Jacobi like algorithm for non-orthogonal joint diagonalization of hermitian matrices

In this paper, we consider the problem of non-orthogonal joint diagonalization of a set of hermitian matrices. This appears in many blind signal processing problems as source separation and independent component analysis. We propose a new Jacobi like algorithm based on a LU decomposition. The main point consists of the analytical derivation of the elementary two by two matrix. In order to determine the diagonalizing matrix parameters, we propose a useful approximation. Numerical simulations illustrate the overall good performances of the proposed algorithm in comparison to two other Jacobi like algorithms existing in the literature.