Joint Separation and Dereverberation of Reverberant Mixtures with Determined Multichannel Non-Negative Matrix Factorization

Abstract

This paper proposes an extension of multichannel non-negative matrix factorization (MNMF) that simultaneously solves source separation and dereverberation. While MNMF was originally formulated under an underdetermined problem setting where sources can outnumber microphones, a determined counterpart of MNMF, which we call the determined MNMF (DMNMF), has recently been proposed with notable success. This approach is particularly notable in that the optimization process can be more than 30 times faster than the underdetermined version owing to the fact that it involves no matrix inversion computations. One drawback as regards all methods based on instantaneous mixture models, including MNMF, is that they are weak against long reverberation. To overcome this drawback, this paper proposes an extension of DMNMF using a frequency-domain convolutive mixture model. The optimization process of the proposed method consists of iteratively updating (i) the spectral parameters of each source using the majorization-minimization algorithm, (ii) the separation matrix using iterative projection, and (iii) the dereverberation filters using multichannel linear prediction. Experimental results showed that the proposed method yielded higher separation performance and dereverberation performance than the baseline method under highly reverberant environments.