Bayesian Multichannel Audio Source Separation Based on Integrated Source and Spatial Models

This paper presents new statistical methods of multichannel audio source separation based on unified source and spatial models that, respectively, represent the generative process of latent source spectrograms and that of observed mixture spectrograms. One possibility of the source model is a factor model based on nonnegative matrix factorization that represents each time-frequency (TF) bin as the weighted sum of basis spectra. Another possibility is a mixture model inspired by latent Dirichlet allocation that exclusively classifies each TF bin into one of basis spectra. Similarly, the spatial model can either be a factor model that represents each TF bin as the weighted sum of source spectra or a mixture model that classifies each bin into one of those spectra. To unify these models in a principled manner and incorporate prior knowledge of a microphone array, we propose hierarchical Bayesian models of all the source-spatial combinations (factor-factor, mixture-factor, factor-mixture, and mixture-mixture models) and derive efficient Gibbs sampling algorithms for posterior inference. Experimental results showed that the proposed unified models outperformed the state-of-the-art method using only the spatial mixture model. Among the four unified models, the spatial factor model tended to work better than the spatial mixture model in exchange for larger computational cost, and the choice of source models had a little impact on the performance and computational cost.