Evaluating the denoised signal of abnormal PCG signals may become challenging. Because there is no normal PCG recording of the patient with which the results can be compared.

Based on the knowledge of signal characteristics, assuming S1 and S2 sounds are the only audible heart sound, the inter and intra sound amplitude variations of denoised signals are examined. To do that, the box plot of each sound component is analyzed and their correlations are evaluated. For adaptive OGS-TVF, the optimal regulation parameterλ value depends on the input SNR level and the group sizeK. In Fig. 3.2, the effect of input SNR and group size on theλ value has been shown. As observed in the figure, increasing the group size Kimproves the performance of the OGS-TVF [1] which in turn increases the computational cost. In our study, the group size is set atK = 10. To test the OGS-TVF incorporating the MAP estimation method by Deng et al. [1], the parameters are set accordingly asθ = 0.8,α = 1 andβ = 50.

In wavelet-decomposition-based filtering, the PCG signals are decomposed using the discrete wavelet transform (DWT) with various wavelet families. The popular wavelet for heart sound analysis are Daubechies ’dB5’, ’dB10’, biorthogonal ’bior3.9’, ’bior5.5’, Coiflet families.

From the detail coefficients d_{3} , d_{4} , and d_{5}, the signal is reconstructed. To determine the
suitable wavelet, the envelope values from the reconstructed signal of each wavelet family are
summed for S1, S2, and silent intervals. The wavelet family that yielded the highest ratio of
the sum of the amplitudes for the S1 and S2 sounds compared to the sum over other intervals
is selected for further use [5].

Fig. 3.7 and Fig. 3.8 illustrate the resulting filtered signal waveform using the conventional and the proposed methods at two different SNR levels, 10 dB and -5 dB respectively. The conventional BPF and wavelet decomposition-based filter is effective against the out-of-band noise signals irrespective of the noise intensity levels. When dealing with low-frequency noise that overlaps with the spectrum of heart sound signals, neither of the methods may have adequate selectivity to reject the noise. It may suppress the noise to some extent when the

0 1 2 3 -1.5

-1 -0.5 0 0.5 1 1.5

Amplitude

(a)

0 1 2 3

-1.5 -1 -0.5 0 0.5 1

1.5 (b)

0 1 2 3

-1.5 -1 -0.5 0 0.5 1 1.5

Amplitude

(c)

RMSE= 0.84

0 1 2 3

-1.5 -1 -0.5 0 0.5 1

1.5 (d)

RMSE= 0.93

1 2 3 4 5 Iterations 0

0.05

0.1 (e)

1 2 3

Iterations 0

0.05

0.1 (f)

1 2

Iterations 0

0.05

0.1 (g)

1 2

Iterations 0

0.05

0.1 (h)

0 1 2 3

-1.5 -1 -0.5 0 0.5 1 1.5

Amplitude

**(i)**

RMSE= 1.08

0 1 2 3

-1.5 -1 -0.5 0 0.5 1

1.5 **(j)**

RMSE= 1

0 1 2 3

time (s) -1.5

-1 -0.5 0 0.5 1 1.5

Amplitude

(k)

RMSE= 0.7

0 1 2 3

time (s) -1.5

-1 -0.5 0 0.5 1

1.5 (l)

RMSE= 0.72

**Figure 3.7:** Illustrate (a) PCG signal, (b) affected by AWGN noise of 10 dB SNR. The resulting
filtered signals from (c) BPF, (d) wavelet transform using‘db10’ (i) adaptive OGS-TVF [1], (j) proposed
OGS-TVF using sample entropy and the dual filtering that combines (k) wavelet transform and (l) BPF
with OGS-TVF are also shown. Theλvalues generated at each iteration corresponding to OGS-TVF
are shown in (e), (f), (g), and (h), respectively.

0 1 2 3 -1.5-1

-0.50.51.501

Amplitude

(a)

0 1 2 3

-1.5-1 -0.50.51.501

(b)

0 1 2 3

-1.5-1 -0.50.51.501

Amplitude

(c)

RMSE= 2.43

0 1 2 3

-1 0 1

(d) RMSE= 2.42

1 3 3 4

Iterations 0

0.1

0.2 (e)

1 2 3 4 5 Iterations 0

0.1

0.2 (f)

1 2 3 4

Iterations 0

0.1

0.2 (g)

1 2 3 4

Iterations 0

0.1

0.2 (h)

0 1 2 3

-1.5-1 -0.50.51.501

Amplitude

(i)

RMSE= 1.76

0 1 2 3

-1.5-1 -0.50.51.501

(j)

RMSE= 1.82

0 1 2 3

time (s) -1.5-1

-0.50.51.501

Amplitude

(k)

RMSE= 1.4

0 1 2 3

time (s) -1.5-1

-0.50.51.501

(l)

RMSE= 1.36

**Figure 3.8:** Illustrate (a) PCG signal, (b) affected by AWGN noise of -5 dB SNR. The resulting
filtered signals from (c) BPF, (d) wavelet transform using‘db10’ (i) adaptive OGS-TVF [1], (j) proposed
OGS-TVF using sample entropy and the dual filtering that combines (k) wavelet transform and (l) BPF
with OGS-TVF are also shown. Theλvalues generated at each iteration corresponding to OGS-TVF
are shown in (e), (f), (g), and (h), respectively.

SNR level is high as shown in Fig. 3.7 (c) and (d). But when the SNR level decreases, the noise interferences are not subdued adequately resulting in noisy output, as shown in Fig.

3.8 (c) and (d).

The denosing results of PCG signal using conventional group-sparse total variation filter
which was suggested by Deng et al. [1] are shown in Fig. 3.7 (i) and Fig. 3.8 (i) at two SNR
levels 10 dB and -5 dB respectively. The λvalues generated by MAP estimation at different
iteration steps are shown in Fig. 3.7 (e) and Fig. 3.8 (e) respectively. The results of denoising
using this method produces better performance compared to BPF and WT filter methods. But
estimating the noise variance using the median absolute deviation (MAD), oversmooth the
signal and yields a large root-mean-square-error (RMSE) value1.03(Fig. 3.7 (i)) and1.76
(Fig. 3.8 (i)). On the other hand, using sample entropy as regularization parameter and as
the stop condition in the proposed method, Proposed_{1}, improves the denoising accuracy as
shown in 3.7 (j) and Fig. 3.8 (j).

Combining LTI filter with sample entropy-based adaptive OGS-TVF filter compensates for the limitations of each filter. The BPF or wavelet-based filter helps remove high-frequency out-of-band noise. This will remove most of the local noise such as voices, murmurs, or ambient noise (Fig. 3.4). The remaining noise is suppressed using the proposed adaptive OGS-TVF algorithm taking smallerλ values and lesser iteration steps (Fig. 3.7 (g), (h) and Fig. 3.8 (g), (h) ). The process also avoids waveform distortion of the denoised signal.

The results of denoising yield a smaller root-mean-square-error (RMSE),0.7and0.72for 10 dB SNR. The plots shown in Fig. 3.7 (k) and Fig. 3.8 (k) are results of dual filtering with wavelet-transform based filter and the proposed adative OGS-TVF. Similarly, Fig. 3.7 (l) and Fig. 3.8 (l) are the results of dual filtering using BPF and the proposed adaptive OGS-TVF.

Both the hybrid methods give comparable results. For easy implemention and computatinal cost, the BPF with OGS-TVF is preferrable.

BPF

adpOGSTVFproposed_1proposed_2proposed_3 4

6 8 10 12 14 16

SFER (dB)

(a) Input SNR 10 dB

BPF

adpOGSTVFproposed_1proposed_2proposed_3 3

4 5 6 7 8 9 10

SFER (dB)

(c) Input SNR 0 dB

BPF

adpOGSTVFproposed_1proposed_2proposed_3 4

6 8 10 12 14

SFER (dB)

(b) Input SNR 5 dB

BPF

adpOGSTVFproposed_1proposed_2proposed_3 0

2 4 6

SFER (dB)

(d) Input SNR -5 dB

**Figure 3.9:**The signal-to-filter-error ratio (SFER) for different input noise.

Fig. 3.9 shows the signal to filter error ratio of the denoising methods, BPF, adaptive
OGS-TVF, ‘Proposed_{1}’, ‘Proposed_{2}’ and ‘Proposed_{3}’ at different SNR levels. At higher SNR
input signal (10 dB), the dual filtering approach (‘Proposed_{2}’ and ‘Proposed_{3}’) gives SFER
values around 13 and 14 respectively. For lower SNR value (-5 dB), the dual filtering apprach

BPF

adpOGSTVFproposed_1proposed_2proposed_3 0

5 10 15

RMSE

(a) Input SNR 10 dB

BPF

adpOGSTVFproposed_1proposed_2proposed_3 2

4 6 8

RMSE

(c) Input SNR 0 dB

BPF

adpOGSTVFproposed_1proposed_2proposed_3 0

2 4 6 8 10 12 14

RMSE

(b) Input SNR 5 dB

BPF

adpOGSTVFproposed_1proposed_2proposed_3 1

1.5 2 2.5 3 3.5 4

RMSE

(d) Input SNR -5 dB

**Figure 3.10:** The root-mean-square error (RMSE) for different input noise.

gives better SFER value between 5 to 6. In Fig. 3.9 (a), (b), (c) and (d), the SFER values are shown for different input SNR levels, 10 dB, 5 dB, 0 dB and -5 dB for conventional BPF, adaptive OGS-TVF and proposed methods respectively. The proposed dual filtering approaches give better performance in terms of SFER metric.

The performance of the filters in terms of RMSE are measured for comparison and shown
in Fig. 3.10. For the large input SNR, the proposed methods, ‘Proposed_{1}’, ‘Proposed_{2}’ and

‘Proposed_{3}’ yield better performance than the conventional methods. In Fig. 3.10 (a), (b),
(c) and (d), the RMSE values are shown for different input SNR levels, 10 dB, 5 dB, 0 dB
and -5 dB respectively for conventional BPF, adaptive OGS-TVF and proposed methods.

Comparison of the RSME metric also reveals that the dual filtering approaches give better performance for heart sound signals.

. S1 S2

Silent 0

0.2 0.4 0.6 0.8 1

Intensity

(a) Input SNR 10 dB

BPF
adpOGSTV
proposed_{1}
proposed_{2}
proposed_{3}

. S1 S2

Silent 0

0.2 0.4 0.6 0.8 1

Intensity

(c) Input SNR 0 dB

BPF
adpOGSTV
proposed_{1}
proposed_{2}
proposed_{3}

. S1 S2

Silent 0

0.2 0.4 0.6 0.8 1

Intensity

(b) Input SNR 5 dB

BPF
adpOGSTV
proposed_{1}
proposed_{2}
proposed_{3}

. S1 S2

Silent 0

0.2 0.4 0.6 0.8 1

Intensity

(d) Input SNR -5 dB

BPF
adpOGSTV
proposed_{1}
proposed_{2}
proposed_{3}

**Figure 3.11:**Intensity distribution of FHS signals.

For analysing the FHS (S1 and S2 sounds), the denoising process should preserve their signal characteristics. Therefore, the proper signal envelope detection and accurate FHS segmentation process depend also on the quality of the denoising process employed. So, the inter and intra sound amplitude variations of denoised signals are needed to be examined. To do that intensity of each sound component is analyzed in the box plot and their dominance in the denoised signals are evaluated in Fig. 3.11. Analysis of signal intensity distribution of different heart sound components at different SNR levels, 10 dB, 5 dB, 0 dB and -5 dB are

shown in Fig. 3.11 (a), (b), (c) and (d) respectively. In all the cases it is seen that the intensity of FHS is well preserved by our proposed denoising schemes. Even the silence periods are well maintained with accurate signal intensity. This has established the performance of the proposed methods.