Equivalence between Frequency-Domain Blind Source Separation and Frequency-Domain Adaptive Beamforming for Convolutive Mixtures

Shoko Araki,Shoji Makino,Ryo Mukai,Tsuyoki Nishikawa,Hiroshi Saruwatari,Yoichi Hinamoto

doi:10.1155/s1110865703305074

Abstract

Frequency-domain blind source separation (BSS) is shown to be equivalent to two sets of frequency-domain adaptive beamformers (ABFs) under certain conditions. The zero search of the off-diagonal components in the BSS update equation can be viewed as the minimization of the mean square error in the ABFs. The unmixing matrix of the BSS and the filter coefficients of the ABFs converge to the same solution if the two source signals are ideally independent. If they are dependent, this results in a bias for the correct unmixing filter coefficients. Therefore, the performance of the BSS is limited to that of the ABF if the ABF can use exact geometric information. This understanding gives an interpretation of BSS from a physical point of view.

Highlights

Blind source separation (BSS) is an approach for estimating source signals si(t) using only the information on mixed signals xj(t) observed at each input channel
We provide an interpretation of BSS from a physical point of view showing the equivalence between frequency-domain BSS and two sets of frequency-domain adaptive beamformers (ABFs)
BSS removes the sound from the jammer direction and reduces the reverberation of the jammer signal to some extent [21] in the same way as an ABF does. This understanding clearly explains the poor performance of the BSS in a real acoustic environment with a long reverberation

Summary

Introduction

Blind source separation (BSS) is an approach for estimating source signals si(t) using only the information on mixed signals xj(t) observed at each input channel. BSS can be applied to achieve noise-robust speech recognition and high-quality hands-free telecommunication. It might become one of the cues for auditory scene analysis. Several methods have been proposed for BSS of convolutive mixtures [1, 2]. EURASIP Journal on Applied Signal Processing transform the problem into the frequency domain to solve an instantaneous BSS problem for every frequency simultaneously [6, 7]. We consider the BSS of convolutive mixtures of speech in the frequency domain

Objectives

Methods

Conclusion