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A comparison of two extensions of the matching pursuit algorithm for the harmonic decomposition of sounds

In the framework of audio signal analysis, it is desired to obtain sparse representations that are able to reflect the harmonic structures, e.g., issued from musical instruments. In this paper, we compare two approaches which introduce some explicit models of harmonic features into the matching pursuit analysis framework. The first approach is the harmonic matching pursuit (HMP), where the harmonic structures are modeled by sets of harmonically related Gabor atoms which are directly optimized in the analysis loop. The second approach, called meta-molecular matching pursuit (M3P), is based on the a posteriori agglomeration of elementary features coming from a short time Fourier transform. We discuss the pros and cons of each method through experiments involving different audio signals, and conclude on possible approaches for combining the two methods.