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

Abstract

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 composed of short term broadband sounds. In this paper, we propose a novel hybrid method built upon Nonnegative Matrix Factorisation (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.

[Retracted] Music Similarity Detection Guided by Deep Learning Model

“…This algorithm relies on the anisotropic continuity of the spectrogram to separate the signal. Since the shock spectrum is continuously and smoothly distributed in frequency, the harmonic spectrum is continuously and smoothly distributed in the time direction [ 17 ]. Equation ( 1 ) is derived from the differences in the spectral representation of impact and harmonic sounds.…”

Phase-aware Harmonic/percussive Source Separation via Convex Optimization

“…( 12), the proposed method directly treats the timedomain signals, and its constraint claims that the separated components satisfy the perfect reconstruction property in the time-domain as in a recent audio source separation method [24]. Some of the conventional HPSS methods (e.g., anisotropic smoothness based methods [5,7] and non-negative matrix factorization based methods [25,26]) assume additivity of power spectrograms, but it requires some statistical assumptions as discussed in [20]. In contrast, the constraint in the proposed method (additivity in the time-domain) is always justified.…”

A New Blind Source Separation Algorithm Framework for Noisy Mixing Model Based on the Energy Concentration Characteristic in Signal Transform Domain

“…In the three-layer wavelet decomposition, the noise energy is mainly distributed on W h (1, k)and W h (2, k), and the signal energy is mainly distributed on W l (2, k). Combining (1), (5), and (6), we can obtain…”

“…Many new technologies are introduced into BSS research. For example, signal sparse component analysis [2,3], dictionary learning [4,5], nonnegative matrix factorization [6,7], bounded component analysis [8,9], tensor decomposition [10,11], and machine learning [12]. However, these algorithms are sensitive to noise.…”