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

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.
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https://hal.telecom-paris.fr/hal-03657196
Contributor : Mathieu Fontaine Connect in order to contact the contributor
Submitted on : Monday, May 9, 2022 - 1:57:31 PM
Last modification on : Thursday, May 12, 2022 - 3:40:36 AM

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Mathieu Fontaine, Kouhei Sekiguchi, Aditya Nugraha, yoshiaki Bando, Kazuyoshi yoshii. Generalized Fast Multichannel Nonnegative Matrix Factorization Based on Gaussian Scale Mixtures for Blind Source Separation. IEEE/ACM Transactions on Audio, Speech and Language Processing, Institute of Electrical and Electronics Engineers, 2022, pp.1-1. ⟨10.1109/TASLP.2022.3172631⟩. ⟨hal-03657196⟩

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