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.
noise so that the TVF will further smooth out the residual weaker noise in the signal. A stop- condition can be devised to skip the TVF denoising and prevent over smoothing the signal by analyzing the sample entropy measure. On comparing the hybrid filtering methods with other existing methods, the hybrid methods show considerable improvements over others.
Enhancement of heart sound envelope
4.1 Heart sound intensities and logistic function . . . 76 4.2 Logistic function amplitude moderation (LFAM) . . . 78 4.3 Projection of parameters in terms of signal amplitude . . . 81 4.4 Estimation of lower and upper cut-off amplitudes . . . 82 4.5 Shannon entropy and Shannon energy based mode selection (SE2MS) . 85 4.6 Evaluation process . . . 88 4.7 Results and discussions . . . 91 4.8 Summary . . . 101
In this Chapter, we will discuss a new method to extract the envelope of the fundamental heart sounds using logistic function. The basic sigmoid function, also known as logistic function, is the key component of this logistic function amplitude moderation (LFAM) method.
The proposed LFAM involves finding critical amplitudes, also known as lower and upper cut-off amplitudes. These critical amplitudes are dependent on the nature and the degree of noise contained in the signal. Their values are regressively obtained from the signal itself by histogram analysis of intensity distribution. We also proposed a Shannon entropy and a Shannon energy based amplitude moderation of the heart sound to extract its envelope. This method selects either Shannon entropy or Shannon energy looking at the signal.
4.1 Heart sound intensities and logistic function
The signal intensities of the fundamental heart sounds (FHS), S1 and S2, have been viewed as key features for the analysis of heart sound signals [5, 100]. This concept originates from the perceptual evaluation of heart sound carried out in the clinical environment. During auscultation, the S1 and S2 sounds are heard as the dominant intensity sounds separated by a silent systolic or diastolic interval in every cardiac cycle. By analyzing the intensity information along with tone and timbre, clinical experts can identify these sounds. For this reason, we proposed a logistic function based amplitude moderation, where the logistic function is parameterized by introducing the scaling parameterαand shifting parameterβ.
These correspond to the upper cut-off intensity level above which the signal is emphasized and the lower cut-off intensity level below which the signal will be attenuated as silent sound intervals.
Mathematically, the intensity information is defined as the envelope of a signal. Some of the conventional envelope extraction methods are absolute value, energy (by squaring), the Hilbert envelope, the homomorphic envelope, and the Teager-kaiser energy (TKE) envelope [5, 6, 34, 38]. The heart sound envelope ideally has two peaks in every heart cycle duration (HCD), indicating the intensity of S1 and S2 sounds. For the uniformity and easy detection
of FHS, it is preferred that these envelope peaks maintain more-or-less identical intensity levels. But, realizing it in the real-time application is challenging. Depending on the site of auscultation, physique or health condition of the subject, the S1 sound may appear louder than the S2 sound, or vice versa. The popular methods to mediate such inconsistency use Shannon entropy or Shannon energy-based envelogram techniques [34, 36, 37]. In these methods, the descending logarithmic weights of the amplitudes emphasize the medium intensity signals as valuable information. The Shannon entropy accentuates the lower medium intensities and makes the envelope peaks substantially uniform. Since this method emphasizes the weaker intensity signal, the envelope may become noisy. On the other hand, the Shannon energy envelope is less affected by noise. It emphasizes higher medium intensity signals and suppresses the lower intensity signals. This method reduces the effect of weaker intensity noise and maintains minimal variation between envelope peaks.
Both methods, Shannon entropy and Shannon energy, have their own advantages and disadvantages. If either of the methods is adopted properly by examining the feasibility of the method with the nature of a given signal, it can improve the detection of FHS in noisy or pathological recordings. To implement this, the system needs to identify whether a PCG signal is clean, noisy, or pathological. There is one major drawback in calculating the Shannon entropy and Shannon energy that is often overlooked. In both the methods, the signal intensities nearing its absolute maximum value are extenuated. In other words, the higher signal intensities are not considered for the candidacy of heart sounds. This results in undesired errors in the derived envelope. On the other hand, these methods do not suppress the low-intensity noise signal as desired. Instead, they equally emphasize the intensity distribution of low and medium amplitude signals, prominently seen in the Shannon entropy-based envelope. The resulting envelope appears noisy. To tackle this limitation, a logistic function based amplitude moderation (LFAM) method is proposed. This is motivated by the sigmoid-curve characteristic of the logistic function. It involves categorizing the levels of signal intensities belonging to either FHS or noise signal categories. Then the LFAM is applied to uniformly enhance all the signal intensities belonging to FHS. With proper calibration of
parameters, the remaining signal intensities are suppressed implicating the silent intervals.
In the proposed method, the logistic function is parameterized by introducing the scaling parameter αand the shifting parameter β. The αandβ values are calibrated according to the upper cut-off intensity level above which the signal is emphasized and the lower cut-off intensity level below which the signal will be attenuated as silent sound intervals, respectively.
In this chapter, we will discuss how to obtain the optimal parameter values from a given PCG.