Fast nonunitary joint block diagonalization with degenerate solution elimination for convolutive blind source separation

This paper addresses the problem of joint block diagonalization (JBD) of a set of given matrices. As is known that the nonunitary JBD algorithm has some advantages over the existing orthogonal one for convolutive blind source separation (CBSS). However, the nonunitary JBD algorithm is prone to converge to some unexpected degenerate solutions (singular or ill-conditioned solutions). Especially for the matrices of large dimension or the case that the number of the diagonal blocks is relatively large, the performances of the nonunitary JBD algorithm degrade more severely. To eliminate the degenerate solutions, we optimize a penalty term based weighted least-squares criterion and thus develop a fast efficient algorithm. The performance of the proposed algorithm is evaluated by computer simulations and compared with the existing state-of-the-art nonunitary JBD algorithm. The simulation results demonstrate the robustness and performance improvement of the proposed algorithm.