Unsupervised Robust Speech Enhancement Based on Alpha-Stable Fast Multichannel Nonnegative Matrix Factorization

This paper describes multichannel speech enhancement based on a probabilistic model of complex source spectrograms for improving the intelligibility of speech corrupted by undesired noise. The univariate complex Gaussian model with the reproductive property supports the additivity of source complex spectrograms and forms the theoretical basis of nonnegative matrix factorization (NMF). Multichannel NMF (MNMF) is an extension of NMF based on the multivariate complex Gaussian model with spatial covariance matrices (SCMs), and its state-of-the-art variant called FastMNMF with jointly-diagonalizable SCMs achieves faster decomposition based on the univariate Gaussian model in the transformed domain where all time-frequency-channel elements are independent. Although a heavy-tailed extension of FastMNMF has been proposed to improve the robustness against impulsive noise, the source additivity has never been considered. The multivariate α-stable distribution does not have the reproductive property for the shape matrix parameter. This paper, therefore, proposes a heavy-tailed extension called α-stable FastMNMF which works in the transformed domain to use a univariate complex α-stable model, satisfying the reproductive property for any tail lightness parameter α and allowing the α-fractional Wiener filtering based on the element-wise source additivity. The experimental results show that α-stable FastMNMF with α = 1.8 significantly outperforms Gaussian FastMNMF (α=2).