M1 Heart tone components due to mitral valve closure M Acc Average of sensitivity and specificity. P2 Heart tone components due to pulmonary valve closure φm WT scaling function.

## The heart and function of the heart valves

This thesis documents our investigation into the analysis of heart sound signals to assess the heart and related pathology. Studying the mechanism behind the production of heart sounds has revealed that heart sounds contain information that reflects the structural and functional integrity of the heart.

## Normal heart sound and pathological changes in the sound

*First heart sound**Second heart sound**Duration and pitch of the normal heart sound**Third and fourth heart sounds**Murmur*

As soon as ventricular diastole starts, the semilunar valves (ie, the aortic and pulmonary valves) close, preventing backflow of blood from the aorta and pulmonary arteries. At the end of systole, the ventricles begin to repolarize and the semilunar valves block the backflow of blood from the arteries.

## Diagnostic system and diagnostic features

*Electrocardiogram-based heart sound detection**Morphology-based method**Feature-based method**Probabilistic model-based methods**Neural network-based methods*

It must meet an energy-based criterion, i.e. the total energy of the selected IMFs must be 99% of the signal energy. From this reconstructed signal, the kurtosis function is recalculated to find heart rate boundaries.

Scope of the work

## Organization of the thesis

In section 2.1, the PCG database, which is used for evaluating the thesis work, is discussed. The performance matrices that will be used to evaluate the thesis are discussed in section 2.5.

## Database

### PCG Data

Any dysfunction of the heart is reflected in the PCG signal as an abnormal sound. The reviews of the prevailing popular algorithms for analyzing PCG signals are discussed in detail in the following sections.

Noise database

## Denoising process

### Wavelet transform (WT)

The level-wise decomposition of the signal into a layer of smaller subbands helps to effectively analyze the PCG signal. A standard method of WT-based denoising of PCG signal is by selecting the details and approximations corresponding to the frequency band of heart sound and using it to reconstruct the signal back.

### Total variation filter (TVF)

The reconstructed signal from the remaining coefficients improved the elimination of out-of-band noise and preserved most features of the heart sound intact. By introducing (2.9) into the expression (2.6) of the cost function F(x), the majorizer function Gi(x) can be obtained.

### Overlapping group sparsity denoising

*Estimating adaptive regularization parameter (λ)*

Therefore, there is a need to set the value of the adjustment parameter by the nature and complexity of the signal and the noise level. OGS adjustment can also be accomplished by estimating the likelihood of a denoised signal with prior knowledge of the original (clean) signal and the noise.

## Feature extraction

### Envelop extraction

Most envelope extraction methods for HSS are derived from either Shannon Entropy, Shannon Energy, Hilbert Transform or Homomorphic envelope. The advantage of homomorphic envelope is its scalable smoothing process, which can be easily tuned.

### Frequency domain features

To check how well the wavelet discriminates the FHS, the ratio of the sum of the absolute values of selected coefficients corresponding to S1 and S2 sounds versus other intervals and over all recordings is measured.

## Hidden semi-Markov model (HSMM)

### HSMM for segmentation of PCG

The model is bounded by the mean value μ indicating the center of the PDF and the variance2 describing the distribution around it. The model will be a cascade of the weighted Gaussian distribution of all possible state durations of a subject.

## Performance matrices

On the other hand, wn1 and wn2 indicate the percentages of good quality and poor signal quality PCG signals available in the normal category. These same matrices will be used in this thesis to evaluate performance.

## Motivation of this thesis work

### Proposed adaptive penalty function

The proposed penalty function tries to incorporate the signal information in terms of the signal complexity measure. Among other measures reported in the literature, the sample entropy (SampEn) is widely used to estimate the complexity of the time series signal.

### Stop condition

The advantage of using this entropy measure is that it reduces bias due to self-matching and is relatively stable across different sequence lengths [98, 99]. Algorithm [1] assumes that the noise variance is known and estimates its value using the MAD rule.

## Proposed dual filtering: LTI band-pass filter with OGS-TVF

In the 'Proposed1' scheme, the complexity of the time series data of PCG is calculated using sample entropy. In the 'Proposed2' scheme, the signal is sent to the BPF filter through the sample entropy-based adaptive OGS-TVF for better denoising.

## PCG dataset used for evaluation

These two filtering approaches, 'Proposed2' and 'Proposed3' are dual filtering and are expected to provide better denoising of FHS signals. The performance of the denoising scheme will greatly affect FHS envelope detection and heart sound segmentation.

## Results and discussions

3.8 (k) are results of double filtering with wavelet-transform based filter and the proposed adative OGS-TVF. The performance of the filters in terms of RMSE is measured for comparison and shown in fig.

## Summary

These critical amplitudes depend on the nature and degree of noise contained in the signal. The signal intensity of the fundamental heart sounds (FHS), S1 and S2, have been seen as key features for the analysis of heart sound signals [5, 100].

## Logistic function amplitude moderation (LFAM)

In the proposed method, the logistic function is parameterized by introducing the scaling parameter α and the switching parameter β. The use of the exponential function (e−x) allows the standard logistic function to obtain the sigmoid curve characteristic that converges to its saturation values between 0 and 1 forx over a small range of [−2π,2π], shown in Fig.

## Projection of parameters in terms of signal amplitude

The example of LFAM transformation for linear intensity distribution at different critical cutoff values is shown in Fig. If this value is estimated to the possible noise intensities, it can suppress noise in a PCG enclosure.

Estimation of lower and upper cut-off amplitudes

## Shannon entropy and Shannon energy based mode selection (SE2MS)

It is clear that the values of xucandxlc depend to a great extent on the nature of the signal. The lower limit amplitudeaxlci is also defined as the amplitude that maximizes the number of signal samples at a quiet sound level and retains most of the signal information in time at the remaining louder signal intensities.

## Evaluation process

It estimates the single best state sequenceQ∗ that carries maximum likelihood from the given observation sequenceO and the modelΛˆ. The HSMM model Λ =ˆ {A, B.π, p} has four crucial parameters:. i) A={ai,j}defines the transition probability from state qt−1 =itoqt=j. The performance of the proposed LFAM-based envelope (LFAM E) and SE2MS-based envelope (SE2MS E) is compared with the envelopes extracted using conventional homomorphic filter (Homo E), Shannon entropy (SEnt E) , and Shannon energy (SEng E) ).

## Results and discussions

### Signal dependency

The parameter estimation from the signal itself improves the LFAM method to improve the heart sound envelope. From the figures (Fig. 4.8 and Fig. 4.9), it is clear that small values of xlc and xuc are suitable to improve the heart sound envelope under minimal or no noise interference.

### Comparison of envelope peaks

In the case of an abnormal heart sound signal, the average peak intensity values of heart sound components with variance are shown in Table 4.2. The envelopes are extracted using the conventional homomorphic filter (Homo E), Shannon entropy (SEnt E), Shannon energy (SEng E) and the proposed SE2MS E and LFAM E methods against normal (blue, thin boxes) and abnormal (thick, black boxes) heart sound signals.

### Evaluation of proposed methods for heart sound segmentation

Both SE2MS and LFAM improve the loudness difference between heart sound components; prominently observed in LFAM methods. The resulting envelope is less affected by noise and allows better separation of the audible heart sound from the expected silent intervals shown in fig.

## Summary

From our application, silent systolic duration (dsiSys) is defined as the duration from the end of the S1 sound to the beginning of the S2 sound. Similarly, silent diastolic duration (dsiDia) is defined as the duration from the end of the S2 sound to the beginning of the S1 sound.

## Proposed multi-modal diastolic duration distribution

Most PCG recordings are of short duration and the number of HCD points available for analysis is small. In our work, the number of clusters is determined by limiting the variance of the data points in each cluster so that the distance between the two nearest centers is always less than μdsiSys.

## Evaluation process

*Dataset**Feature extraction**Estimation of parameters**Estimation of observation probability**Testing*

The reference locations used to validate the S1 and S2 sounds are the locations of the R peak and the end of the T wave in the corresponding ECG. If the onset of detected sounds S1 and S2 are located within 50 ms of their respective references, this is considered a true positive (TP).

## Results and discussion

*Effect of multi-centroid duration model**Effect of TVF denoising**Effect of short duration test data**Comparison with DRNN-method*

Take the value ofσdsiDia determined by Eq. 5.4), the model distribution will ignore any abnormal state duration outside the set interval. Analysis of the noisy PCG showed its superior denoising ability compared to BPF, as shown in Fig.

## Summary

The spectral properties of the heart sound signal have been well established and used for the classification of generic classes representing FHS components [18]. The spectral ranges are limited and limited to the frequency composition of the normal heart sound.

## Evaluation process

### Dataset used for evaluation

Correlations of the S2 segment with others are omitted because the intensity of the S2 sound is relatively inconsistent compared to the S1 sound in this data set. Each of the data sets is subcategorized as normal, noise, extra heart sound, and artifacts.

### Feature extraction

Noisy PCG data is created by adding additional noise to the normal PCG signal at various noise levels. PCG signals are also labeled for their underlying heart sound segments (S1, systole, S2, and diastole) using the HSS algorithm which is discussed in Chapter 5.

### Support vector machine (SVM)

In this work, the radial basis kernel function (RBF) is implemented, defined in Equation 6.9. 6.9) To use SVM for multi-class classification, the problem is simplified by dividing the task into a series of binary problems. Then the predictions are made based on the model that has the most confidence level.

## Results and discussion

*Performance of MFCC feature**Performance of SBE feature**Correlation coefficients**Performance with combination of features*

But some coefficient values may show high correlation if the noise has noises. In the case of the noise category, the noise sound can appear in systole or diastole intervals.

## Summary

Finally, the potential of the HSMM classifier for segmentation of heart sound signals is discussed. Coimbra, “Deep convolutional neural networks for heart sound segmentation,” IEEE Journal of Biomedical and Health Informatics , vol.

Illustrate (a) PCG signal, (b) affected by AWGN noise of 10 dB SNR. The

Illustrate (a) PCG signal, (b) affected by AWGN noise of -5 dB SNR. The

The signal-to-filter-error ratio (SFER) for different input noise

The root-mean-square error (RMSE) for different input noise

Intensity distribution of FHS signals

The standard logistic function generates the approximate sigmoid curve for

The clusters produced at different dissimilarity values are shown in the dendro-

Block diagram for HSMM based heart sound segmentation algorithm

The derived state labels of a PCG using the existing LR-HSMM algorithm

The derived state labels of a PCG using proposed duration model

Example of HEoDF envelope for noisy PCG (SNR -5 dB) after dual filtering

A segmented noisy PCG using the proposed algorithm

Mel filter bank

Block diagram of heart sound classification scheme

First six mfcc coefficients

Sub-band energy feature defined over frequency ranges: (a) 25-50Hz, (b)

Correlation coefficients measured against the pair of (a) S1 and systole, (b) S1

Frequency bandwidth of heart sounds [2]

Symptoms of cardiovascular diseases (CVD) [3]

Profiles of PCG database

Notations for determining the modifier performance matrices [4]

Envelope peak intensities and variance of different heart sound components

Envelope peak intensities and variance of different heart sound components ex-

Evaluation of the Conventional Amplitude Moderation methods against the

Comparison of performance scores (%) of existing and proposed methods

Results of the proposed algorithm train on 50% of PCG data and tested on the

Comparison of our proposed LR-HSMM extension with existing LR-HSMM [5]