Blind source separation of nonlinearly constrained mixed sources using polynomial series reversion

A novel polynomial-based neural network is proposed for nonlinear blind source separation. We focus our research on a recently presented mono-nonlinearity mixture where a linear mixing matrix is slotted into two mutually inverse nonlinearities. In this paper, we generalize the mono-nonlinearity mixing system to the situation where different nonlinearities are applied to the source signals. The theory of Series Reversion is merged with the neural network demixer to perform two layers of mutually inverse nonlinearities. The corresponding parameter learning algorithm for the proposed polynomial-based neural network demixer is also presented. Simulations have been carried out to verify the efficacy of the proposed approach. We demonstrate that the proposed network can successfully recover the original source signals in a blind mode under nonlinear mixing conditions.