is some tolerance in this assumption and it is taken to be within 50 ms as suggested in [5].
If the start of the detected S1 and S2 sounds are located within 50 ms of their respective references then it is considered as truly positive (TP). Otherwise, they are graded as falsely positive (FP). If the heart sounds are not detected at the intended reference position then it is considered as falsely negative (FN). Then, the sensitivity (Se), positive predictivity (P+) and F1 score were measured. The observations are repeated multiple times over 30 iterations for both the algorithm taking random training set and test set.
Table 5.1:Comparison of performance scores (%) of existing and proposed methods using various input features and across 30 iterations.
Features Classifier Se P+ F1
* Homomorphic [16] LR-HSMM 95.25±0.50 95.85±0.43 95.55±0.45 Proposed 97.83±0.18 98.24±0.11 98.03±0.13
* HEoDF LR-HSMM 95.38±0.41 96.00±0.23 95.69±0.30 Proposed 98.08±0.19 98.50±0.14 98.29±0.16
* Hilbert, Homomorphic, LR-HSMM 95.02±0.51 95.78±0.39 95.40±0.43 PSD, Wavelet [5] Proposed 97.99±0.24 98.58±0.16 98.28±0.19
* HEoDF, modified PSD, LR-HSMM 95.32±0.48 96.06±0.54 95.69±0.49 Hilbert and Wavelet Proposed 98.28±0.19 98.45±0.16 98.36±0.17 Table 5.2: Results of the proposed algorithm train on 50%of PCG data and tested on the whole dataset with additive noise at various signal-to-noise ratio (SNR) and across 30 iterations.
Types of noise
SNR in dB Features AWGN AC Ambulance Hospital
−5 a 95.21±0.41 96.65±0.25 93.29±0.41 95.63±0.52 b 96.74±0.48 97.53±0.29 95.80±0.55 97.66±0.32 0 a 97.02±0.37 97.26±0.20 96.82±0.20 97.32±0.22 b 97.47±0.21 97.91±0.24 97.66±0.28 97.63±0.20 5 a 97.86±0.23 97.54±0.29 97.54±0.05 97.63±0.20 b 98.10±0.24 98.02±0.20 98.11±0.20 98.11±0.19 10 a 97.86±0.23 97.59±0.19 97.66±0.21 97.71±0.19 b 98.18±0.21 98.22±0.19 98.20±0.18 98.24±0.19 These show theF1scores (%) of HSS at different noise conditions. The notation ‘a’ feature represents the homomorphic, Hilbert, PSD, and wavelet envelopes used in David’s work [5]. The ‘b’
features are the proposed HEoDF and Hilbert envelope after the dual filtering process, modified PSD, and wavelet envelopes.
feature, the proposal is compared with the existing features [5]. Their outcomes are shown in Table 5.2.
The performance scores shown in Table 5.1 and Table 5.2 illustrate that incorporating the multi-modal distribution model in HSMM has improved the segmentation accuracy especially in heart sound signals with considerably large heart rate variation. The incorporation of the dual-filter before feature extraction has also improved the segmentation of noisy recordings.
This achievement has been elaborately discussed as under.
5.4.1 Effect of multi-centroid duration model
An example of HSS mentioned in [5, 16] is shown in Fig. 5.4. The corresponding duration model pi(d) for each state i is depicted in Fig. 5.5. In this existing method, the diastolic duration distribution is modeled such that the expected state duration is within the model permissible limit defined byµdi±σdi. This duration distributionpi(d)is non-zero within this interval and zero elsewhere. Taking the value ofσdsiDia determined by Eq. (5.4), the model distribution will ignore any abnormal state duration outside the stipulated interval. Therefore, the state duration will be forcibly selected within the model limit by the maximum likelihood criterion. If a subject suffers from abnormally large heart rate variation, the model may incorrectly estimate diastole interval.
In the proposed model, the silent diastolic durationdsiDia is estimated from every instance covering all potential duration values. Also, defining the model boundaries betweendminsiDia anddmaxsiDiaoperates the estimation process within this adequate limit. Each weighted mode of the multi-modal distribution can be considered as a search space where the actual duration is expected. The true dsiDia is close to any of the modes represented by the distribution peaks. The final value is derived cumulatively from the probability of past state sequence, the transition probabilityaij, duration probability, and the probability of the present observation sequence, as defined by Eq. (2.54). This step ensures the derived state duration automatically adjusts itself to its best value. The modified duration model is illustrated in Fig. 5.7 and the outcome of the segmentation is shown in Fig. 5.6.
4 4.5 5 5.5 6 6.5 PCG
S1 siSys S2 siDia
Time (s)
Derived states R−peak end−T−wave
Figure 5.4: The derived state labels of a PCG using the existing LR-HSMM algorithm.
200 400 600 800 1000
0 0.2 0.4 0.5
p i(d)
200 400 600 800 1000
0 0.1 0.2 0.3
Duration ‘d’ [ms]
p siDia(d)
S1 siSys S2 siDia
(b) (a)
dsiDia
dsiDia+ σ siDia
Figure 5.5: (a) The duration density pi(d) for each statei. (b) The densitypsiDia(d)using only mean valueµdsiDia.
4 4.5 5 5.5 6 6.5
PCG S1 SiSys S2 SiDia
Time (s)
Derived states S1
S2
Figure 5.6: The derived state labels of a PCG using proposed duration model.
0 200 400 600 800 1000
0 0.2 0.4 0.5
p i(d)
0 200 400 600 800 1000
0 0.05 0.1 0.15
Duration ‘d’ [ms]
p siDia(d)
S1 siSys S2 siDia
(b) (a)
c1
c3 c2
Figure 5.7: (a) The proposed duration density pi(d) modeled for each state. (b) The density psiDia(d) is distributed across the centroid loca- tionsc1,c2andc3.
5.4.2 Effect of TVF denoising
The dual filtering process of the standard band-pass filter (BPF) and TVF filter has consid- erably suppressed the noise elements that may be present in the silent interval between the S1 and S2 sounds in PCG. Analysis of the noisy PCG has shown its superior denoising capability compared to BPF, as shown in Fig. 5.8.
4 4.5 5 5.5 6 6.5 HEoTVF
TVF Filter BPF Filter Noisy PCG PCG
Time (s)
(e) (d) (b)
(c) (a)
Figure 5.8:Example of HEoDF envelope for noisy PCG (SNR -5 dB) after dual filtering process.
4 4.5 5 5.5 6 6.5
PCG S1 siSys S2 siDia
Time (s)
Derived states S1
S2
Figure 5.9: A segmented noisy PCG using the proposed algorithm.
This is because TVF is a piecewise constant smoothing technique. It smooths out low amplitude highly varying signal components and preserves the discontinuities in the signal. When used after processing with BPF, it suppresses leakage frequency components.
Therefore, the HEoDF envelope extracted from the resulting filtered signal will hold more accurate signal characteristics than the normal homomorphic envelope, giving us distinct peaks and uniformly attenuated envelope segments that improve the discrimination of FHS from the silent intervals. Also, the duration parameters estimated from this envelope will be precise. The combination of the HEoDF feature with the proposed duration model has yielded considerable segmentation accuracy of98.28±0.19 Seand98.45±0.16P+in Table 5.1. An example of a noisy PCG segmentation is shown in Fig. 5.9. The significance of this dual filtering technique is further illustrated by the performance scores at different degrees of additive noise in Table 5.2.
5.4.3 Effect of short duration test data
During recordings, the initial PCG is prone to the motion artifacts or noise generated during the stabilization of the recording instrument. Such noise usually has a high amplitude and may falsely appear in the HEoDF envelope even after the dual-filtering process. The outcome may cause an erroneous estimation of HCD. If the test data is too short, there is not enough HCD information to identify such errors, leading to an incorrect duration model. Usually, this issue is resolved by neglecting the first two heart cycles. Therefore, it is preferable to use longer PCG recordings (>5 HCD) for analysis.
5.4.4 Comparison with DRNN-method
Table 5.3 shows the comparison of results achieved with our proposed method and the DRNN-method. In contexts to the task (segmentation and identification of the four major FHS components) addressed in this work, our extended multi-mode duration model-based HSMM model exhibits much improvement over the existing one. If the problem statement is extended to identify the extra sounds such as S3 and S4 sounds, pathological murmurs and noise,
Table 5.3:Comparison of our proposed LR-HSMM extension with existing LR-HSMM [5] and DRNN- method [6].
Features Classifier Se P+ F1
HEoDF, modified PSD,
Proposed 98.28 98.45 98.36 Hilbert and Wavelet
Hilbert, Homomorphic,
LR-HSMM [5] 95.02 95.78 95.40 PSD, Wavelet
LMS, MFCC,∆,∆2,
DRNN [6] 95.10 96.10 95.60 Hilbert, Homomorphic,
Hilbert and Wavelet
the HSMM based methods may not be feasible because this method predicts the state by maximization of likelihood scores of the expected events. Faulty prediction is always expected if the trained model of any particular extra sound does not exist in the test PCG signal.