Using Taylor Series Expansions and Second-Order Statistics for Blind Source Separation in Post-Nonlinear Mixtures

Abstract

In the context of Post-Nonlinear (PNL) mixtures, source separation based on Second-Order Statistics (SOS) is a challenging topic due to the inherent difficulties when dealing with nonlinear transformations. Under the assumption that sources are temporally colored, the existing SOS-inspired methods require the use of Higher-Order Statistics (HOS) as a complement in certain stages of PNL demixing. However, a recent study has shown that the sole use of SOS is sufficient for separation if certain constraints on the separation system are obeyed. In this paper, we propose the use of a PNL separating model based on constrained Taylor series expansions which is able to satisfy the requirements that allow a successful SOS-based source separation. The simulation results corroborate the proposal effectiveness.