5.5 Results and Discussions
5.5.2 Evaluation of the compression performance
5. Exploiting Multi-scale Signal Information in Joint Compressed Sensing Recovery
70 75 80 85 90 95
0 5 10 15 20 25 30 35
Compression Ratio (CR %)
Average Joint PRD
SWMNM PWMNM MNM BP SOMP IR−l1/l
2
VG G
85.6 89.6 91.2
Figure 5.6: Comparison plot between proposed techniques (SWMNM, PWMNM) and existing techniques at different compression ratios (CR) in terms of average jointP RD. Results are averaged over all data-sets taken from the PTB database.
5.5 Results and Discussions
when no weighting is done, i.e., w=I1×N. The MNM as a joint sparse recovery algorithm, is earlier used by Mamaghanian et al. [34] for joint CS reconstruction of MECG signals. However, the trend of P RD in Figure 5.6 indicates that WMNM performs much better than MNM for joint CS MECG recovery. Incorporation of additional information through the proposed subband weighting schemes in the joint recovery algorithm helps identify the supports of subband coefficients having high clinical relevance. So, these clinically important coefficients are emphasized during the recovery process in all the channels even when data recovery is done at smaller M value. This helps proposed WMNM techniques to preserve the overall diagnostic quality in the reconstructed MECG signals at higherCR.
However, MNM lacks this type of feature as it only leverages group sparsity leading to performance degradation, especially, at higher CR values.
IR-ℓ1/ℓ2 algorithm [134, 149] is a reweighted version of standard MNM and is an MMV exten- sion of reweighted ℓ1 [132]. The proposed SWMNM approach differs with this technique in terms of weight selection criterion. It can be noted in Figure 5.6 that performance of IR-ℓ1/ℓ2 can be substantially improved in low measurement scenarios by using a wavelet subband-based weighting scheme (i.e., SWMNM). Prior knowledge-based PWMNM, which uses decaying characteristics of sub- band coefficients, can give further performance improvement. Marginal improvement in the recovery performance of IR-ℓ1/ℓ2 is observed in low data compression conditions (low CR). However, in the intended resource-constrained ambulatory applications, lowCRis undesirable as it increases the band- width requirement and energy consumption resulting in higher system cost [1,34]. Basis pursuit (BP) is a classic CS recovery algorithm for SMV models and has been used in earlier CS ECG works [1,41].
When the group BP is used for joint MECG recovery, it is outperformed by both SWMNM and PWMNM. A greedy algorithm, SOMP was modified in [97] by utilizing prior signal knowledge with it. Authors have used it for jointly recovering consecutive ECG beats of single channel ECG. We used the same modified SOMP for the joint recovery of all the channels and found that it performs poorly compared to WMNM techniques. It gets saturated early and the performance gains marginally even at lower CR values.
Channel-wise performance comparison with some other works is given in Table 5.3 in terms of P RD, SN R, W EDD, and QS. The average quantitative values calculated over all the datasets of PTB database are listed. A higher level of distortion can be noted in the case of regular MNM recovery
5. Exploiting Multi-scale Signal Information in Joint Compressed Sensing Recovery
compared to the proposed PWMNM technique at M = 70. The proposed method shows substantial reduction in the distortion levels in all distortion metrics in each channel. In order to demonstrate the database robustness of the proposed methods, the performance is also calculated using the CSE multilead library database. The existing works that use CSE database [34, 44], are also compared in Table 5.3. Significant reduction in the reported average P RD is noted for most of the leads. For the CSE database, level of distortions are relatively high compared to the PTB database at the same value of M. This may be due to the higher noise contents and a relatively lower sampling frequency (fs) of the MECG signals in the CSE database. The low value of fs may reduce the level of redundancies and hence sparsity, resulting in low compressible ECG signals. Most of the existing CS-based data compression works [45,46] deal with single channel ECG recovery. So, it is interesting to compare these works with the proposed work, where all channels are recovered simultaneously. Table 5.3 includes the results when each channel of the MIT-BIH database is recovered individually in earlier reported works [45, 46] and when both channels are jointly recovered by the proposed method. Results suggest that the proposed technique performs better than the above works in terms of reducedP RDvalue at same reportedM = 192 and CR= 6.4 (M = 125). The proposed method exploits the inter-channel correlation information while jointly recovering both channels resulting in reducedP RDat sameM or CRvalues, whereas [45,46] ignores this information. This also validates the importance of correlation information in CS-based MECG telemonitoring systems and makes the proposed WMNM techniques a preferable choice for joint data recovery.
5.5ResultsandDiscussio Table 5.3: Performance comparison between proposed technique and other existing techniques. Results are averaged over all the PTB data records and 40 data records of the CSE Multilead Library database (M01 001-M01 040).
Techniques M Metrics ECG channels
Database Lead I Lead II Lead III aVR aVL aVF V1 V2 V3 V4 V5 V6 Average
MNM [34] 70
PRD 19.51 14.92 16.02 16.85 14.51 13.83 20.51 19.49 19.01 22.43 19.80 20.58 18.12
PTB SNR 14.19 16.52 15.90 15.46 16.76 17.18 13.76 14.20 14.42 12.98 14.07 13.73 14.93
(fs= 1000 Hz) WEDD 19.19 14.43 13.71 17.67 12.01 12.55 21.44 20.31 18.67 23.03 20.07 22.01 17.92
Proposed 70
PRD 8.73 6.02 7.78 5.93 7.52 5.96 6.35 5.58 5.54 6.59 6.74 6.54 6.60 SNR 21.18 24.41 22.18 24.54 22.47 24.49 23.95 25.07 25.13 23.62 23.43 23.68 23.67 WEDD 8.13 6.65 6.69 5.65 6.39 5.44 5.70 4.73 4.89 6.14 6.27 6.20 6.07 MNM [34] 70 PRD 33.68 34.22 32.74 33.58 34.34 33.18 32.69 36.24 37.68 39.10 38.50 36.33 35.19 WEDD 28.98 29.97 29.04 28.68 30.13 28.98 29.98 33.11 33.80 35.65 34.01 31.25 31.13 CSE
(fs= 500 Hz) MCS [44] 70 PRD 20.26 19.51 21.97 17.91 23.84 23.75 14.66 13.97 17.73 18.91 19.35 15.88 18.97
Proposed 70 PRD 16.56 16.76 16.52 15.28 18.84 16.76 13.24 15.36 17.19 19.20 19.00 16.27 16.74 WEDD 12.92 13.60 13.50 11.87 15.02 13.67 11.57 13.47 15.05 17.15 16.22 13.54 13.96
WLM [46] 192 PRD1 - - - 3.64
MIT-BIH
Proposed 192 PRD1 - - - 1.13
(fs= 360 Hz)
MMB-IHT [45] 125 PRD1 - - - 3.74
QS - - - 1.71
Proposed 125 PRD1 - - - 1.31
QS - - - 4.88
127
5. Exploiting Multi-scale Signal Information in Joint Compressed Sensing Recovery
50 100 150 200 250
10 20 30 40 50 60 70 80
Number of Measurements (M)
Average Joint PRD
MNM SWMNM PWMNM Color discription−
blue− Noiseless
black− Noisy with SNR=35 dB green− Noisy with SNR= 25 dB red− Noisy with SNR= 15 dB
Figure 5.7: Recovery performances of the proposed methods (SWMNM, PWMNM) at different measurement noise levels