Independent component analysis: Jacobi-like diagonalization of optimized composite-order cumulants

In the field of blind source separation, Jacobi-like diagonalization-based approaches constitute an important tool for independent component analysis (ICA). Recently, simultaneous diagonalization of cumulant matrices of third- and fourth-order has been studied by a number of authors. In this work, we present an optimal parametrized composition of these cumulants that puts two classical contrasts, namely, the cumulant-based ICA and the weighted fourth-order contrast in a common framework. It is shown that the optimal weight parameter depends on the a priori statistical knowledge of the original mixing sources. Following the same spirit of the ICA algorithm, we derive the analytical solution for the case of two sources. Finally, a number of computer simulations have been performed to illustrate the behaviour of the Jacobi-like iterations for the maximization of the proposed parametrized contrast.