An alternating least-squares algorithm for approximate joint diagonalization and its application to blind source separation

This paper presents an iterative alternating least-squares (ALS) algorithm for alternately solving two different least-squares approximate joint diagonalization (LS-AJD) problems for application to convolutive frequency-domain blind source separation (BSS). The constrained forward-model LS-AJD criterion is minimized to estimate the mixing matrix by using the method of Lagrange multipliers. The other criterion, based on backward modeling, is to find the diagonal matrices by the method of least squares. The method of Lagrange multipliers is well suited for accelerating the convergence of the ALS algorithm. The correlation between the interfrequency power ratios is used to prevent misalignment permutation for the new BSS. Finally, we compare our results with those of conventional BSS in highly reverberant environments.