Recurrent networks for separating extractable-target nonlinear mixtures. Part II. Blind configurations

While most reported blind source separation methods concern linear mixtures, we here address the nonlinear case. In the first part of this paper, we introduced a general class of nonlinear mixtures which can be inverted using recurrent networks. That part was focused on separating structures themselves and therefore on the non-blind configuration, whereas the current paper addresses the estimation of the parameters of this large class of structures in a blind context. We propose a maximum likelihood approach to this end. The main advantage of this approach is that it exploits the knowledge of the parametric model of mixing transformation in the separation procedure while its implementation does not require the knowledge of the explicit inverse of the model because the separating structure can be designed using a recurrent network. In particular, we illustrate in detail the proposed approach for a linear-quadratic mixture by using an extended recurrent network with self-feedback parameters which guarantee its local stability. Simulation results show the very good performance of the proposed algorithm.

► We propose a maximum likelihood approach for blindly separating a general class of nonlinear mixtures.
► Our approach exploits the knowledge of the parametric model of mixing transformation in the separation procedure.
► The implementation of our approach does not require the knowledge of the explicit inverse of the mixing model.
► We use an extended recurrent network as separating structure.
► We illustrate in detail the proposed approach for a linear-quadratic mixture.