Analysis-synthesis of the phonocardiogram based on the matching pursuit method

The matching pursuit method of Mallat and Zhang (1993) is applied to the analysis and synthesis of phonocardiograms (PCGs). The method is based on a classical Gabor wavelet or time-frequency atom which is the product of a sinusoid and a Gaussian window function, it decomposes a signal into a series of time-frequency atoms by an iterative process based on selecting the largest inner product of the signal (and the subsequent residues) with atoms from a redundant dictionary. The Gaussian window controls the envelope duration and time position of each atom; and the sinusoid represents the frequency. The method was applied to two sets of PCGs: one with very low-noise level and the other with 10% noise energy. Each database includes 11 PCGs representing the normal and the pathological conditions of the heart. The normalized root-mean-square error (NRMSE) was computed between the original and the reconstructed signals. The results show that the matching pursuit method is very suitable to the transient and complex properties of the PCGs, as it yielded excellent NRMSEs around 2.2% for the two sets of 11 PCGs tested.