Joint diagonalization of correlation matrices by using Newton methods with application to blind signal separation

The paper addresses the blind signal separation problem in the presence of sensor noise for the case where the source signals are non-stationary and/or non-white. This problem can be formulated as a joint-diagonalization problem where the objective is to jointly diagonalize a set of correlation matrices {R_p}, using a single matrix W. We derive a Newton-type algorithm for two joint-diagonalization cost functions, which are related to the aforementioned blind signal separation problem. To this end, we derive the gradient and also the Hessian of the joint diagonalization cost function in closed form. The most general case is considered, in which the source signals and the unknown mixing matrix are assumed to be complex.