Many wavelet based ECG compression methods are reported and the tests are carried out using the noisy records from themitadatabase and the percentage root mean square difference (PRD) criterion in the liter- ature. A major design goal of any compression method is to obtain the best clinical quality with the highest compression ratio (CR) using the optimal coding parameters such as threshold or/and quantization bit ob- tained for a quality or distortion specification. But the measurement of distortion in the compressed signal is difficult because the distortion introduced by different types of compressors are very diverse. The effect of noise filtering is one of the features using the wavelet transform for compression and it is demonstrated in various compression results reported in the literature. In this case, the magnitude of insignificant errors may not be of much relevance from the point of view of clinical quality of the compressed signal. The ef- fects of noise on the rate-distortion performance of the proposed methods and the SPIHT based methods are demonstrated in the previous chapter. Although PRD does not exactly correspond to the result of a clinical subjective test, it is easy to calculate and compare, so it is widely used in the ECG compression literature.
Thus, in order to introduce closed loop CR or quality control, one needs an adequate diagnostic distortion measure for the compressed signal. Moreover, the choice of which distortion measure must be used for compressed signal is of critical importance when noise suppression and signal compression are established simultaneously. In the area of ECG signal compression, little attention has been paid towards the evaluation of distortion of clinical information. A suitable objective distortion measure can help proper evaluation of the well-designed ECG compression methods under noisy environments. Otherwise, the quality of the compressed signal has to be evaluated by subjective test, visual inspection of the clinical features. However, performing subjective test is a difficult task in closed loop rate or quality control method in which the op- timal coding parameters are adaptively chosen to compress time-varying PQRST morphology effectively.
A number of researchers have proposed variety of speech and image quality measures for local and global assessment. But very little effort has been made to provide an objective quality measure for the assessment of distorted ECG signal. The compression system typically involves tradeoff between the rate and quality of the output. Undoubtedly, there is a need for an objective measure for local and global assessment, and thus assessment of distorted signal quality is an open problem today.
In this chapter, a novel wavelet energy based diagnostic distortion measure is proposed for compressed ECG signal quality assessment. The proposed measure is a weighted percentage root mean square dif- ference between subband coefficients of the original and compressed signals with weights equal to the relative wavelet subband energy of the corresponding subbands. These weights may represent the actual contribution of each subband that are used to discriminate different frequency subbands particularly bands corresponding to noise. The proposed measure appears to be a correct representation of the amount of signal distortion at all scales. Experiments show that the proposed measure works substantially better than the conventional PRD and the wavelet based weighted PRD (WWPRD) measures. The proposed measure
correlates well with subjective assessments and leads to provide a better evaluation of rate-distortion per- formance of the compression method. This Chapter is organized as follows. Section 4.2 discusses ECG distortion measures and their limitations. In Section 4.3, a novel wavelet energy based diagnostic distortion measure is proposed. In Section 4.4 preliminary evaluation of the WEDD measure is presented. In Section 4.5, subjective quality assessment of the clinical features of the compressed signal is presented. In Section 4.6, quantitative and qualitative analysis of the WEDD measure is performed.
To solve the above mentioned problems, researchers have proposed objective error measures which take into account the diagnostic distortion of the local waves such as P-wave, Q-wave, QRS complex, ST segment and T-wave. Chen [129] suggested a new distortion measure, the weighted PRD to improve the local distortion measure for evaluating the fidelity of the compressed ECG signal. However, there is no procedure reported to select the optimal weights for the local waves [129]. The weighted PRD measure depends on the accurate extraction of local waves within each beat and the weights for the significant waves.
Although the WDD measure correlates well with visual inspection, it suffers from high computational complexity mainly due to the accurate evaluation of all diagnostic features and the calculation of optimal weights for the significant features. The nonstationarity of ECG signal and the artifacts may lead to a false detection of diagnostic features. This error may degrade the accuracy of the WDD measure. However, there are no standard protocols for finding the optimal weights and for implementing the weighted PRD and the WDD measures in closed loop quality control. A wavelet based quality measure, WWPRD, is based on the decomposition of the segment of interest into subbands and the weighted score is given to the band depending on the dynamic range and its diagnostic significance. The PRD measure is used as error measure for each subband is called wavelet PRD (WPRD). In WWPRD measure, the weight of each subbands is calculated as the ratio of sum of the absolute values of coefficients within that band and the sum of absolute values of wavelet coefficients in all the bands. The WWPRD measure provides a local or subband error estimation. However, it is observed in Chapter 2 that the insignificant errors in higher subbands dominate the global error.
In literature, the compression methods are commonly tested using the mita database which contains many time-varying and noise-contaminated ECG signals. In general, noise filtering capabilities of the transform based methods may not be similar for a specified compression rate. It is observed in Chapter 2 that not only the significant feature is reproduced, but also the compressed signal quality is upgraded because the insignificant coefficients dominating in higher subbands are removed for data compression.
In this case, the conventional PRD or WWPRD does not always correspond to a better clinical quality.
Moreover, noise decreases the compression ratio of any coder for a desired PRD value since the coder will spend extra bits on approximating the noise with the specified accuracy. Thus, noise will degrade the overall rate-distortion (coding) performance of any coder. Although some distortion measures correlate well with subjective quality measure for a given compression algorithm, they are not reliable for an evaluation across different algorithms. Therefore, the objective distortion measure should be coder-independent, so that it can compare the subjective qualities of various compression methods possibly entailing quite different types of distortion. Based on the results obtained in previous studies on weighted distortion measures, it appears that weighting works, however, there is no clear explanation for the reason why and how it works and how to choose an optimal set of weights. The above facts have motivated a great deal of research on objective distortion measures with clinical relevance. The multiresolution signal decomposition technique has already proven its ability in splitting signal and noise in time-frequency domain. The scope of this Chapter is to
The wavelet transform (WT) provides a description of the signal in the time-scale domain, allowing the representation of the temporal features of a signal at different resolutions. Therefore, it is a suitable tool to analyze the ECG signal which is characterized by local wave patterns (QRS complexes, P and T waves) with different frequency content. Moreover, the noise and artifacts appear at different frequency bands, thus having different contribution at various scales [147, 170]. The WT is established on basis functions formed by dilation and translation of a prototype wavelet function. They are much better suited for repre- senting short bursts of high frequency signals or long duration, slowly varying signals. The ECG data to be compressed may contain signal and various noises. The noises are often stochastic signals with broadband, whose frequency bands will overlap with the interested signals. In the traditional signal processing, the out-of-band noise can be removed by applying a linear time-invariant filtering method. However, it cannot be removed from the portions where it overlaps the signal spectrum. Therefore, it is difficult to eliminate the noise from the signals effectively with general filtering methods. In addition, traditional methods re- quire some information and assumptions about the signals that one wants to extract from the noise. The wavelet transform has already proven its ability in splitting signal and noise in wavelet domain. Recently, researchers from biomedical signal processing community have applied wavelet transform in signal com- pression, feature extraction and denoising. The reason for selection of wavelet domain processing of the ECG signal is due to varying characteristics of signal and presence of noise which restrict the application of conventional linear filtering scheme. The key idea in this technique is to utilize the wavelet localization property. As presented in Chapter 2, wavelet transforms are able to detect and localize frequency contents effectively. Therefore, we attempt to use the multiresolution signal decomposition technique for the quality assessment of distorted ECG signals in this Chapter.
The information can be organized in a hierarchical scheme of nested subspaces called multiresolution analysis inL2(ℜ). In multiresolution signal decomposition (MSD), the signalx(t)∈L2(ℜ)is decomposed to detailed and approximated versions using the scaled and translated versions of the wavelet (ψj,k(t)) and scaling functions (φj,k(t)). The approximations are the low-frequency components of the signal and the details are the high-frequency components. The MSD is used to exploit two important issues. The first is the localization property in time and will appear by the presence of large coefficients at the time. The second property is the partitioning of the signal energy at different frequency bands. The MSD for a given signalx(t)is given by
x(t) =
∞ k=
∑
−∞AJ(k)φJ,k(t) +
J
∑
j=1∞ k=
∑
−∞Dj(k)ψj,k(t) (4.1)
with AJ(k) =R−∞∞x(t)φJ,k(t)dt and Dj(k) = R−∞∞x(t)ψj,k(t)dt where J is the number of decomposition levels, AJ ={aJ(k)}k∈Z are the approximation coefficient vectors at resolution levelJ and
{Dj ={dj(k)}k∈Z}j=1,2,...J are the detail coefficient vectors. The wavelet coefficients vector is given by C= [D1D2D3· · ·DJAJ]. The frequency range of subbands Ajand Dj are given by
[0,2−j−1Fs], for approximation subbands (4.2) [2−j−1Fs,2−jFs], for detail subbands
where Fs is the sampling frequency. The signalx(n)can be expressed as the summation of approximation AJ(n)signals and detail{Dj(n)}1≤j≤J signals, that is:
x(n) =
J
∑
j=1Dj(n) +AJ(n),n=1, 2, 3...N. (4.3) The above MSD technique provides a mathematical tool with powerful structure and enormous freedom that decompose a given signal into several subsignals with different frequency bands. Eq. (4.3) provides a hierarchical and fast scheme for the computation of the wavelet coefficients of a given signal. The DWT is implemented using a multiresolution signal decomposition algorithm with the wavelet filters h(n)and g(n).
The first step in signal decomposition consists of computing these approximation and detail coefficients using the filters h(n)and g(n), respectively. The approximation signal captures the low-frequency informa- tion and the detail signal captures the high-frequency information contained in the ECG signal. Then, the wavelet coefficients of any scale (or resolution) could be computed from the wavelet coefficients of the next higher resolutions. The low frequency part is divided again into high and low frequencies. Depending upon the number of decomposition levels, the end product of a multiresolution decomposition results in a set of these signals at different frequencies, as shown in Eq. (4.4)
x(n) =xH(n) +xM1(n) +xM2(n)...+xMJ−1(n) +xL(n) (4.4) where xL is the low-frequency signal, xH is the high-frequency signal and xMi,j =1,2, ...J−1 are the medium-scale signals. For example, if a five-level decomposition of the signal is done, it results in one approximation signal (low-frequency) and five detail signals (high- and intermediate-frequency).
The process of decomposition uses a subband filtering (filter bank) that is illustrated in Figs. 4.1 (a) and (b). The DWT can be computed using the low-pass filter h(n), high-pass filter g(n)and down-sampling process. Fig. 4.1 (b) illustrates the analysis part of a five-level decomposition scheme. The original sampled signal is filtered with the scaling function and the wavelet function and down-sampled by two, resulting in the approximation and detail coefficients at level one. The approximated signal is then used as the original signal and filtered with the scaling function and the wavelet to yield the coefficients at level two. This process is repeated depending upon the number of decomposition levels desired.
G H
G
G
G
G
low-frequency components
H
H
H
H
high-frequency components
(a) Multiresolution signal decomposition: A0(n) is a sampled signal of x(t) and Fs is the sampling rate. h(n) and g(n) are the low-pass and high-pass filters, respectively. A1(n) and D1(n) are the smoothed or approximated and detailed versions, respectively.
(b) Five level multiresolution signal decomposition of signal A0. Frequency bands of the signal sampled at 360 Hz (MIT-BIH arrhythmia database).
Coefficients vectors
Aj(n) [0, Fs/2j+1] Hz A1(n)
[0, Fs/4] Hz
A0(n) [0, Fs/2] Hz
D1(n) [Fs/4, Fs/2] Hz h(n) 2
g(n) 2
D2(n) [Fs/8, Fs/4] Hz h(n) 2
g(n) 2
Dj(n) [Fs/2j+1, Fs/2j] Hz h(n) 2
2 A2(n)
[0, Fs/8] Hz
Level 1 (scale 21) Level 2 (scale 22) Level 3 (scale 23)
Level 5 (scale 25) Level 4 (scale 24)
180 Hz 90 Hz
45 Hz
22.5 Hz 11.25 Hz 5.625 Hz
0 Hz D1
D2
D3
D4
D5
A5
level 1
level 2
level 3
level 4
level 5
Original signal A0
A1
A2 D2
A3 D3
A4 D4
A5 D5
A5 D5 D4 D3 D2 D1
D1
D2
D3
D3
g(n)
Figure 4.1: The analysis part of the discrete wavelet transform implementation using the subband filtering and decimation process. Five-level multiresolution signal decomposition of original signal A0(n)orx(n).
4.3.1 Local-wave Energies of the ECG Signal
The mean value of the original ECG signal and the compressed signal is measured and then it is subtracted from them as the first step. Both signals are decomposed using biorthogonal 9/7-tap wavelet filters [186] up toJdecomposition level. In this work, the five-level analysis structure is used for the decomposition of the ECG signals. This level is sufficient for the ECG signal sampled between 250 Hz and 360 Hz [190]. For the sampling frequency of 360 Hz, the frequency bands A5, D5, D4 and D3 occupy the region of frequencies ranging from 0 Hz to 45 Hz. According to the power spectra of the ECG signal, noise and artifact [15], this frequency range has most of the coefficients of the local waves of the ECG. Fig. 4.2 shows the P-wave,