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Complex ISNMF: a phase-aware model for monaural audio source separation

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Original languageEnglish
Pages (from-to)20-31
Number of pages12
JournalIEEE/ACM Transactions on Audio Speech and Language Processing
Issue number1
Publication statusPublished - 10 Oct 2018
Publication typeA1 Journal article-refereed


This paper introduces a phase-aware probabilistic model for audio source separation. Classical source models in the short-term Fourier transform domain use circularly-symmetric Gaussian or Poisson random variables. This is equivalent to assuming that the phase of each source is uniformly distributed, which is not suitable for exploiting the underlying structure of the phase. Drawing on preliminary works, we introduce here a Bayesian anisotropic Gaussian source model in which the phase is no longer uniform. Such a model permits us to favor a phase value that originates from a signal model through a Markov chain prior structure. The variance of the latent variables are structured with nonnegative matrix factorization (NMF). The resulting model is called complex Itakura-Saito NMF (ISNMF) since it generalizes the ISNMF model to the case of non-isotropic variables. It combines the advantages of ISNMF, which uses a distortion measure adapted to audio and yields a set of estimates which preserve the overall energy of the mixture, and of complex NMF, which enables one to account for some phase constraints. We derive a generalized expectation-maximization algorithm to estimate the model parameters. Experiments conducted on a musical source separation task in a semi-informed setting show that the proposed approach outperforms state-of-the-art phase-aware separation techniques.

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