Hybrid Projective Nonnegative Matrix Factorization With Drum Dictionaries for Harmonic/Percussive Source Separation

One of the most general models of music signals considers that such signals can be represented as a sum of two distinct components: a tonal part that is sparse in frequency and temporally stable and a transient (or percussive) part that is composed of short-term broadband sounds. In this paper, we propose a novel hybrid method built upon nonnegative matrix factorization (NMF) that decomposes the time frequency representation of an audio signal into such two components. The tonal part is estimated by a sparse and orthogonal nonnegative decomposition, and the transient part is estimated by a straightforward NMF decomposition constrained by a pre-learned dictionary of smooth spectra. The optimization problem at the heart of our method remains simple with very few hyperparameters and can be solved thanks to simple multiplicative update rules. The extensive benchmark on a large and varied music database against four state of the art harmonic/percussive source separation algorithms demonstrate the merit of the proposed approach.