Student's t multichannel nonnegative matrix factorization for blind source separation

This paper presents a robust generalization of multichannel nonnegative matrix factorization (MNMF) for blind source separation of mixture audio signals recorded by a microphone array. In conventional MNMF, the complex spectra of observed mixture signals are assumed to be complex Gaussian distributed and are decomposed into the product of the power spectra, temporal activations, and spatial correlation matrices of individual sources in such a way that the complex Gaussian likelihood is maximized. Since the mixture spectra usually include outliers, we propose MNMF based on the complex Student's t likelihood, called t-MNMF, including the original MNMF as a special case. The parameters of t-MNMF can be iteratively optimized with an efficient multiplicative updating algorithm. Experiments showed that t-MNMF with a certain range of degrees of freedom tends to be insensitive to parameter initialization and outperform conventional MNMF.