Second-order statistics based blind source separation using a bank of subband filters

Abstract

This paper presents a novel approach to blind source separation of narrowband signals in additive either white (i.e., time-uncorrelated) noise or colored (i.e., time-correlated) noise of which the frequencies of its spectral peaks are either known or can be estimated. The main idea behind this approach is that a signal vector can be decomposed into a set of subband signal vectors in order to separate the spectra of the signals of interest from the noise spectra. It is shown that the subband technique can provide an unbiased estimate of the second-order statistics of a noisy observed signal vector. The proposed blind source separation algorithm is developed: (1) by whitening the noisy observed signal vector using the eigenvalue decomposition (EVD) of an unbiased estimate of the zero time-lag correlation matrix computed on the basis of the subband signals; and (2) by applying the joint approximate diagonalization (JAD) on a new proposed set of time-lag correlation matrices of the whitened signal vector. In this set, each correlation matrix of the whitened signal vector at certain time-lag is decomposed into a subset of the correlation matrices between the whitened signal vector and its subband vectors. This is motivated by the capability of separating and then omitting the cross-correlation matrices belonging to the subbands of the colored noise from the set. Simulation results using computer-generated signals, real-world speech and real-world biomedical signals confirm the high efficiency and usefulness of the proposed approach.