Fast Multichannel Correlated Tensor Factorization for Blind Source Separation
Kazuyoshi Yoshii, Kouhei Sekiguchi, Yoshiaki Bando, Mathieu Fontaine, Aditya Arie Nugraha · 2020
This paper describes an ultimate covariance-aware multichannel extension of nonnegative matrix factorization (NMF) for blind source separation (BSS). A typical approach to BSS is to integrate a low-rank source model with a full-rank spatial model as multichannel NMF (MNMF) based on full-rank spatial covariance matrices (CMs) or its efficient version named FastMNMF based on jointly-diagonalizable spatial CMs do. The NMF-based phase-unaware source model, however, can deal with only the positive cooccurrence relations between time-frequency bins. To overcome this limitation, we propose an efficient multichannel extension of correlated tensor factorization (CTF) named FastMCTF based on jointly-diagonalizable temporal, frequency, and spatial CMs. Integration of the jointly-diagonalizable full-rank source model proposed by FastCTF with the jointly-diagonalizable full-rank spatial model proposed by FastMNMF enables us to completely consider the positive and negative covariance relations between frequency bins, time frames, and channels. We derive a convergence-guaranteed parameter estimation algorithm based on the multiplicative update and iterative projection and experimentally show the potential of the proposed method.