Under-determined reverberant audio source separation using Bayesian Non-negative Matrix Factorization

Abstract

In this paper, we address the task of audio source separation for a stereo reverberant mixture of audio signals. We use a full-rank model for the spatial covariance matrix. Bayesian Non-negative Matrix Factorization(NMF)frameworks are introduced for factorizing the time-frequency variance matrix of each source into basis components and time activations. We also propose to incorporate the temporal dependencies in the Bayesian model through (1) recursively updating the prior hyperparameters or (2) applying a prior with Markov chain structure to favor the smoothness of the solution and we compare the performance of these two schemes. The EM algorithm is applied to derive the update relations of the unknown parameters. The separation performance improvement over the non-Bayesian standard NMF method as well as the conventional full-rank unconstrained method are investigated by calculating objective separation evaluation metrics.