Convolutive Blind Source Separation Using an Iterative Least-Squares Algorithm for Non-Orthogonal Approximate Joint Diagonalization

In this paper, we present an approach of recovering signal waveforms of speech sources from observed signals in noisy and reverberant environments. The approach is based on approximate joint diagonalization estimate to provide interference suppression of source signals and reduce echoes and distortions of separated signals. In the proposed approach, the mixing matrix is estimated by minimizing the constrained direct least-squares (LS) criterion in direct model. Exclusively under the condition where the estimated mixing matrix is not of full rank, it is replaced by a full-rank matrix. The unmixing matrix from the estimated mixing matrix is obtained by setting the frequency response of the composite mixing-unmixing filter to identity matrix. The cross-spectral density diagonal matrices of the source signals are precisely estimated by minimizing the indirect LS criterion in indirect model. These operations are fulfilled by using alternating least-squares algorithm. The correlation between the interfrequency power ratios is used to prevent a misalignment permutation of the unmixing matrix. Finally, we compare the proposed BSS with a number of conventional BSS methods in noisy and reverberant environments under both artificial and actual conditions.