A Joint Diagonalization Based Efficient Approach to Underdetermined Blind Audio Source Separation Using the Multichannel Wiener Filter

01/21/2021
by   Nobutaka Ito, et al.
0

This paper presents a computationally efficient approach to blind source separation (BSS) of audio signals, applicable even when there are more sources than microphones (i.e., the underdetermined case). When there are as many sources as microphones (i.e., the determined case), BSS can be performed computationally efficiently by independent component analysis (ICA). Unfortunately, however, ICA is basically inapplicable to the underdetermined case. Another BSS approach using the multichannel Wiener filter (MWF) is applicable even to this case, and encompasses full-rank spatial covariance analysis (FCA) and multichannel non-negative matrix factorization (MNMF). However, these methods require massive numbers of matrix inversions to design the MWF, and are thus computationally inefficient. To overcome this drawback, we exploit the well-known property of diagonal matrices that matrix inversion amounts to mere inversion of the diagonal elements and can thus be performed computationally efficiently. This makes it possible to drastically reduce the computational cost of the above matrix inversions based on a joint diagonalization (JD) idea, leading to computationally efficient BSS. Specifically, we restrict the N spatial covariance matrices (SCMs) of all N sources to a class of (exactly) jointly diagonalizable matrices. Based on this approach, we present FastFCA, a computationally efficient extension of FCA. We also present a unified framework for underdetermined and determined audio BSS, which highlights a theoretical connection between FastFCA and other methods. Moreover, we reveal that FastFCA can be regarded as a regularized version of approximate joint diagonalization (AJD).

READ FULL TEXT

page 1

page 10

research
02/03/2020

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

In this paper, we address a convolutive blind source separation (BSS) pr...
research
02/12/2021

Joint Dereverberation and Separation with Iterative Source Steering

We propose a new algorithm for joint dereverberation and blind source se...
research
05/24/2018

FastFCA-AS: Joint Diagonalization Based Acceleration of Full-Rank Spatial Covariance Analysis for Separating Any Number of Sources

Here we propose FastFCA-AS, an accelerated algorithm for Full-rank spati...
research
06/28/2014

Convex Analysis of Mixtures for Separating Non-negative Well-grounded Sources

Blind Source Separation (BSS) has proven to be a powerful tool for the a...
research
04/29/2020

Determined BSS based on time-frequency masking and its application to harmonic vector analysis

When the number of microphones is equal to that of the source signals (t...
research
05/20/2020

Consistent ICA: Determined BSS meets spectrogram consistency

Multichannel audio blind source separation (BSS) in the determined situa...
research
12/03/2013

Generalized Non-orthogonal Joint Diagonalization with LU Decomposition and Successive Rotations

Non-orthogonal joint diagonalization (NJD) free of prewhitening has been...

Please sign up or login with your details

Forgot password? Click here to reset