A Decoupled Jacobi-Like Algorithm for Non-Unitary Joint Diagonalization of Complex-Valued Matrices

We consider the problem of non-orthogonal joint diagonalization of a set of complex matrices. This appears in many signal processing problems and is instrumental in source separation. We propose a new Jacobi-like algorithm based both on a special parameterization of the diagonalizing matrix and on an adapted local criterion. The optimization scheme is based on an alternate estimation of the useful parameters. Numerical simulations illustrate the overall very good performances of the proposed algorithm in comparison to two other Jacobi-like algorithms and to a global algorithm existing in the literature.