Fast non-unitary simultaneous diagonalization of third-order tensors

We consider the problem of non-orthogonal joint diagonalization of a set of real-valued third-order tensors. This appears in many signal processing problems and it is instrumental in source separation. We propose a new Jacobi-like algorithm based on a special parameterization of the so-called diagonalizing matrix. One important point is that each Jacobi estimation parameters is done entirely analytically using two different strategies, each one based on an appropriate criterion and an alternate estimation. Numerical simulations illustrate the overall very good performances of the proposed algorithm.