Joint-diagonalizability-constrained multichannel nonnegative matrix factorization based on time-variant multivariate complex sub-Gaussian distribution

Abstract

Multichannel nonnegative matrix factorization (MNMF) is a common blind source separation technique that employs full-rank spatial covariance matrices (SCMs). The full-rank SCMs can simulate reverberant mixing systems where the sources are spatially spread. In conventional MNMF, spectrograms of observed signals are modeled by some types of distribution, e.g., the Gaussian distribution and Student’s t distribution. However, MNMF based on the sub-Gaussian distribution has not been proposed because its cost function is difficult to minimize. In this paper, we address the statistical model extension of MNMF to the sub-Gaussian distribution to improve the source separation accuracy. In the proposed method, the generalized Gaussian distribution is utilized as the sub-Gaussian model. Moreover, to design an auxiliary function for the proposed cost function, we introduce the joint-diagonalizability constraint to SCMs similarly to FastMNMF. Two types of update rule for the proposed MNMF are derived on the basis of the majorization-minimization (MM) and majorization-equalization (ME) algorithms. Since the optimization speed of each parameter affects the source separation performance, we experimentally analyze the best combination of MM- and ME-algorithm-based update rules in the proposed method. Experiments of blind source separation reveal that the proposed MNMF based on the sub-Gaussian model can outperform conventional methods.