2.6 Evaluation of ECG Compression Methods
2.6.5 Scalar Quantization Approaches for Wavelet Coefficients
In multiresolution ECG signal decomposition, we can observe that there are large numbers of small magni- tude coefficients in higher subbands and are only small numbers of large coefficients. Most of the energy in an ECG signal is concentrated in the small size low frequency subbands. Large wavelet coefficients are
Table 2.9: Variation of PRDs with variableT found based on target PRD2 and fixed quantization step.
Test PRD2=1% PRD2=2% PRD2=3%
record PRD2T PRD2Q PRD2T PRD2Q PRD2T PRD2Q
100 0.96 1.91 2.03 2.33 2.99 3.12
101 1.04 1.37 2.05 2.14 3.00 3.04
102 0.98 1.51 2.02 2.16 3.00 3.06
103 1.00 1.37 1.95 2.12 3.03 3.10
107 0.98 1.36 1.97 2.11 3.03 3.11
109 1.03 1.34 1.99 2.09 3.00 3.04
111 0.97 2.15 2.01 2.47 3.03 3.23
115 1.04 1.26 2.00 2.06 3.01 3.03
117 0.98 1.03 2.00 2.01 3.01 3.02
118 0.99 1.10 1.96 2.00 3.02 3.04
119 1.02 1.30 2.01 2.09 2.95 3.00
more important than small wavelet coefficients. Therefore, large wavelet coefficients get quantized accu- rately while small coefficients are discarded in the compression methods. In this section, we investigate the performance of different approaches for quantization of the wavelet coefficients of the ECG since there is a tradeoff between signal quality and bit rate (or degree of quantization).
Scalar quantization is an example of a lossy compression method where it is easy to control the CR or quality. The quantization error is perceived as noise or distortion that depends on the type quantizer. The uniform quantizer is the most commonly used scalar quantizer due to its simplicity. It is also referred as a linear quantizer in some of the compression methods. In USQ, the decision levels are uniform and the reconstruction levels are also equally spaced and located in the middle of the decision levels [195, 196, 200].
There are many ways to choose the decision levels or boundaries and the output or reconstruction levels.
We concentrate on the uniform scalar quantizers such as midtread quantizer, midrise quantizer and dead zone quantizer in this section. To design a uniform quantizer, we have to determine the dynamic range of the coefficients vector, the desired coefficients resolution (number of quantization levels) and select the proper type of quantizers (e.g., midtread or midrise or dead zone). The quantizer is generally described as a functionQthat maps a transformed coefficient to a quantization indexq. For a given wavelet coefficient c, the quantizer output is a signed integerqgiven byq=Q(c). Givenq, the decoder produces an estimate of cas c=Q−1(q) [195]. These quantizers are completely characterized by the quantization step size∆.
Since the midrise quantizer does not have the zero output level, large number of small magnitude wavelet coefficients are quantized into first output level. This may introduce quantization noise and its magnitude depends on the quantization step size. The quantization noise may result in some noticeable distortion of amplitude, duration and shape features of the ECG segment at lower quantizer resolution. Although the midrise quantizer has more number of output levels, it will introduce the quantization noise and the signal
distortion caused by rounding and clipping of the coefficients simultaneously. The quantization noise can be avoided in compression system by accommodating the zero output value. The zero output level is useful in waveform coding scheme where we need to represent zero value of the signal or in transform coding where we set large number of small coefficients to zero. Due to this reason, the midtread quantizer is popular in the transform coding scheme.
We study the performance of these quantizers using the ECG signal block from the commonly used mitarecords 107, 117 and 119 [137, 142, 143, 203]. In this study the block size of 1024 samples is chosen and then the wavelet coefficients obtained for the 5-level 9/7-tap filters DWT of the signal block are directly quantized using the above three quantizer with different resolutionb={6,7,8,9,10}. The quantization and the dequantization are performed according to the expression for the quantizers presented in section 2.3.5.
For each quantizer resolution, the entropyHQin bits per coefficient is determined without entropy coding.
The PRD1 and PRD2 criteria are used to measure the distortion between the original and the compressed signals. To reveal the visual quality of the compressed signals, the original signal and the compressed signals obtained with 6-, and 8-bit quantization for records 107, 117 and 119 are shown in Fig. 2.15. The compressed and original signals are examined to obtain the subjective quality ratings. Fig. 2.15(a) shows that the clinical features are distorted due to quantization noise introduced by the midrise quantizer. As can be seen in Fig. 2.15(b), the clinical features are preserved in the compressed signals when the midtread quantization is employed. Furthermore, the main effect of the smoothing of background noise can be seen for higher quantizer resolution since the coefficients due to noise that lie inside the zero zone interval are quantized to zero. Therefore, we give more importance to midtread quantizer and its variants. Table 2.10 shows the entropy of the midrise and midtread quantizers with various numbers of quantization levels, the subjective ratings and the PRD values. Note that PRD2 is commonly used for comparing the compression performance with other algorithms, and the number of bits required for quantization is selected according to the measured PRD2 value. But we have considered PRD1 measure for comparison purposes. Experiment shows that midtread quantizer achieves good rate-distortion performance and the output of this dequantizer is free from quantization noise. There are two main sources for signal distortion:1) the zeroing of the wavelet coefficients in the zero zone interval and 2) the quantization of the coefficients in the outer zone interval. An increase of step size can lead to higher compression, but ”very bad” quality of compressed signal. It is well known that signal distortion and rates are controlled by the widths of the zero zone and the outer zones applied for quantization. Since the zero zone and the outer zone widths are equal to the step size∆, the midtread quantizer may not be quite flexible to control the tradeoff between the rate and signal distortion.
Since large zero zone quantization rule is often used in many transform based image and video coding schemes [195, 198, 199, 201], we also apply this approach to quantize the wavelet coefficients of the ECG signal [202]. The zero zone quantizer is characterized by two parameters such as zero zone width and outer zone width. In many applications, the width of the zero zone is equal to twice the outer zone width.
Table 2.10: Performance of the midrise, midtread and zero zone quantizers.
mita Midrise quantizer,Q1 Midtread quantizer,Q2 Zero zone quantizer,Q3 COMP(Q3,Q2) Record b HQ PRD1 PRD2 MOS HQ PRD1 PRD2 MOS H(b) PRD1 PRD2 MOS HQ PRD1
(%) (%) (%) (%) (%) (%) %↓ %↑
6 0.7366 16.2916 15.9658 2 0.919 4.015 3.935 3.5 0.725 5.393 5.285 1.5 21.110 25.552 107 7 0.9943 8.3299 8.1633 2.75 1.205 2.372 2.324 4.25 0.990 3.132 3.069 3.5 17.842 24.266 8 1.3011 4.4261 4.3376 3.5 1.633 1.550 1.519 5 1.299 1.939 1.901 4.75 20.453 20.062 9 1.7664 2.4088 2.3606 4 2.243 0.940 0.921 5 1.764 1.258 1.233 5 21.355 25.278 10 2.4608 1.3122 1.2860 4.75 3.015 0.545 0.534 5 2.460 0.747 0.732 5 18.408 27.042 6 0.7896 17.4699 4.7516 1.25 1.090 5.936 1.615 4 0.791 7.488 2.037 1.75 27.431 20.727 7 1.1966 9.2168 2.5069 2.75 1.579 3.731 1.015 4.5 1.190 4.839 1.316 4 24.636 22.897 117 8 1.7582 5.2628 1.4314 3.5 2.379 2.244 0.610 4.75 1.747 3.151 0.857 4.5 26.566 28.785 9 2.6648 2.9114 0.7919 4.25 3.312 1.164 0.317 5 2.661 1.796 0.489 5 19.656 35.189 10 3.8305 1.4945 0.4065 4.75 4.174 0.571 0.155 5 3.830 0.804 0.219 5 8.242 28.980
This quantization rule is followed here to study its rate-distortion performance. The entropy rates of the zero zone quantizer with different resolutions are summarized and their compressed signals are shown in Fig. 2.15(c). As shown in Table 2.10, the midtread quantizers obtain better compression performance than midrise quantizer. In Fig. 6, we compare the zero zone quantizerQ3 with the midtread quantizerQ2 approach. Since the objective measure will be employed in an automatic quality control system, we have considered the measured PRD1 values instead of MOS values for performance comparison. At the range of 6≤b≤10, the averageHQ ofQ3 andQ2 are 1.4476 and 1.8030, respectively and the average PRD1s ofQ3 andQ2 are 2.493 and 1.844, respectively. The HQ3 is improved by 19.71% at the cost of increased PRD1 of 24.44 % for the specific ECG signal from themita107. The behavior of the quantizer is same for other signals from themita117 and 119. Experiments show that the performance of the quantizers depend on the distribution of the wavelet coefficients of the ECG signal. Thus, for a given distribution, the optimal quantizer can be completely described by the parameters such as zero zone width and outer zone width.
In [203], a larger zero-zone (defined by thresholdT) is expected to set more high-frequency coefficients to zero in order to achieve high compression performance [203]. The authors observed that for good com- pression performance ∆ should be among 1.2T −1.8T. Finally, they fixed the relationship between the quantization step size∆ and the threshold T as∆=1.55T which is a satisfactory choice for ECG signals tested. However, this fixed relationship may not always result in good compression performance for the ECG signals with varying PQRST morphologies [202]. The reason lies on the fact that although a large thresholdT preferred for the zero zone is ensured by selecting a large quantization step size ∆, the outer zone with this ∆ value can produce unacceptably large clinical distortion due to rounding or clipping of the significant coefficients. Unfortunately, smaller outer-zone width leads to lower compression ratios with good compressed signal quality. Furthermore, global quantization approach may introduce severe clinical
200 400 600 800 1000
−1
−0.5 0 0.5
Original signal
200 400 600 800 1000
−1 0 1
Rec. signal at 6−bit resolution
Amplitude
200 400 600 800 1000
−0.2 0 0.2
Error signal
200 400 600 800 1000
−0.2 0 0.2
Error signal
200 400 600 800 1000
−1
−0.5 0 0.5
Rec. signal at 6−bit resolution
200 400 600 800 1000
−1
−0.5 0 0.5
Original signal
200 400 600 800 1000
−0.2 0 0.2
Error signal
200 400 600 800 1000
−1
−0.5 0 0.5
Rec. signal at 6−bit resolution 200 400 600 800 1000
−1
−0.5 0 0.5
Original signal
200 400 600 800 1000
−1
−0.5 0 0.5
Rec. signal at 8−bit resolution
200 400 600 800 1000
−0.2 0 0.2
Error signal
200 400 600 800 1000
−1
−0.5 0 0.5
Rec. signal at 8−bit resolution
200 400 600 800 1000
−0.2 0 0.2
Error signal
Sample number 200 400 600 800 1000
−1
−0.5 0 0.5
Rec. signal at 8−bit resolution
Amplitude
200 400 600 800 1000
−0.2 0 0.2
Error signal
Midrise Quantizer (Q1) Midtread Quantizer (Q2) Zero zone Quantizer (Q3)
(a) (b) (c)
Figure 2.15: Performance of the uniform scalar quantizers for 6- and 8-bit resolution: (a) Midrise quantizer, (b) Midtread quantizer, (c) Zero zone quantizer ((with the zero zone width to be twice the outer zone width).
distortion since more small magnitude coefficients are set to zero due to large step size∆obtained for large dynamic range of the wavelet coefficients vector. The question is how to quantize the wavelet coefficients most efficiently. In [202], to improve the compression performance, the zero zone quantizer is applied to the three frames of the coefficients created based on the energy contribution efficiency of the subbands.
However, there are the questions of how many quantization levels and what type of reconstruction values (e.g. centroid, uniform) used to give reasonable good compression performance.
In [143], the wavelet coefficients are thresholded with a thresholdT found iteratively for a user specified PRD2 value. In the next step, the nonzero wavelet coefficients (NZWC) are quantized adaptively by the linear quantizer as in (2.16) of the lowest possible resolution. This adaptive quantization strategy provides an optimal dynamic bit allocation according to the nature of each ECG signal if the thresholdT is greater
than half of the step size of midtread quantizers [202]. If the rate-distortion property of a zero zone quantizer in terms of zero zone and outer zone widths can be exploited, it is possible to reduce the computational cost.
Moreover, an optimal quantizer design requires a distortion criterion since the uniform scalar quantizers are optimized in an operational rate-distortion sense. In fact, the quantization and dequantization introduces distortion to the compressed signal. The PRD2 is used as a distortion criterion since it is easy to calculate and compare. Although it does not mean that a lower PRD2 value provides a better clinical quality, this criterion is often used in the literature to choose a quantizer resolution. Because the subjective quality criterion is so difficult to adopt in minimization problem of the optimal quantizer design, a meaningful objective distortion criterion which measures the quantization errors is required to achieve optimal compression. In general, an optimal choice of the quantization parameters viz. zero zone width and the outer zone width with an effective distortion criterion can provide a good rate-distortion performance. The above issues will be considered in a design of optimal quantizer in this work to retain the coding performance and to provide a simultaneous signal denoising and compression.