Performance improvement of closed-form joint diagonalizer of non-negative Hermitian matrices

Joint diagonalization of a series of non-negative Hermitian matrices is one of important techniques in the fields of signal processing, such as blind source separation based on second order statistics. In our previous works, we introduced a closed-form solution of a joint diagonalizer of non-negative Hermitian matrices and also proposed a method for improving the performance of the solution for the cases where given series of Hermitian matrices are not jointly diagonalizable strictly. However, the performance of the method may degrade when the number of given Hermitian matrices are comparatively small. In this paper, we propose an improved version of the closed-form joint diagonalizer of given set of Hermitian matrices by increasing the number of Hermitian matrices virtually. Some numerical examples are also shown to verify the efficacy of the proposed method.