Evaluation of Proposed Denoising Factors

3.3 Evaluation of Proposed Denoising Methods

3.3.1 Results for Denoising using Higher Order Statistics

3.3.1.1 Evaluation of Proposed Denoising Factors

Four denoising factors (DF_jM1, DFd_jM1, DF_j1M1, DF_j2M1 ) and soft threshold (ST) [28] are esti- mated for three subbands (cD1, cD2, cD3) using their ECE and Kurtosis values. These three sub- bands are normally thresholded for denoising applications [71].

Table-3.5 shows the results. TheDF values for cD1, cD2 and cD3 subbands are dependent

3.3 Evaluation of Proposed Denoising Methods

Table 3.5:DFjM1,DF\jM1,DFj2,DFj1and ST: Dataset-M01-003, CSE mutlilead measurement library

Values of DF,DF,d DF_j2,DF_j1and ST: Dataset-M01-003, CSE mutlilead measurement library

Parameters Lead-I Lead-II Lead-III aVR aVL aVF V1 V2 V3 V4 V5 V6

DF_jM1-cD3 0.1149 0.2469 0.0670 0.0521 0.1766 0.1481 0.2328 0.0545 0.0284 0.0253 0.0242 0.0280 DF_jM1-cD2 0.1839 0.1466 0.0916 0.0505 0.2102 0.1538 0.1378 0.1096 0.0300 0.0239 0.0224 0.0268 DF_jM1-cD1 0.4227 0.1706 0.3526 0.0716 0.2563 0.3816 0.1869 0.1557 0.1066 0.0787 0.1221 0.2515 DF\_jM1-cD3 1.6561 2.9339 1.5457 1.2366 2.0579 1.7376 6.4577 1.6849 1.1925 1.2456 1.3656 1.4816

\

DFjM1-cD2 2.6509 1.7425 2.1147 1.2002 2.4503 1.8055 3.8230 3.3856 1.2635 1.1795 1.2645 1.4187

\

DF_jM1-cD1 6.0941 2.0278 8.1398 1.7005 2.9869 4.4787 5.1839 4.8087 4.4812 3.8803 6.9061 13.3254 DFj2M1-cD3 0.1805 0.1680 0.4427 0.5061 0.0900 0.2098 0.3994 0.6522 0.9030 1.0677 1.2281 1.2466 DFj2M1-cD2 0.0843 0.0934 0.1387 0.1325 0.0813 0.0488 0.0298 0.0965 0.1543 0.1853 0.2115 0.1848 DF_j2M1-cD1 0.0139 0.0236 0.0203 0.0604 0.0167 0.0144 0.0091 0.0028 0.0035 0.0059 0.0067 0.0057 DF_j1M1-cD3 1.2517 1.4137 1.9176 2.1306 0.7724 1.7880 1.4399 2.1112 2.1473 2.1651 2.1719 2.3529 DF_j1M1-cD2 0.5846 0.7859 0.6007 0.5577 0.6974 0.4158 0.1074 0.3123 0.3668 0.3758 0.3740 0.3489 DF_j1M1-cD1 0.0964 0.1986 0.0881 0.2542 0.1433 0.1223 0.0330 0.0092 0.0083 0.0119 0.0118 0.0107 ST-cD3 0.0139 0.0069 0.0135 0.0076 0.0118 0.0057 0.0042 0.0020 0.0011 0.0015 0.0028 0.0022 ST-cD2 0.0047 0.0037 0.0046 0.0031 0.0041 0.0022 0.0015 0.0008 0.0004 0.0005 0.0010 0.0012 ST-cD1 0.0027 0.0016 0.0026 0.0015 0.0022 0.0014 0.0008 0.0004 0.0002 0.0002 0.0005 0.0007 Note: DF: Denoising factor, ST: Soft thresholding.

on ECE values, Kurtosis values and maximum amplitudes of the coefficients in the subbands. The coefficients which have higher values compared to the value of the Denoising Factor (DF) or the threshold are retained. Normally, more threshold value is required for cD1 subband where noise con- tent is more. For Lead-I signal,DFjM1values for subbands cD1, cD2 and cD3 are found as 0.4227, 0.1839 and 0.1149 respectively. The higher frequency subbands contain more noise whereas lower frequency subbands have most of the ECG wave components. In other words, higher frequency subbands have lower SNR values compared to lower frequency subbands. Other three Denoising FactorsDF\_jM1,DF_j1M1,DF_j2M1 based on DECE and ECE are also computed. DF_j1M1,DF_j2M1 denoising factors have maximum values for cD3 subband and their values are lowest for cD1 sub- band. This shows an inverse trend for values of denoising factors compared to the DF_jM1 values.

The soft thresholding (ST) method as proposed in [28] has also been evaluated (t=σp

2 log(N)/N , wheretis threshold,σ is variance of noise andN is the numbers of samples). Theσ is calculated based on median absolute deviation (MAD) [148, 151, 152]. The estimated noise variance, σ, in a wavelet subband is given as σ = C.M AD where ‘C’ is a constant scale factor which depends on distribution of noise. For a univariate data set with samplesx₁,x₂,...,x_n, the MAD is defined as [153]

M AD=median(|xi−median(xi)|) (3.14)

where xi is i^th data andmedian(xi) is the median. For normally distributed data ‘C = 1.4826’ is the75^th percentile of the normal distribution with unity variance. So, estimated noise variance can be written as σ = _0.6745^{M AD} [148]. MAD gives statistical dispersion of data and the basis of using it is higher breakdown point upto50% that is better than interquartile range which has breakdown point 25%[151]. Also MAD is aim at symmetrical distribution and its Gaussian efficiency is about37%. In Table-3.5, it is found the threshold set for cD3 is higher and cD1 is lower.

For qualitative comparison, four filtered signals using the four denoising factors are plotted with the original one in Figure-3.7. It is observed thatDFjM1performs better compared to the other three denoising factors. The filtered signal in Figure-3.7(b) has all the minute details of the original signal while removing the noise. It is observed in Figure-3.7(c), that the QRS complexes are smoothed out due to high values of denoising factors or thresholdDFd_jM1. In Figure-3.7(d), the filtered or denoised signal withDFj2M1threshold, shows noise is not completely removed as marked at 1 and 2. This is due to the lower value of the denoising factorDFj2M1as shown in fifth column corresponding to aVL channel, in Table-3.5. Similarly, the denoised signal in Figure-3.7(e) withDF_j1M1 threshold fails at points marked 3 through 8. In Figure-3.8, original signal, wavelet filtered signal using soft threshold (ST) and wavelet filtered signal using proposed DFjM1 are shown. It is observed (Fig 3.8(b)) that ST-based method does not remove the noise effectively. This is the reason for the low PRD (1.1085) and WWPRD (1.6015) values shown in Fig 3.8(b) for the filtered signal with the soft threshold. The proposedDFjM1is effective and denoising is distinctly visible in the filtered signal shown in Fig 3.8(c).

Table 3.6: Performance Analysis: CSE mutlilead measurement library database, dataset-M01-003

CSE mutlilead measurement library database, dataset-M01-003

Parameters Lead-I Lead-II Lead-III aVR aVL aVF V1 V2 V3 V4 V5 V6

PRD-DFjM1 9.137 6.362 11.148 10.022 7.424 4.599 5.450 4.411 3.560 3.473 4.160 4.844 PRD-DF\_jM1 17.202 17.369 20.909 24.566 16.269 12.304 11.229 18.338 26.518 28.646 27.939 26.053 PRD-DF_j2M1 7.795 4.531 14.838 19.599 4.297 3.518 5.986 10.110 25.826 27.198 26.962 25.292 PRD-DFj1M1 17.006 16.816 20.909 24.566 12.951 12.086 8.931 18.114 26.101 28.171 27.510 25.578

PRD-ST 1.307 0.943 1.606 1.048 1.108 0.441 1.698 2.075 1.946 1.944 1.960 2.132

WWPRD-DF_jM1 21.710 11.367 26.054 18.096 15.716 12.165 10.604 8.547 5.381 5.190 8.506 11.343 WWPRD-DF\jM1 36.934 28.661 44.331 40.279 31.555 26.667 23.093 29.260 33.586 37.046 39.765 40.710 WWPRD-DF_j2M1 12.099 7.344 25.846 30.669 7.330 7.059 7.237 11.716 26.370 28.400 31.269 30.475 WWPRD-DF_j1M1 35.968 26.330 44.331 40.279 24.265 24.127 13.800 25.969 26.879 29.939 32.745 32.497

WWPRD-ST 1.748 1.378 1.818 1.521 1.604 0.776 1.755 1.968 1.751 1.827 1.924 1.940

WEDD-DF_jM1 3.061 1.992 3.799 2.252 1.871 2.825 2.998 2.871 2.147 1.928 2.843 3.2188 WEDD-DF\_jM1 12.030 7.141 16.802 12.005 9.176 9.965 10.789 19.041 24.694 27.933 28.366 27.285 WEDD-DF_j2M1 1.915 1.423 8.140 10.169 1.189 2.411 2.103 6.667 19.431 21.798 22.502 21.853 WEDD-DF_j1M1 12.428 7.494 16.802 12.005 6.744 7.844 6.345 17.809 19.483 22.025 22.635 21.925

WEDD-ST 0.924 0.539 1.252 0.473 0.725 0.275 1.286 1.709 1.611 1.719 1.918 1.970

3.3 Evaluation of Proposed Denoising Methods

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8 7

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Figure 3.7: (a) Original signal and wavelet filtered signal using proposed denoising factors (b) DFjM1, (c) DF\jM1, (d)DFj2M1and (e)DFj1M1(CSE mutlilead measurement library database, dataset: MO1-003, Lead- aVL)

Table-3.6 shows the different distortion values for four proposed denoising factors and for the soft threshold. All the 12-channel data are evaluated. It is observed that the distortion values for soft threshold are minimum in all cases. This is due to the very low soft threshold values shown in Table-3.5. Low distortion or error values appear as noise part of the signal is not filtered out. Among the four denoising factors,DF_jM1 shows minimum PRD value for Lead-III, aVR, V1, V2, V3 and V4 channels. Minimum WWPRD values are obtained with the same denoising factor for aVR, V2, V3, V4, V5 and V6 channels. Similarly, minimum WEDD values are observed for Lead-III, aVR, aVL, V2, V3, V4, V5 and V6 channels. It is also found that minimum distortion values are obtained with DFj2M1in all other channels. This has resulted due to low values of the denoising factorDFj2M1. It is shown in Figure-3.7(d) that the filtered signal withDFj2M1 denoising factor fails to remove the noise

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Amplitude

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(a) Original signal (Lead−aVL, Dataset M01−003, CSE)

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(c) Filtered signal after denoising (using proposed DF)

Sample

PRD: 1.1085 WWPRD: 1.6015

PRD: 7.4244 WWPRD: 15.7168

Figure 3.8: Original and filtered signals using soft thresholding and using proposed DF (a) original signal (Lead-aVL, Dataset M01-003, CSE), (b) filtered signal after denoising (using soft thresholding), (c) filtered signal after denoising (using proposed DF) (CSE mutlilead measurement library database, dataset: MO1-003, Lead-aVL)

efficiently. These results prove that the denoising factor DF_jM1 will be the most effective not only from the point of view of effectively filtering the noise but also help retain the diagnostic information in the ECG signal.

It will be helpful to investigate if the values of the denoising factorDF_jM1 for the three subbands, cD1, cD2 and cD3, are optimal from the point of view of the distortions in the signal. Figure-3.9 show the WEDD and WWPRD values when each of the three subbands are individually thresholded. For these results the signal in aVL channel is tested. It is observed that the maximum distortion value is attained when the threshold or denoising factor value exceeds certain value. For the signal in aVL channel the WEDD and WWPRD values (Table-3.6) withDF_jM1 denoising factor are found as 1.8718 and 15.7168 respectively. The denoising factor,DF_jM1, has values (Table-3.5) in cD1, cD2

3.3 Evaluation of Proposed Denoising Methods

and cD3 subbands as 0.2563, 0.2102 and 0.1766 respectively. If these denoising factor values are

0 0.5 1

0.8 0.9 1 1.1 1.2

1.3Only cD1 denoised

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WEDD

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Figure 3.9: WEDD and WWPRD values using DFjM1,(a) and (d) only cD1 subband denoised, (b) and (e) only cD2 subband denoised (c) and (f) only cD3 subband denoised, Dataset: MO1-003, Lead-aVL, from CSE mutlilead measurement library.

used individually, as shown in Figure-3.9, for the three subbands, the WEDD values are 0.95, 1.2 and 1.0 for cD1, cD2 and cD3 subbands, this would have resulted in a total WEDD value of 3.15. But the observed WEDD value is 1.8718 when the three subbands are simultaneously thresholded. Similar results are observed with the WWPRD values. This shows that a proper choice of a set of optimal values for the denoising factor for the three subbands may results in an improved performance. To investigate further, two subbands, cD2 and cD3, are thresholded simultaneously. Table-3.7 shows

Table 3.7: WEDD values against thresholds of cD2 and cD3 subbands

Thresholds cD3

cD2 0.1 0.2 0.3 0.4 0.5

0.1 1.1895 0.9629 1.8755 1.7089 1.7771 0.2 2.3070 1.9412 3.0293 2.8843 2.9514 0.3 2.3423 1.9764 3.0648 2.9188 2.9869 0.4 2.5783 2.2669 3.4279 3.2727 3.3408 0.5 2.6530 2.3433 3.5061 3.3507 3.4187

the WEDD values for different threshold values in cD2 and cD3 subbands. It is observed that simul- taneous thresholding has resulted in lower WEDD values. The WEDD value is 1.9412 for both the threshold values of cD2 and cD3 subbands as 0.2. Both threshold values as 0.2 is close to the values of the denoising factor for the both subbands which are 0.2102 and 0.1766. This value of WEDD is close to the observed value of WEDD (1.8718) as shown in Table-3.6. The lower WEDD value is due improved retention of diagnostic features in the signal when both the subbands are simultane- ously thresholded. The results also indicate that the choice of a set of denoising factor values for the subbands based on Kurtosis and ECE values will result as an optimal set of threshold values for the subbands.