Percussive/harmonic sound separation by non-negative matrix factorization with smoothness/sparseness constraints

Abstract

In this paper, unsupervised learning is used to separate percussive and harmonic sounds from monaural non-vocal polyphonic signals. Our algorithm is based on a modified non-negative matrix factorization (NMF) procedure that no labeled data is required to distinguish between percussive and harmonic bases because information from percussive and harmonic sounds is integrated into the decomposition process. NMF is performed in this process by assuming that harmonic sounds exhibit spectral sparseness (narrowband sounds) and temporal smoothness (steady sounds), whereas percussive sounds exhibit spectral smoothness (broadband sounds) and temporal sparseness (transient sounds). The evaluation is performed using several real-world excerpts from different musical genres. Comparing the developed approach to three current state-of-the art separation systems produces promising results.

A structured nonnegative matrix factorization for source separation

“…For example, it is shown in [6] that enforcing temporal smoothness improves the physical meaning of the decomposition. Similarly in [7], Canadas & al. used four constraints in order to achieve a specific harmonic/percussive decomposition.…”

Online/offline score informed music signal decomposition: application to minus one

“…For example, uniformly spaced subbands on the equivalent rectangular bandwidth scale are assumed in [57]. In this work, a resolution of 1/4 of a semitone in frequency is used as in [37,67]. The time-frequency representation is obtained using 8192-point STFT and integrating the frequency bins corresponding to the same 1/4 semitone interval.…”

“…NMF [33] is an unsupervised factorization technique used for linear representation of two-dimensional nonnegative data that has been successfully applied to the decomposition of audio spectrograms [34][35][36][37][38]. In the context of audio signal processing, the popularity of this technique is related to its ability to obtain parts-based representation of the most representative objects (e.g., notes and chords) by imposing non-negative constraints that allow only additive, not subtractive, combinations of the input data unlike many other linear representations such as ICA [39] and principal component analysis (PCA) [40].…”

Harmonic-Percussive Source Separation with Deep Neural Networks and Phase Recovery

“…Alternatively, models based on non-negative matrix factorization (NMF) [10] have been applied to this task. Specific NMF methods for the task of HPSS include the use of constraints such as sparsity of percussive sources along the direction of time [11], structured factorization models that take into account the quasi-stationarity of harmonic sources [12] and extensions of NMF that account for the non-stationarity of percussive components [13,14].…”