A Coordinate Descent Algorithm for Complex Joint Diagonalization Under Hermitian and Transpose Congruences

This paper deals with the problem of joint complex matrix diagonalization by considering both the Hermitian and transpose congruences. We address the general case where the searched diagonalizing matrix is a priori nonunitary. Based on the minimization of a quadratic criterion, we propose a flexible algorithm in the sense that it allows to directly consider a rectangular diagonalizing matrix and to take into consideration both the Hermitian and transpose congruences within the same framework. The proposed algorithm is a coordinate descent algorithm that is based on an approximate criterion leading to the analytical derivation of the minima arguments. Computer simulations are drawn to illustrate the usefulness and performances of the algorithm and a comparison to state-of-the-art algorithms is presented. Finally, an application to independent component analysis based on fourth-order statistics is also presented.