Application of the matching pursuit method for the analysis and synthesis of the phonocardiogram

The matching pursuit method of Mallat and Zhang (1993) is applied to the analysis and synthesis of phonocardiograms (PCGs) using a 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 method was applied to a data base which includes eleven PCGs representing the normal and pathological conditions of the heart. The normalized root-mean-square error (NRMSE) was computed between the original and the reconstructed PCGs. 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 eleven PCGs tested.