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Single-channel audio source separation with NMF: divergences, constraints and algorithms

Cédric Févotte 1, 2 Emmanuel Vincent 3 Alexey Ozerov 4 
1 IRIT-SC - Signal et Communications
IRIT - Institut de recherche en informatique de Toulouse
3 MULTISPEECH - Speech Modeling for Facilitating Oral-Based Communication
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : Spectral decomposition by nonnegative matrix factorisation (NMF) has become state-of-the-art practice in many audio signal processing tasks, such as source separation, enhancement or transcription. This chapter reviews the fundamentals of NMF-based audio decomposition, in unsupervised and informed settings. We formulate NMF as an optimisation problem and discuss the choice of the measure of fit. We present the standard majorisation-minimisation strategy to address optimisation for NMF with common beta-divergence, a family of measures of fit that takes the quadratic cost, the generalised Kullback-Leibler divergence and the Itakura-Saito divergence as special cases. We discuss the reconstruction of time-domain components from the spectral factorisation and present common variants of NMF-based spectral decomposition: supervised and informed settings, regularised versions, temporal models.
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Submitted on : Wednesday, November 8, 2017 - 6:20:11 PM
Last modification on : Monday, July 25, 2022 - 3:44:41 AM
Long-term archiving on: : Friday, February 9, 2018 - 1:21:50 PM


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  • HAL Id : hal-01631185, version 1


Cédric Févotte, Emmanuel Vincent, Alexey Ozerov. Single-channel audio source separation with NMF: divergences, constraints and algorithms. Audio Source Separation, Springer, 2018. ⟨hal-01631185⟩



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