A structured nonnegative matrix factorization for source separation

Abstract

In this paper, we propose a new unconstrained nonnegative matrix factorization method designed to utilize the multilayer structure of audio signals to improve the quality of the source separation. The tonal layer is sparse in frequency and temporally stable, while the transient layer is composed of short term broadband sounds. Our method has a part well suited for tonal extraction which decomposes the signals in sparse orthogonal components, while the transient part is represented by a regular nonnegative matrix factorization decomposition. Experiments on synthetic and real music data in a source separation context show that such decomposition is suitable for audio signal. Compared with three state-of-the-art harmonic/percussive decomposition algorithms, the proposed method shows competitive performances.Index Termsnonnegative matrix factorization, projective nonnegative matrix factorization, audio source separation, harmonic/percussive decomposition.

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

“…In theory, it seems that the PNMF and the ONMF lead to similar decompositions, as the W matrix estimated by the PNMF is almost orthogonal (i.e., W T W −I k 2 is small) [41]. However in practice, enforcing orthogonality of the basis functions at every iteration is a too strong constraint to decompose audio signals [42].…”

“…We can expect that most of the harmonic components will be represented by the orthogonal part while the percussive ones will constitute the regular NMF components. Using a similar model to our preliminary work [42], let V be the magnitude spectrogram of the input data. The model is then given by:…”

“…The data matrix is approximated by an almost orthogonal sparse part that codes the harmonic instruments V H = W H W T H V and a non-constrained NMF part that codes the percussive instruments V P = W P A P . The main advantage of the HPNMF relies in the fact that the method has few parameters compared to the CoNMF [10] and the NMPCF [40] methods while still obtaining similar results [42].…”

“…A fully unsupervised HPNMF model does not allow for a satisfying harmonic/percussive source separation [42]. To alleviate this problem, we use here a fixed drum dictionary W p for the percussive part of the HPNMF.…”

Applying Source Separation to Music

“…Orthogonal NMF and projective NMF (PNMF) (Choi, 2008) are typical examples of such decompositions. For example, Laroche et al (2015) used PNMF to obtain an initial nearly-orthogonal decomposition well adapted to represent harmonic instruments. This decomposition is further extended by a nonorthogonal component that reveals to be particularly relevant to represent percussive or transient signals.…”