A new non-orthogonal approximate joint diagonalization algorithm for blind source separation

A new algorithm for approximate joint diagonalization of a set of matrices is presented. Using a weighted leastsquares (WLS) criterion, without the orthogonality constraint, it is compared with an analoguous algorithm for blind source separation (BSS). The criterion of our algorithm is on the separating matrix while the other is on the mixing matrix. The convergence of our algorithm is proved under some mild assumptions. The performances of the two algorithms are compared with usual standard algorithms using BSS simulations results. We show that the improvement in estimating the separating matrix, resulting from the relaxation of the orthogonality restriction, can be achieved in presence of additive noise when the length of observed sequences is sufficiently large.