subband matrices, the relative energy contribution from individual matrix is proposed as multiscale multivariate energy contribution efficiency (MMECE). Lower energy content in lower order subband matrices may be due to non-clinic components.
Multiscale Correlations
This may be due to the presence of components of the MECG, such as P waves, T waves and part of QRS complexes. The coefficients are arranged in different subbands and multiscale matrices are formed by block shown as multiscale subband matrices. To get the reconstructed subband matrices from the dimension-reduced data set, the following matrix operation is performed as.
Selection of Principal Components
- Selection of PC based on Wavelet Subband Weights
- Selection of PC based on Fractional Energy
It is proposed to assign weights to select the number of PC at wavelet subband matrices as WAL=. In Equation (4.18) and Equation (4.19), weights for approximation and detail subband matrices are derived from energy characteristics. The average fractional energy contribution (AFEC) of the eigenvalues in approximation and details subband matrices is defined as.
Proposed MSPCA based Compression Method
After PCA operation on wavelet scales, the transformed coefficients are uniformly quantized and Huffman coded for multichannel compression. Finally, in the fourth step, PCA coefficients are uniformly quantized and Huffman coded to achieve multi-channel compression. For reconstruction of the original signals, Huffman coded PCA coefficients are decoded using Huffman decoder.
Results and Discussion
Results for Multiscale PCA
- Evaluation of Signal Distortion
Since this is evaluated in the covariance matrices, it indicates that the higher order wavelet scale has more redundant signal information compared to the lower order scales. It is observed that the matrices formed by taking the lower order subband coefficients contribute less compared to other higher order subband matrices. By applying the proposed PC selection method, the dimensions are reduced to three subband matrices of the lowest order.
Results for MSPCA based Compression Method
Due to higher correlation values in D5, D6 and Table 4.7: Number of PCs selected using the proposed method. This suggests that the number of PCs selected due to the uncorrelated signal present in the matrix. In Table 4.9, the MOS errors for ECG segments or diagnostic features and the MOS error for the overall reconstructed signals are shown for lead-I, lead-aVL and lead-V5 signals (Fig.4.12).
Evaluation of MSPCA based Compression Method under Noise Conditions
In Figure 4.16, Gaussian noise and baseline drift are added to the lead-II signal. a) Lead-II signal with noise and baseline wander. In Figure 4.17, the input signal (lead-II) is corrupted with Gaussian noise, baseline wander and power line noise. The corrupt signal is subjected to MSPCA-based dimensionality reduction and then. a) Lead-II signal with baseline wander and powerline noise.
Summary
PCA based Clinical Entropy
A multivariate N ×n signal matrix, S, is constructed with n number of channels as columns and N number of samples in each channel. Figure 5.1 shows the ECG signal of lead I and the corresponding reconstructed signal after extraction of selected principal components. Thus, the self-information and eigenvalue entropy for conventional PCA can be estimated using this probability value.
Multiscale PCA based Clinical Entropy
In conventional PCA, the threshold, TALandTDj, for approximation and the details for PC selection are defined as. So, the choice of PC number based on the content of clinical information is more meaningful. This reduced number of PCs can help express data with new dimensions to preserve clinical content.
Multiscale Distortion Measure
The deviation of the signal energy from the original due to dimensionality reduction using MSPCA is well reflected in the proposed method. Thus, multilevel distortion (MD) is proposed and defined as. 5.18) This measure of error represents the distortion introduced by the multistage operation of the signals.
Results and Discussions
Evaluation of Multiscale Distortion
Multichannel ECG (MECG) signals from standard ECG database, CSE multilead measurement library, dataset-M01-021, are considered. In panels (a) Original Lead-V6 signal, (b) Signal with distortion introduced in first three beats by random Gaussian noise (c) reconstructed signals using proposed Centropy-based MSPCA. In panels (a) Original Lead-V6 signal, (b) Signal with distortion introduced in the isoelectric region by random Gaussian noise (c) reconstructed signals using proposed Centropy-based MSPCA.
Summary
Panas, "ECG Data Compression Using Wavelets and Higher Order Statistics Methods," IEEE Transactions on Information Technology in Biomedicine, vol. Hung, "A New ECG Data Compression Method Based on Nonrecursive Discrete Periodized Wavelet Transform," IEEE Transactions on Biomedical Engineering, vol. A kurtosis-based hybrid threshold method for mechanical signal decomposition," Transactions of the ASME, vol. et al., "Peak-valley segmentation algorithm for kurtosis analysis and classification of fatigue time series data," European Journal of Scientific Research, ISSN 1450-216X, vol.
Clinical components of an ECG signal with their duration and amplitude
Bipolar limb leads configuration and Einthoven’s triangle
Unipolar leads: Augmented limb leads and chest leads
Viewing the heart in horizontal plane with chest leads
Electrical axes for vertical directional views of the heart for bipolar limb leads and
Signals in limb leads and chest leads due to activation sequence
System block diagram
Wavelet decomposition (Analysis) structure
Original time domain Lead-I signal and reconstructed subbands signals due to six
Original time domain Lead-aVR and V6 signals and their reconstructed subbands sig-
Spectrums (Weltch method) of wavelet sub-bands (Decompositions up to 6 level), CSE
