Joint-diagonalization of cumulant tensors and source separation

We extend the results leading the popular JADE and STOTD algorithms to cumulants of any order greater than or equal to three. We first exhibit a new contrast function which constitutes an unified framework for the underlying contrasts of JADE and STOTD which thus appear as particular cases. Then we generalize the link between these new contrasts and a joint-diagonalization criterion. Moreover for the generalized JADE´s contrast, the analytical optimal solution in the case of two sources is derived and shown to keep the same simple expression whatever the cumulant order. Finally, some computer simulations illustrate the potential advantage one can take considering statistics of different orders for the joint-diagonalization of cumulant matrices