A comparative study of approximate joint diagonalization algorithms for blind source separation in presence of additive noise

A comparative study of approximate joint diagonalization algorithms of a set of matrices is presented. Using a weighted least-squares criterion, without the orthogonality constraint, an algorithm is compared with an analoguous one for blind'source separation (BSS). The criterion of the present algorithm is on the separating matrix while the other is on the mixing matrix. The convergence of the 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 and when the mixing matrix is not close to an orthogonal matrix.