Exploring embedding matrices and the entropy gradient for the segmentation of heart sounds in real noisy environments

In this paper we explore a novel feature for the segmentation of heart sounds: the entropy gradient. We are motivated by the fact that auscultations in real environments are highly contaminated by noise and results reinforce our suspicions that the entropy gradient is not only robust to such noise but maintains a high sensitivity to the S1 and S2 components of the signal. Our whole approach consists of three stages, out of which the last two are novel contributions to this field. The first stage consists of typical pre-processing and wavelet reconstruction to obtain the Shannon energy envelogram. On the second stage we use an embedding matrix to track the dynamics of the system, which is formed by delay vectors with higher dimension than the corresponding attractor. On the third stage, we use the eigenvalues and eigenvectors of the embedding matrix to estimate the entropy of the envelogram. Finite differences are used to estimate entropy gradients, in which standard peak picking approaches are used for heart sound segmentation. Experiments are performed on a public dataset of pediatric auscultations obtained in real environments and results show the promising potential of this novel feature for such noisy scenarios.