Source Separation of the Second Heart Sound Using Gaussian Mixture Models

Abstract

In this work, we present a method to separate aortic (A2) and pulmonary (P2) components from second heart sounds (S2). The proposed approach captures the different dynamical behavior of A2 and P2 components via a joint Gaussian mixture model, which is then used to perform separation via a closed-form conditional mean estimator.The proposed approach is tested over synthetic heart sounds and it is shown guarantee a reduction of approximately 25% of the normalized root mean-squared error incurred in signal separation, with respect to a previously presented approach in the literature.

Source Separation of the Second Heart Sound via Alternating Optimization

“…In this section, numerical results obtained with synthetic heart sound signals are shown in order to validate the proposed method and to compare its separation performance with that of the methods described in [8] and [10], which rely on a similar set of assumptions regarding the variability of A2 and P2 components in different S2 sounds.…”

“…In particular, Fig. 1 contains the normalized root mean-squared error (NRMSE) values obtained by the proposed separation algorithm and the methods in [8] and [10] when generating synthetic S2 sounds for each heart sound recording with A2-P2 splits drawn from a uniform distribution over the interval [0, ∆ max ] ms, for different values of ∆ max .…”

“…This results is possibly explained by the increased flexibility of the proposed approach modeling assumptions which do not impose perfect alignment of A2 sounds in all the observed S2 recordings. On the other hand, for low SNR values, the approach in [10] achieves better performance, but this is obtained at the expense of the use of annotated training data to fit the GMM used for reconstruction.…”

“…Therefore, assuming that A2 and P2 components keep approximately the same form (apart from time shifts) in successive S2 sounds, the A2 components are estimated by averaging over the collected S2 sounds and the P2 components are obtained by subtraction. Similar assumptions on the dynamic behavior of A2 and P2 components have been adopted by the approach presented in [10], which attempts to recover A2 and P2 components using a joint multivariate Gaussian mixture model (GMM) spanning samples extracted from S2 sounds at different heartbeats. However, this approach requires the availability of a training set with already isolated A2 and P2 components, which is difficult to collect in common clinical practice.…”

Separation of the Aortic and Pulmonary Components of the Second Heart Sound via Alternating Optimization

“…Secondly, the assumption that A2 is obtained by averaging is a restrictive assumption that makes the algorithm sensitive to alignment of S2 sounds. Other work attempts to recover the A2 and P2 components using a joint multivariate Gaussian mixture model (GMM) from S2 sounds [27]. However, this approach is a supervised machine learning approach that requires the availability of ground truth annotated A2 and P2 components.…”