3.2 Construction of Adaptive Subband Coding Scheme
3.2.3 Wavelet Thresholding and Threshold Selection
3.2.3.3 Threshold Finding Algorithm and Results of Wavelet Thresholding Phase 112
In this section a simple threshold finding algorithm with EPE criterion is presented and tested using the signal blocks taken from the most widely usedmitadatabase. Many threshold based methods use a unique threshold valueT for all wavelet coefficients. But varyingT controls the CR and the distortion. The pre- sented algorithm finds a threshold for each frame continuously to meet the desired EPE value assigned for that frame. Experimental results show that most of the energy is concentrated in frame F1. As a result, thresholding of approximation coefficients in the first frame will distort the base of the PQRST morpholo- gies. Thus, the first frame F1 is not thresholded in this work. This procedure helps to preserve the low frequency components (low pass shape) of the ECG signal that are most important for reconstruction. As a result, the morphologies of P-wave and T-wave, the small q-wave and the ST segment may not be dis- torted. This preserves the diagnostic information in the signal to a large extent. Meanwhile, the thresholds for the higher frames are set higher in order to attain a good performance in the rate-distortion sense. Us- ing the RWSE values, the EPEs are chosen to decide the thresholds T2 and T3 for the second and third frames, respectively. For a specified EPE, the threshold value is determined using the simple sorting al- gorithm (SA) shown in Table 3.2. For the specified EPEF2 and EPEF3, the respective thresholdsT2 andT3 are calculated using a simple algorithm [134]. Thresholded wavelet coefficient (TWC) vector is given as,
Table 3.2: Sorting algorithm (SA) for determining the thresholdT value and thresholding process.
Step 0: Initialization
(a) Give a required EPEi(in percentage) value for theith frame.
(b) Get the wavelet coefficients of theithframe. Fi(p), p=1,2,3, ...Pi. Step 1: Calculate the total energy of theith frame by TEi=∑Pp=1i [Fi(p)]2. Step 2: Calculate the retained energy of theith frame by REi= (EPE100i)×TEi.
Step 3: Sorting of the absolute value of the wavelet coefficients in the Fiin descending order.
Step 4: Find the threshold (Ti) value. Ec=0; p=0;
{ while Ec<REi
Ec=Ec+ [Fi(p)]2; // calculation of energy p=p+1;
} Ti = Fi(p); // threshold value { for (p=1; p≤Pi;p= p+1)
if Fi(p)<Ti Fi(p) =0 ; else
Fi(p) =Fi(p);
}
TWC =[F1 F2 F3 ], whereF2andF3are the second and the third frame thresholded coefficient vectors.
The nonzero wavelet coefficient (NZWC) vector is constructed by removing the zero valued coefficients from TWC. The integer significance map (ISM) is a positive integer vector which contains the positions of the significant or nonzero coefficients. The NZWC and positive integer vectors are coded in the next section.
The EPE values for the second and the third frame is assigned based on the RWSE values of approx- imation and detail coefficients of each ECG record. The smaller EPE value results in larger compression ratio but most of the diagnostic information is lost in the compressed signal. The shapes of P and T waves may be altered. Sometimes PR segment and small Q wave are lost in the reconstructed signal. The small Q wave is important for diagnosis of myocardial infarction. Hence, proper selection of EPE value is important for each ECG record. For all mitarecords, the reconstruction error (PRD1 value) versus energy packing efficiency (EPEF3) are shown in Fig. 3.6. It can be observed that the PRD1 value varies for each record for a specified EPEF3 value and hence a proper selection of EPE value is important for each record. The PRD1 value cannot reflect the exact amount of distortion of the PQRST complex features. For a given ECG signal, the value of PRD1 is same for dissimilar distortions introduced by the compression method. A compression method might achieve a low PRD1 error ignoring the local wave between QRST complexes, totally losing the small P-wave, and faithfully reproducing the QRST complex. Therefore, to ascertain that the clinical
90 92 94 96 98 100 0
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EPEF3 %
PRD1 %
EPEF3 %
EPEF3 % EPE
F3 % EPEF2=99.9 %
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0 5 10 15 20 25
PRD1 %
90 92 94 96 98 100
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100 101 102 103 104 105 106 107 108 109 111
200 201 202 203 205 207 208 209 210 212 213 214
112 113 114 115 116 117 118 119 121 122 123 124
90 92 94 96 98 100
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215 217 219 220 221 222 223 228 230 231 232 233 234 EPEF2=99.9%
M=N=2048 samples
EPEF2=99.9%
M=N=2048 samples
EPEF2=99.9%
M=N=2048 samples
EPEF2=99.9%
M=N=2048 samples
Figure 3.6: PRD1 versus EPEF3 of all records of the MIT-BIH arrythmia database.
information is preserved, the compressed signal quality is evaluated by comparing it visually with the orig- inal signal. In this work, more importance is given to the quality of judgement via visual inspection rather than the objective measures.
3.2.4 Threshold Control Zero-zone Nearly Uniform Midtread Quantization Scheme
The possibility of compression by thresholding or/and quantizing wavelet coefficients relies on the assump- tion that details at higher subbands are less relevant to the reconstruction. A common way to reduce the number of bits required for the compression phase is to quantize the coefficients and apply some lossless compression such as Huffman or arithmetic coding on the quantized coefficients or their representative in- dexes. The quantizers used in standard compression methods are designed to approximately minimize the MSE between the original and reconstructed signals for a given bit rate. In ECG compression method, the
nonzero wavelet coefficients or the wavelet coefficients can be quantized using the scalar quantization (SQ) schemes or the vector quantization (VQ) schemes. Comparing SQ versus VQ should take into consideration three aspects: compression ratio achieved and its signal quality, computational complexity and coding delay.
The compression issues involved in quantization strategy are discussed in Chapter 2 with different sets of experiments. We present here issues of the simple quantization strategy with frequently used quantization rules and then propose a better adaptive quantization strategy for wavelet coding.