It is observed that cA6 subband reflects the parts of low frequency components such as P-wave and T-wave in leads (Figure 2.3(a) and (b)). The cD6 and the cD5 subbands show the lower frequency component of QRS-complex with higher frequency component of T-wave. The cD4 and the cD3 subbands show the significant higher frequency component of QRS-complex. The cD2 and the cD1 subbands contain some higher frequency component of QRS-complex and noise. It is seen that in same subband levels of both the cases, there are similarities between segmented signal components.
So, it is expected to get higher correlation between different channels in the same subband level.
The signals at a wavelet scale across different channels show similarity in terms of morphol- ogy, beat patterns, the frequency content and energy contribution. So, there is a scope of applying multivariate data analysis at a wavelet scale by arranging the coefficients of all the channels as mul- tivariate data. These multivariate data are expected to show inter-channel redundancies at a wavelet scale. Also, it is expected to have similar pattern of multiscale energy for multivariate data. Based on these assumptions, dimensions can be reduced applying PCA at wavelet scales for non-significant multivariate data. Higher order wavelet scales may show higher correlations (Figure 2.3(a) and (b)), but they have vital clinical components. To avoid losing clinical details, data in three lower order scales can be considered for dimension reduction. Other data in higher scales may not be subjected to dimension reduction. This motivates to develop multiscale principal component analysis for mul- tichannel electrocardiogram data. Multivariate analysis of multichannel ECG as multivariate data in wavelet domain may introduce distortion in signals. It is necessary to find the processing errors which may alter the clinical information. So, it may be necessary to develop distortion measure for MSPCA application.
The proposed investigations in this thesis are planned as
• To explore wavelet based preprocessing stage for multichannel ECG signals which rely on real data. Higher order statistics at different wavelet subbands is investigated for significant infor- mation of the data in time and frequency. The fourth order cumulant, Kurtosis, can be used as a measure of Gaussianity. Median absolute deviation (MAD), is scaled by a normalized wavelet subband Kurtosis instead of conventional statistical quantile function for Gaussian distribution.
Combining these with the relative signal energy of wavelet subband, thresholds are derived for
2.6 Motivation for This Work
removal of noise. The observations made in this preprocessing stage, motivates us for further analysis of multichannel signals in wavelet domain.
• To investigate multiscale principal component analysis of multichannel ECG. The multiscale properties of wavelet transform and the correlations between subband ECG data of different channels are evaluated. Also, the relative energy contribution of wavelet subbands for all mul- tichannel ECG signals are investigated. The study of correlations and multiscale energies of subbands are exploited for efficient processing of multichannel data. The inter-lead correlations in wavelet domain may lead us to develop signal enhancement and data compression scheme.
• To compress multichannel ECG signals using multiscale PCA. In wavelet domain, if similar sub- bands of multichannel signals are arranged in matrix, principal components analysis (PCA) can be performed. This multiscale PCA for multiscale data helps reduce dimension and remove redundant information present in original data set. The proper selection of principal compo- nents (PC), gives fair representation of original data with reduced number of PCA coefficients.
Multichannel compression is implemented using uniform quantizer and entropy coding of PCA coefficients. For data reduction application for signals like multichannel ECG, the method for selection of PC is an important step. The selected PC has to represent the clinical information while discarding non-significant PC has to remove redundant information.
• To develop a clinical entropy measure to better represent clinical information. Clinical entropy (Centropy) can be defined which is relevant to clinical information present in an ECG signal. The eigenvalues at different wavelet scales capture the energy of the signal and clinical information.
Clinical entropy is investigated from the diagonal eigenvalue matrix. Centropy based PC selec- tion may be applied in PCA and MSPCA based processing of multichannel ECG signal. Also, a signal distortion measure for multichannel ECG is investigated for MSPCA application. Af- ter reconstruction of MSPCA processed multichannel signals, Multiscale Multivariate Distortion (MMD) is evaluated for matrices at different wavelet scales. The average Multiscale Distortion (MD) is evaluated based on MMDs.
3
Preprocessing of Multichannel ECG
Contents
3.1 Wavelet based Denoising of Multichannel ECG . . . 47 3.2 Proposed Denoising Methods . . . 48 3.3 Evaluation of Proposed Denoising Methods . . . 60 3.4 Summary . . . 78
The recorded ECG may contain undesired signals like high frequency slur and noises and artifacts.
Preprocessing of ECG emphasizes the signal. It improves the signal quality for more accurate anal- ysis, measurement and interpretation. The conventional bandpass filtering techniques may not be effective for ECG signal. The main challenge is to retain clinically relevant features of the P-wave, T-wave, ST-segment etc, having overlapping spectra with noise. Also, these methods require a priori knowledge of noise and signal distributions. Spectral substraction method may introduce artificial noise and disturb the original signal [23]. Due to non-stationary nature of ECG and noise signals, Wiener filter may not yield good result [24]. Adaptive filtering is one of the popular methods for ECG filtering [25, 26] due to its ability to denoise signal with overlapping spectra.
Wavelet based denoising method is simple, but to find a suitable threshold, a priori knowledge of signal and noise distributions in different subbands are required. Wavelet based denoising captures the energy of the original signal to a higher percentage by thresholding the noisy coefficients [110].
The performance of this threshold depends on an efficient estimation of noise variance. The motiva- tion of the present work is to derive a more meaningful threshold which depends on noise variance, number of samples and higher order statistics.
In this Chapter, two denoising methods are proposed and evaluated. The first denoising method is based on evaluation of higher order statistics at different wavelet bands for an electrocardiogram (ECG) signal. Higher order statistics at different wavelet bands provides significant information about the statistical nature of the data in time and frequency. The fourth order cumulant, Kurtosis, and the Energy Contribution Efficiency (ECE) of signal in a wavelet subband are combined to assess the noise content in the signal. Accordingly, four denoising factors are proposed. In the second denoising method, a threshold is derived by considering energy contribution of a wavelet subband, noise variance which is based on a novel Gaussian measure, Kurtosis, and number of samples.
The robust noise estimator, median absolute deviation (MAD), is scaled by a normalized wavelet subband Kurtosis instead of conventional statistical quantile function for Gaussian distribution. Sig- nal distortion is evaluated using percentage root mean square difference (PRD), wavelet weighted percentage root mean square difference (WWPRD) and wavelet energy based diagnostic distortion (WEDD) measures. The results are compared with existing standard thresholding methods. The Section 3.1, discusses wavelet based denoising of multichannel ECG signals. In Section 3.2, two
3.1 Wavelet based Denoising of Multichannel ECG
proposed wavelet denoising methods are described. Section 3.3, and Section 3.3.3 give evaluations of proposed denoising methods and comparison of both the methods respectively.
3.1 Wavelet based Denoising of Multichannel ECG
The electrocardiogram (ECG) signal denoising in wavelet domain is based on the soft or the hard thresholding methods. Based on noise variance, the wavelet coefficients are thresholded at t = σp
2 log(N)/N, wheret is threshold, σ is the variance of noise and N is the numbers of samples [28, 29]. It is claimed that the noise is better suppressed while the desirable features of the original signal remained unaltered. In this approach, the threshold value depends on noise variance, σ, and the length or number of samples, (N), of the data. The values of transform coefficients whose magnitudes lie below the threshold are set to zero. It is shown that the threshold is optimum if power of discarded wavelet coefficients equals the noise power [111]. Another method of noise reduction based on energy features of wavelet coefficients at conjunctive scales and their neighborhoods is proposed [112]. Wavelet based denoising method requires a priori knowledge of signal and noise distributions in different subbands are required. A nonlinear Bayesian filtering framework for single channel ECG signal denoising is demonstrated over conventional bandpass filtering, adaptive filtering and wavelet denoising [19]. In this, denoising of abnormal ECGs with cardiac arrythmia and over- filtering of signal which may result in loss of clinical and diagnostic information are not addressed. A comparison between adaptive filtering and wavelet shrinkage for denoising of nonlinear time series is carried out [30].
Higher order statistics is useful when dealing with non-Gaussian or possible nonlinear processes and many real world applications are truly non-Gaussian [139]. Higher order statistics-based meth- ods are used by authors for evaluation of noise in the signals. Noise reduction in magnetocardiog- raphy by using the higher order statistics is reported [140]. In this paper, fourth order cumulant, is evaluated from the time domain signal for assessment of abrupt changes in the signal. Kurtosis in wavelet subband is used for spike detection in human muscle sympathetic nerve activity [141]. In this work, local Kurtosis is computed over Nkdetails coefficients at level j. Similarly, a mechanical fault signal denoising is proposed [142]. The denoising is based on a hybrid method where Kurtosis of the signal in wavelet domain is used. Kurtosis is used in engineering for detection of fault symptoms
because of its sensitivity to high amplitude events [143]. In this work, information in the form of higher order statistics at wavelet subbands are exploited to find an effective denoising method for ECG sig- nals. Then denoising method is further investigated by estimating threshold which depends on noise variance, number of samples and higher order statistics.