  This paper describes heavy-tailed extensions of a state-of-the-art versatile
blind source separation method called fast multichannel nonnegative matrix
factorization (FastMNMF) from a unified point of view. The common way of
deriving such an extension is to replace the multivariate complex Gaussian
distribution in the likelihood function with its heavy-tailed generalization,
e.g., the multivariate complex Student's t and leptokurtic generalized Gaussian
distributions, and tailor-make the corresponding parameter optimization
algorithm. Using a wider class of heavy-tailed distributions called a Gaussian
scale mixture (GSM), i.e., a mixture of Gaussian distributions whose variances
are perturbed by positive random scalars called impulse variables, we propose
GSM-FastMNMF and develop an expectationmaximization algorithm that works even
when the probability density function of the impulse variables have no
analytical expressions. We show that existing heavy-tailed FastMNMF extensions
are instances of GSM-FastMNMF and derive a new instance based on the
generalized hyperbolic distribution that include the normal-inverse Gaussian,
Student's t, and Gaussian distributions as the special cases. Our experiments
show that the normalinverse Gaussian FastMNMF outperforms the state-of-the-art
FastMNMF extensions and ILRMA model in speech enhancement and separation in
terms of the signal-to-distortion ratio.
