2.6 Evaluation of ECG Compression Methods
2.6.6 Quality Controlled Coding Methods Based on PRD and WWPRD Criteria
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.
Table 2.11: Illustration of the adaptive quantization strategy using themitarecord 117.
Quantizer PRDtar=2%, PRDT=1.99% PRDtar=0.5%, PRDT=0.496%
resolution QPRD2 QPRD1 Threshold Step size Entropy QPRD2 QPRD1 Threshold Step size Entropy
(b) (%) (%) (T) (∆) (HQ) (%) (%) (T) (∆) (HQ)
6 2.15 7.95 15.78 18.44 0.68 1.87 6.93 2.06 18.44 1.67
7 2.03 7.51 15.78 9.15 0.75 1.13 4.18 2.06 9.15 2.02
8 2.00 7.39 15.78 4.56 0.81 0.69 2.54 2.06 4.56 2.34
9 1.99 7.36 15.78 2.27 0.87 0.54 2.01 2.06 2.27 2.61
10 1.99 7.36 15.78 1.14 0.93 0.51 1.89 2.06 1.14 2.90
PRDTdenotes the obtained PRD after the thresholding process (before quantization).
components of the local waves. Moreover, this noise measurement criterion is difficult to incorporate in well designed SPIHT algorithm which codes the wavelet coefficients by exploiting the redundancies among wavelet scales. Noise decreases the CR of the SPIHT coder for a specified PRD value since the coder will spend extra bits on approximating the noise with the specified accuracy. Furthermore, the choice of the distortion criterion that must be used in quality control is of critical importance when noise suppression and signal compression is established simultaneously. In this experiment, the performance of the recently reported wavelet thresholding based method [143] which outperforms other methods is tested using the widely used mita database records and the PRD2 measurement criterion. We study the performance of this method for a user specified PRD2 value based on the following parameters and dataset used in the implementation [143]: N =43,200 samples, 5-level, bior4.4 wavelet, b={6,7,8,9,10}and test dataset:
mitarecords 100, 101, 102, 103, 107, 109, 111, 115, 117, 118, and 119. Two criteria such as the PRD2 and the entropyHQof the quantizer are considered. Table 2.11 illustrates the adaptive quantization strategy when applied to themita record 117 for the user specified PRD2 values of 2% and 0.5%. The QPRD2 (PRD2 after quantization) is found for each quantizer resolution. The tolerance for the adaptive thresholding and the adaptive quantization strategies are chosen equal to ε =1%andεQ=10%, respectively. Note that the mean of the signal block is -0.8172. As we have demonstrated in the previous section that the PRD1 is better than the PRD2 and the PRD3 measures, the QPRD1 is thus calculated and preferred here to select an optimal quantization bit for a specified tolerance εQ. Table 2.11 shows that QPRD2 increases when the quantizer resolutionbdecreases while the dynamic range of the nonzero wavelet coefficients (NZWC) vector is fixed. Since the threshold T is greater than ∆2, the increment of the QPRD2 values is mainly due to the round off error and the overload error. From Table 2.11, it is clearly noticed that for b=6 the linear quantizer fulfills the requirement that is εQ =10%. Note that the QPRD1 value is 7.95% for this quantizer resolution. For a specified PRDtar=0.5%, it is clear that T is smaller than ∆2 for a set of b={8,7,6}and then the resulting errors are due to quantized nonzero wavelet coefficients (QNZWC) and zeroed nonzero coefficients. It is also observed that the quantizer may not fulfills the tolerance requirement
Table 2.12: Local and global objective error measures.
Bit rate controlled SPIHT Quality controlled SPIHT mita target Error Local/Subband Error, PRDs(%) global target obtained decreased Record CR Measures A5 D5 D4 D3 D2 D1 / total(%) value CR CR
PRD1 2.83 1.72 2.54 4.49 33.83 84.11 4.93 4.93% 5.5:1 31.2%
100 8:1 WWPRD [190] 0.86 0.31 0.52 0.71 3.26 4.77 10.43 10.43% 3.92:1 51%
PRD1 3.01 4.67 18.93 34.72 78.34 99.89 4.851 107 16:1 WWPRD [190] 2.09 0.74 1.35 1.38 1.90 1.19 8.65
for b={8,7,6}. This experiment shows that computation time of the adaptive quantization strategy can be reduced by providing some constraint. Finally, average compression performances are studied using the same dataset for the target PRD2 value of 2.75%, 3.30% and 4.65%. This test is performed to determine the QPRD1 value and to evaluate the compressed signal quality. The QPRD2 values of 2.89%, 3.51% and 4.84%, and the QPRD1 values of 5.15%, 6.31% and 8.63% are obtained for averagebvalues of 7.73, 7.18 and 6.82, respectively. The local waves of some of compressed signals are distorted for the target PRD2 value of 3.30%. From this experiment, the deficiency of the PRD2 as a quality measure is demonstrated and also the problems of this adaptive quantization strategy are illustrated to provide a faster and better adaptive quantization mechanism with meaningful distortion criterion.
In this experiment, the performance of the SPIHT coding strategy [145] is evaluated using signal block of 1024 samples. The high efficiency, high speed, and low complexity make the SPIHT algorithm an attractive candidate for compression of biomedical signals [145]. Note that the performance of the threshold based methods depends on many optimal parameters. Since the 9/7-tap biorthogonal wavelet (BW) filters for WT and SPIHT coding are proven to offer an excellent coding gain [145], they are also adopted here. We hereby show the effectiveness of the PRD1, and WWPRD criteria based quality controlled SPIHT coding strategy.
The ECG signals from themitarecord 100 and 107 are compressed at CR=8:1 and CR=16:1, respectively.
The original and the compressed signals are shown in Figs. 2.16(a) and (c), respectively and the behavior of local and global error measures are shown in Table 2.12. In WWPRD criterion, insignificant errors in bands D2and D1dominate the global error while significant errors in other bands are low. Thus, the selection of upper bound distortion (D) level is very difficult since the WWPRD measure is not subjectively meaningful in the sense that the small and large values correspond to “good” and “bad” quality, respectively [see Fig.
2.16 and Table 2.12]. Moreover, experiments show that the rate-distortion performance of the SPIHT coder is poorly seen in the PRD1 and WWPRD measurement criteria. The signal block from themitarecord 100 with SNR=45 dB is compressed for PRD1=4.93% and WWPRD=10.43% which are obtained for a target CR value of 8:1 [see Fig. 2.16(a) and (b)]. The compression ratios achieved are 5.5 and 3.92, respectively. Thus, the compression ratio is decreased by 31.2% and 51%, respectively [for example, 100*((8-5.5)/8)=31.2%].
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Figure 2.16: Compression results of the SPIHT coder. (a)mitarec. 100 (CR=8:1, PRD=4.93% and WW- PRD=10.43%). (b) Compression of noisy signal for a target error percentage: At the case of PRD=5.04%
and WWPRD=10.45%, the compression ratios of SPIHT are 5.5 and 3.92, respectively. (c) mitarec. 107 (CR=16:1, PRD=4.851% and WWPRD=8.65%).
This phenomenon is shown in Fig. 2.16(b) which reveal the clinical quality of the compressed signals for each specified error percentage. We observe that not only the significant feature is retrieved, but also the signal quality is upgraded because the insignificant coefficients dominated in subbands D2and D1 are removed for data compression. For a given quality specification, rate-distortion performance of the well designed SPIHT based quality controlled compression methods based on the PRD and WWPRD criteria is poor due to noise coding. Therefore, in order to introduce automatic quality control one needs an adequate objective distortion measure for measurement of error of the compressed signal.