Generalized Fast Multichannel Nonnegative Matrix Factorization Based on Gaussian Scale Mixtures for Blind Source Separation

TL;DR

This paper introduces a generalized heavy-tailed extension of FastMNMF using Gaussian scale mixtures, improving blind source separation performance in speech tasks.

Contribution

It proposes GSM-FastMNMF, a unified framework that encompasses existing heavy-tailed FastMNMF variants and introduces a new instance based on the generalized hyperbolic distribution.

Findings

Normal-inverse Gaussian FastMNMF outperforms existing methods.

The framework unifies various heavy-tailed distributions under one model.

Experiments show improved speech separation and enhancement results.

Abstract

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.