Fast Multichannel Source Separation Based on Jointly Diagonalizable Spatial Covariance Matrices

Abstract

This paper describes a versatile method that accelerates multichannel source separation methods based on full-rank spatial modeling. A popular approach to multichannel source separation is to integrate a spatial model with a source model for estimating the spatial covariance matrices (SCMs) and power spectral densities (PSDs) of each sound source in the time-frequency domain. One of the most successful examples of this approach is multichannel nonnegative matrix factorization (MNMF) based on a full-rank spatial model and a low-rank source model. MNMF, however, is computationally expensive and often works poorly due to the difficulty of estimating the unconstrained full-rank SCMs. Instead of restricting the SCMs to rank-1 matrices with the severe loss of the spatial modeling ability as in independent low-rank matrix analysis (ILRMA), we restrict the SCMs of each frequency bin to jointly-diagonalizable but still full-rank matrices. For such a fast version of MNMF, we propose a computationally-efficient and convergence-guaranteed algorithm that is similar in form to that of ILRMA. Similarly, we propose a fast version of a stateof-the-art speech enhancement method based on a deep speech model and a low-rank noise model. Experimental results showed that the fast versions of MNMF and the deep speech enhancement method were several times faster and performed even better than the original versions of those methods, respectively.

Fast Multichannel Nonnegative Matrix Factorization With Directivity-Aware Jointly-Diagonalizable Spatial Covariance Matrices for Blind Source Separation

“…Several studies have been proposed to restrict the SCMs of sources to JD yet full-rank matrices for multichannel BSS. Ito and Nakatani proposed a fast version of FCA called Fast-FCA [28], [29] and then proposed a fast version of MNMF called FastMNMF1 [20] independently and concurrently with our work [19]. To estimate a non-singular matrix called diagonalizer used for jointly diagonalizing the SCMs of sources at each frequency bin, we used a convergence-guaranteed IP method as in FastCTF [37], while a fixed point iteration (FPI) method without convergence guarantee was used in [20].…”

“…As an intermediate (over)determined (M ≥ N ) BSS method between MNMF and ILRMA, we proposed a computationallyefficient variant of MNMF called FastMNMF1 that restricts all source SCMs of each frequency bin to jointly-diagonalizable (JD) yet full-rank matrices [19]. Note that another FastMNMF1 based on the same formulation had been developed independently and concurrently [20].…”

Regularized Fast Multichannel Nonnegative Matrix Factorization with ILRMA-Based Prior Distribution of Joint-Diagonalization Process

“…Details of these update rules are described in [7]. [13,19] In convolutive BSS, the frequency-domain instantaneous mixing process is translated into a model using a rank-1 spatial covariance matrix aina H in for each source. In this case, the observed signal xij is modeled as follows:…”

Efficient Full-Rank Spatial Covariance Estimation Using Independent Low-Rank Matrix Analysis for Blind Source Separation

“…To confirm the efficacy of the proposed method, we conducted a BSS experiment using a simulated mixture of a target speech source and diffuse noise. We compared seven methods, namely, ILRMA [5], BSSA [19], the original MNMF [11], MNMF initialized by ILRMA (ILRMA+MNMF) [5], [15], the original FastMNMF [14], FastMNMF initialized by ILRMA (ILRMA+FastMNMF), and the proposed method (α = 0.7 and β = 10 −16 were selected experimentally). In ILRMA, the observation x ij was preprocessed via a sphering transformation using PCA.…”