3.3 Rate- and Distortion-Driven Subband Coding Algorithms
3.3.2 The TDL Driven ECG Compression Algorithm
3.3.2.3 Time Varying PQRST Complex Morphologies
In this experiment, the effect of time varying morphologies on the compressed data rate (CDR) is investi- gated using selected mitarecords 200, 214, 231, 210, 106, 107, 113, 208, 104, 233, 103, 105, 230, 213, 115, 124, 117, 119, 123 and 116 which are referred as dataset-III. These records are chosen because they have different PQRST complex morphologies and low noise level. A block of 1024 samples is used from each record for the testing purpose. The compression results for these records are shown in Fig. 3.19(f). It shows that the resultant CDRs of the blocks are unequal for different local wave morphologies.
To investigate the CDR of each block from the same test record for a specified target PRD1 value, 15- min duration each of records 101, 111, 208 and 228, which are referred to as dataset-IV, is chosen for testing purpose [151]. A block of 1024 samples is chosen and a total number of 316 blocks are considered from each record. Each block is encoded and decoded separately at a given target PRD1 value. Three different target PRD1 values of 3%, 6% and 9% are considered for this experiment. The average CDR values of 316 blocks along with standard deviations at each target PRD1 value for a test ECG signal are shown in Table 3.12. The average PRD1 value and its standard deviation are also tabulated to observe its closeness with respect to the target value. Standard deviation of the PRD1 values of the proposed algorithm are small for all long duration test records. These experimental results show that the compression error value is close
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Figure 3.20: Type-III experiment results for test mitarecord 101. (a) Compressed data rate (CDR). (b) PRD1 values. (c) number of iterations, Ni. (d) the execution time, te(sec).
to the specified target value. To reveal this, the PRD1 value of each block is shown in Figs. 3.20 (b) and 3.21 (b) at a target PRD1 value of 3% for the tested mita record 101 and 111, respectively. Along with this, the CDR of each block, the number of iterations, Ni, required to achieve convergence and accuracy, and the execution time, te are shown in the figures. It is observed that the CDR values of the blocks are unequal and there is a large variation in CDR value of two blocks within a record. The experimental results in Table 3.12 show that there is a large variation in the CDR of the tested block for a record. In this situation, the minimum and maximum CDR of block is considered for real time case. The minimum and the maximum CDR values are 310 bps and 1224 bps, respectively for the testmitarecord 101. Similarly the minimum and the maximum CDR values are 356 bps and 1273 bps, respectively for the testmitarecord 111. These variations in the CDR values cannot establish an efficient ECG data transmission through limited
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Figure 3.21: Type-III experiment results for test mita record 111. (a) Compressed data rate (CDR). (b) PRD1 values. (c) number of iterations, Ni. (d) the execution time, te(sec).
and assigned channel capacity.
The compression performance of the proposed algorithm is better than the direct AVQ and WT+AVQ algorithms. The standard deviations of CDR values of the proposed algorithm are less compared to AVQ and WT+AVQ algorithms for all test records with a target PRD1 value of 3%. But the performance of the proposed algorithm is worse than the WT+AVQ algorithm with a target PRD1 value of 6% for the mita records 101, 111 and 208. Similarly performance of WT+AVQ algorithm is better for the mita records 111 and 228 with a target PRD1 value of 9%. By comparing these experimental results, it cannot be concluded that the performance of the proposed algorithm is better than the other ECG coders. ECG signal compression algorithms with target PRD1/RMSE criteria will not assure that the local waves are faithfully reproduced. In most of the algorithms the coding efficiency at a given PRD1/PRD2/PRD3/RMSE
Table 3.13: Performance of the TDL algorithm. Block of 1024 samples taken frommitadataset-I.
PRD1tar 3% 5% 7% 8% 9%
APRD1±σ 3.13±0.05 5.06±0.08 7.16±0.07 8.1±0.09 9.07±0.12
CD 100% 90.91% 63.63% 45.45% 18.18%
ACDR±σ 733±219 536±145 433±95 396±76 373±68
min. CDR 407 333 303 281 290
max. CDR 1067 764 633 582 548
Ni 18.8 15.2 15.8 13.4 13.6
Note:- APRD1: average PRD1, ACDR: average CDR,σ: standard deviation, CD: correct diagnosis.
value is compared with the specified target CR directly. Although the present algorithm maintains a user- specified PRD for each block of an ECG signal, some local distortions have occurred. For example, the small amplitude Q wave may be lost in the compressed signal. To detect such distortions, a distortion measure capable of quantifying the diagnostic distortion is needed. The quality is evaluated via correct diagnosis test by visual inspection in this work. This test result is shown in Table 3.8 in subsection 3.3.1.1.
It is reported [121], [142] that the quality of the reconstructed signal is either ’very good’ or ’good’ if the PRD1(%) value is between 0 and 9. But the defined PRD1 range is applicable only for the specific compression method. Because the compression artifacts in the decompressed signal depends on the type of methodology, viz. transform types (DCT, KLT, DWT), quantization, prediction, etc. used for the im- plementation of compression algorithm. Maintaining the PRD1 value below 9% will never assure that the original diagnostic features are faithfully reproduced in the reconstructed signal. Therefore, visual or clini- cal inspection of the reconstructed signal is always important for all type of compression algorithm even if the PRD1 value is small.
To demonstrate the need of visual or clinical inspection, a block of 1024 samples is used from eachmita record of dataset-I. The coding parameters and the test PRD1 range (3% - 9%) are used as WPFEC [142].
Each block is compressed and decompressed at a target PRD1 value as mentioned above. The experimental results are shown in Table 3.13. The desired target distortion level is achieved with a lower CDR value using the TDL algorithm in few iterations. Clinical information in the reconstructed signals are evaluated by visually comparing them with the original signals. The percentage correct diagnosis (CD) is calculated from the number of CD at a target PRD1 value. It can be observed that 100% of CD is achieved only for a target PRD1 value of 3%. The percentage CD value is less for the target PRD1 value of 7% and above. Consequently, this PRD1 range cannot be used if the proposed compression algorithm is used with the same coding parameters. To reveal the visual or clinical quality of the signal for selected test records, the original signal, the compressed signal at a PRD1 value of 7% and the error signal are shown in Fig.
3.22. The distortions of the diagnostic features are marked in the compressed signals. The error signals are plotted to observe their distributions. The structured errors are also marked in the error signals. It is
mita record 100
mita record 101
mita record 102
mita record 103
mita record 107
mita record 109
mita record 111
mita record 117 mita record 119 mita record 118
Figure 3.22: Compression results for arrhythmia ECG signal extracted from dataset-I at a target PRD1 = 7%.
Some of the distortion of the diagnostic features are marked in the reconstructed signals. From top to bottom, the plots display the original ECG, the reconstructed ECG, and the difference between original and reconstruction.
observed that important diagnostic features are distorted and the small and short local waves are missing in Figs. 3.22. Hence, the compressed signal is not quality guaranteed by using a predefined PRD1 value. In WPFEC [142], PRD2 value is used as target which is meaningless because it depends on the mean value of the original signal. This effect is already discussed in the previous section. We prefer 100% CD for a PRD1 value of 3% for further analysis and comparison. Table 3.13 shows that the target TDL algorithm meets the required error value but it does not satisfy the requirements of data rate even if the PRD1 value is clearly defined at the clinically acceptable level. For example, for a PRD1 value of 3% the minimum and maximum CDR values are 407 bps and 1067 bps, respectively. This variation in CDR value leads to inefficient utilization of the required data rate or channel capacity (≥maximum CDR). Data rate variability may not fulfill the demand of compressed data rate. To rectify the above problem, the TDR driven wavelet compression is presented and its performance is analyzed with respect to the clinically acceptable quality.
Table 3.14: Target data rate (TDR) driven wavelet threshold based ECG compression algorithm.
The CR and the PRD1 can be written as: CR = f(Xn, M, N, EPEi, b );
Step 1: Blocking and buffering N input samples.
// where,Xn={x[0],x[1],x[2], ...x[M−1]},M is the data length, N is the block length,
// EPEiis the energy packing efficiency of theithframe, and the quantization bits,b={6, 7, 8, 9}. PRD1 = f(Xn,M,N,EPEi,b); ∀n = 0,1,2, ...M−1.
Encoder:
Step 2: Decompose the signal,Xn, using 9/7 wavelet filters.
Step 3: Initialization
(a) Specify the target CRtaror CDRtarvalue.
(b) Define the value of EPEF2and the range of search for EPEF3is [0 100]%.
(c) Get all three frames F1, F2and F3.
(d) Get the relative bound error,e, for CRtarcalculation.
Step 4: Calculate T2at desired EPEF2by SA in Table 3.2.
(a) Get copy of F2and threshold it at T2. for(k = 1; k<=K; k=k+1 )
// where K is the number of quantization bits. Here, K = 4.
{While|(CR(EPEi)−CRtar)/CRtar| ×100 > e
{Step 5: Calculate TF3at EPE3= (EPE3min+EPE3max)/2 ; (a) Get copy of F3and threshold it at TF3.
Step 6: Compute the compression ratio (CR).
(a) Get the thresholded Wavelet coefficient (TWC) vector, TWC = [F1F2TF3T] (b) Create two vectors:
the nonzero thresholded coefficient (NZTC) vector and the integer significance map (ISM) vector.
(c) Quantize the NZTC by using the proposed quantizer at desired resolution,bbits.
(d) On the other side, encode the ISM vector using the proposed index coding scheme.
(e) Finally, encode the QNZTC and the output of the index coder and calculate the CR.
Step 7:IfCR (EPE3)<CRtar {EPE3max= EPE3;} else
{EPE3min= EPE3;} } EPEq(k)= EPE3;
Step 8: Reconstruct the signal and calculate the PRD1.
PRD1q(k)=PRD1 ;
}Step 9: Get{EPEq(k)}and{PRD1q(k)} ∀k=1,2, ...K.
Step 10: Get combination of{EPE3, b}by{EPE3,b}=min{PRD1q};
Step 11: Using the above EPE3andb, compress the original signalXnat CRtar with minimal distortion.
Reconstruction: 1) Decoding, 2) De-quantization and 3) Inverse DWT.
Note:- SA: sorting algorithm in Table 3.2.