Factorization of Overlapping Harmonic Sounds Using Approximate Matching Pursuit

Factorization of polyphonic musical signals remains a difficult problem due to the presence of overlapping harmonics. Existing dictionary learning methods cannot guarantee that the learned dictionary atoms are semantically meaningful. In this paper, we explore the factorization of harmonic musical signals when a fixed dictionary of harmonic sounds is already present. We propose a method called approximate matching pursuit (AMP) that can efficiently decompose harmonic sounds by using a known predetermined dictionary. We illustrate the effectiveness of AMP by decomposing polyphonic musical spectra with respect to a large dictionary of instrumental sounds. AMP executes faster than orthogonal matching pursuit yet performs comparably based upon recall and precision.