A Simple Nonorthogonal Approximate Joint Diagonalization Algorithm and Its Application for Blind Source Separation

Approximate joint diagonalization (AJD) of a set of matrices is an effective method for the blind source separation (BSS) problem. It is said that the separation performance of nonorthogonal AJD is better than that of orthogonal AJD, so this paper is devoted to designing a novel nonorthogonal AJD criterion. The proposed criterion does not impose any restriction on the diagonalizing matrix, but it can automatically exclude the degenerate solution during the learning iterations. It takes not only the off-diagonal elements but also the diagonal elements of diagonalized matrices into account, so it can achieve better diagonalization results. Simulation experiments are presented to demonstrate the validity of the proposed algorithm.