Algebraic joint zero-diagonalization and blind sources separation

This paper adresses the problem of the joint zero-diagonalization of a given set of matrices. We establish the identifiability conditions of the zero-diagonalizer, and we propose a new algebraical algorithm based on the reformulation of the initial problem into a joint-diagonalization problem. The zero-diagonalizer is not constrained to be unitary. Computer simulations illustrate the behavior of the algorithm. Moreover, as an application, we show that the blind separation of correlated sources can be performed applying this algorithm to a particular set of spatial quadratic time-frequency distribution matrices. In this case, computer simulations are also provided in order to illustrate the performances of the proposed algorithm and to compare it with other existing ones.