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To the faculty members of the department who directly or indirectly helped me during my research work. Furthermore, the accuracy of the proposed method is evaluated without overfitting the training and testing datasets.

ECG and its Morphological Features

ST segment: It represents the period from the end of systole to the beginning of repolarization of the ventricles. Therefore, during the diagnosis of heart problems, the amplitude of the deviation and the shape of the ST segment play an important role.

Multilead Electrocardiogram

It can be classified as a non-event because it appears as a straight line between the QRS complex and the T wave. However, myocardial infarction or ischemia can cause ST-segment depression or elevation.

ECG/MECG Data Processing

One of the common problems in this case is the separation of fetal ECG from maternal ECG [11]. Nowadays, beat detection has become part of the pre-processing stage in most of the ECG applications.

Correlations Exploitation for Dimensionality Reduction

Time-domain-based methods

The limitations of this method are the fixed and poor SRR (2:1) and distortions in the reconstructed signal. However, these methods do not deal well with the diagnostic characteristics of the ECG signal, so the reconstructed signal accuracy is not acceptable to cardiologists.

Transform-domain-based methods

Data independent transforms
Data dependent transforms
Hybrid transforms

The modified SPIHT algorithm used the redundancy present among medium and high frequency subbands of the wavelet coefficients. The proposed method was able to exploit intra- and inter-beat correlations of the ECG signal.

Feature Extraction for MI Classification

While time-domain features are direct measures of MI, these feature or parameter values change in the presence of noise. Instead of classifying one or two types of MI from normal subjects, this method classifies six types of MI.

TWA Analysis

Methods based on time-domain ECG signal processing have included the use of QRS measurements and neural networks [70], ST elevation parameters using neural-fuzzy approaches [71], Q- and T-wave amplitudes, and ST-deviation features [ 66], ST conjunction analysis using multiple instance learning [67]. To extract information that may not be readily available from the original time domain signal, transform domain tools are applied to single or multi-lead ECG signals to capture more distinctive features.

Scope of the Present Work

Meanwhile, the correlations have been exploited to reduce data dimensionality in most of the articles. It is expected that exploiting correlations present in wavelet coefficients will not only improve storage efficiency and computation time, but also help for other purposes.

Organization of the Thesis

Multiresolution/multiscale analysis and synthesis

The scaling and wavelet functions together resolve the signal into coarse (low resolution) and fine (high resolution) components, respectively, as x(t) =Aj(t) +Dj(t) +Dj−1(t ) +· · ·+D1(t) (2.5) where Aj(t) andDj(t) are the approximation and detail components in the levels. In general, at the j decomposition level, the detail subbands are denoted as Dj, j L and the approximation subband is denoted as AL, where L is the wavelet decomposition level.

Multiscale decomposition of MECG data

The recombination of the wavelet coefficients to reconstruct the original signal is basically a synthesis problem. In this thesis, correlations found in both subband wavelet coefficients (Chapters 3 and 4) and reconstructed subband signals (Chapter 5) were exploited.

Figure 2.1: Original ECG leads after baseline-wander removal and their subband coefficients with six level decomposition

PCA- and SVD-based ECG Analysis: A Methodological Review

PCA/KLT and SVD

Although KLT and PCA are described interchangeably in the literature and are quite equivalent, the only difference is that KLT analyzes the spectrum of the covariance matrix (RX), whereas PCA analyzes the spectrum of the sample covariance matrix (RˆX), where the sample means have been removed. The matrix U contains eigenvectors for the covariance matrix R1 =XXT, while V contains the eigenvectors for the covariance matrix R2 = XTX.

Steps for implementation of PCA- or SVD-based methods

Preprocessing stage
Transform stage
Thresholding stage with performance measure

A multiscale PCA (MSPCA) algorithm was proposed to preserve the diagnostic information of MECG data [16]. In this method, essentially a fixed percentage of the information energy of the data matrix is preserved.

Feature Extraction Methods for MI Classification

Support vector machine classifier

TWA Analysis Methods

Spectral method

Detection is performed using a significance measure called the TWA Ratio (TWAR), which is calculated as the ratio of the alternator's power divided by the standard deviation of the noise. The global TWA amplitude is estimated as the square root of the alternating power and is given as.

Modified moving average method

Since the spectrum is based on measurements taken once per beat, its frequencies are in units of cycles per beat (cpb). The frequency corresponding to an oscillation that occurs every other beat is 0.5 cpb and is called the alternans frequency.

Recent methods for TWA analysis

A multilead TWA analysis scheme using periodic component analysis (πCA) was also proposed by the same authors in [95]. The limitation of this method is that it cannot be used to determine lead-wise TWA analysis.

ECG Databases

PTB database

TWA/CinC challenge database

ECG Performance Evaluation Measures

Distortion measures

Although the WDD measurement correlates well with visual inspection, it suffers from high computational complexity due to the requirement to accurately evaluate all diagnostic features and calculate optimal weights for significant features. Source error due to classification and comparison of waveform irregularities can degrade the accuracy of the WDD measure.

Classification performance measures

Also, the non-stationary nature of the ECG signal and artifacts can lead to a false detection of morphological features. Specificity (Spe) is the probability referring to negative MI results, and is calculated as

Motivation of the Thesis

Work Plan of the Thesis

This can help exploit correlations between beats and between MECG data leads. Due to the inherent property (two-factor variational modeling) of SVD, the morphological features of MECG data in different subbands of waltzes can be analyzed using SVD.

Figure 2.2: Schematic representation of the contribution of the thesis.

Proposed Multiscale SVD Method for MECG Data

Multiscale subband matrix formation

The MRA property of DWT is applied to each lead of the preprocessed MECG data (Xm×p) individually, where m and p represent the number of leads and ECG samples of each lead, respectively. Another advantage is that the shape of the scaling and decomposed wavelet functions of these filters resembles the ECG signal [133].

SVD on subband matrices

Consequently, the p−mrows of the unit matrix will have no effect in the product of the unit matrix with the singular value matrix (3.6). Low or near-zero MRED values of D1 for both normal and pathological data are due to absence of the most important diagnostic components.

Thresholding of singular values

As the value of ν increases, the drop in the selected SVs is quite large in the case of high-frequency subband matrices. The energy content of high-frequency subband matrices is comparatively very low than the entire TH subband.

Figure 3.4: Average number of SVs selected for different values of ν. With increase in ν, the drop in selected SVs for low frequency subband matrices A 6 , D 6 and D 5 is marginal and is opposite to high frequency subband matrices D 1 , D 2 and D 3 , where

Performance Measures and Comparative Analysis

Dimensionality reduction performance

Compressed MECG performance measure
Distortion measure evaluation

It is observed that the SVs are selected depending on the diagnostic significance of the subbands, i.e. reduction in the number of SVs with corresponding left and right singular vectors of high frequency subbands will result in faster processing during encoding and transmission.

Figure 3.5: Compression ratio, quantization bits/sample and distortion measures, (a) CR vs quantization bits/sample (b) APRD, AWEDD vs CR

Comparison with existing methods

Simulation Study of the Proposed Method for WBSN Applications

Transmission of Huffman encoded MECG bit-stream

The value of Ex/No that results in an error-free bit stream is chosen to be optimal. Since the quantized coefficients are produced by the Huffman coding method, a complete error-free bit stream is required at the receiver.

Figure 3.7: (a), (b): Original signals and (c), (d) (e) and (f): Reconstructed Signals at E x /N o = 8 dB and 10 dB of Lead-III and V5 respectively, Dataset: s0008_rem, PTB Diagnostic ECG Database

Computational complexity measure

In the DS-UWB modulation technique, each bit of the binary bit stream is represented as a number of pulses. Therefore, it is certain that the number of calculations increases with the number of non-zero coefficients to be coded (Ns).

Summary

There are three types of correlations, namely intra-beat, inter-beat and inter-lead correlations present in the MECG data. This is one of the purposes of this third-order tensor representation for the MECG data.

Tensor Notations and Conventions: A Preview

Higher-Order SVD

Hence, firstp′ =mnfrontal slices of the kernel tensor have significant nonzero values, and restp−p′frontal slices have entries on the order of 10−12 or less, which can be set to zero. The above ordered property gives information about the energy of the nuclear tensor concentrated in the s111 element.

Figure 4.2: HOSVD visualization and approximation for a third-order tensor)

Proposed MHOSVD-based Method

Signal preprocessing
Construction of third-order MECG tensor
Multiscale decomposition of the MECG tensor
HOSVD application on subband tensors
Thresholding of mode singular values
Feature selection

The decreasing nature of the MSVs along different modes of each subband tensor can be used as a measure of the approximation [128, property 10]. The NMWE for the approximation or detail subband tensors along mode-3 is given as.

Figure 4.3: (i) Block diagram of MECG tensor dimension reduction and feature extraction for MI detection and localization

Dimensionality Reduction Performance Evaluation

Performance measures

These high values are the result of inaccurate detection of some characteristic properties of these noisy conductors. This may be due to the irregular nature of the heartbeat, where the QRS detection algorithm does not detect the exact R peaks.

Comparison with existing data reduction methods

High PRD (> 24) in leads aVR and aVF does not mean poor quality of reconstruction, but it is a result of noise removal in these leads (Figure 4.6). This problem can be solved by an efficient QRS detection algorithm for dysrhythmia or similar type of diagnostic classes.

MI Classification Performance Evaluation

MI detection

Random sampling can select cases from the same subject during the training and testing process. To avoid this redundancy problem in this work, examples from the set of subjects are considered during training.

MI localization

From these results, it is clear that the SVM classifier with the χ2 kernel function performs better than the other two kernels. As described in Section 4.3.6, a 51-dimensional feature set is treated as input to the MSVM classifier.

Comparison performance

During the training of the MSVM classifier, 100 instances each of five MI subsets are considered as five classes with the same kernel parameters.

Summary

Signal preprocessing
Tensor MECG formation
T-wave reconstruction using multiscale analysis-by-synthesis
TWA analysis using HOSVD on T-wave tensor
TWA detection decision and estimation

In temporal approximation (Figure 5.2), the TWA analysis was performed with the time domain ECG signal. A segmentation window of 320 ms, after the end of the QRS complex, was selected for the TWA analysis.

Figure 5.1: Visualization of TWA in some leads (I, V1, V2, and V5). Average heart rate = 113.705 beats/min over a 32-beat analysis window

Datasets

Semi-synthetic dataset

Since clean and noisy signals are sampled at different sampling rates, noisy signals were resampled at 500 Hz. To add the noise signal to the clean signal, a noise segment of length equal to the length of the clean signal was extracted.

Physionet TWA database

Experiments on 8-lead Semi-synthetic Signals

Observations with temporal method
Observations with MAS method
Observations with MAS-HOSVD method
Comparison with the state-of-the-art methods

For the TWA amplitude range of 10 to 60 µV, the MAS-HOSVD method detects alternately by at least PD = 0.197 higher than the multi-PCA method. Reduction in PD for a given Valt of the MAS-HOSVD method is lower than the multi-PCA method.

Figure 5.3: Variation of P D vs P FA for SNR = 20 dB

Experimental Observations on 8-lead TWA ECG signals

Observations with MAS-HOSVD method

These fragments are added with SNR of 20 dB and the resulting ECG fragments are shown in Figure 5.8 (c) and (d). The TensorTinfo information of leads V4 and V5, after applying MAS-HOSVD, are shown in Figure 5.8 (k) and (l), respectively.

Figure 5.8: ECG fragments of two chest leads (V4 and V5). (a) and (b): baseline removed original ECG fragments, observed TWA amplitudes in V4 and V5 are 61.5 and 24.6 µV , respectively (c) and (d): ECG fragments of (a) and (b) with SNR of 20 dB, (e) and (f

Comparison using Kendall rank correlation coefficient

Study of MI Progression using TWA Analysis

In contrast to the IMI case, persistent TWA is experienced in some subjects due to the infarct in the lateral wall of the ventricle. The presence of TWA (change in amplitude) is more prominent in different chest leads depending on the type of acute MI.

Figure 5.9: Variation of TWA amplitude in leads I, II, V1 – V6 for (a) HC, (b) AMI, (c) ALMI, (d) ASMI, (e) IMI, and (f) ILMI cases, respectively

Summary

Martinez, “Multilead analysis of T-wave alternans in the ECG using principal component analysis,” IEEE Trans. Dandapat, “Exploiting multi-lead ECG correlation using robust 3-matrix tensor decomposition”, IET-Healthcare Technology Letters, vol.2, issue 5, p.