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

•The task of audio source separation for an underdetermined mixture of audio signals in a reverberant environment is addressed.•Two Bayesian NMF frameworks are proposed to factorize the source variance matrix in the full-rank model for the purpose of providing a more powerful model.•Temporal dependencies are taken into account via choosing suitable prior structures.•The performance improvement over other conventional methods has been shown through calculating BSS evaluation metrics in reverberant conditions.

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.