An information theoretic approach to a novel nonlinear independent component analysis paradigm

This paper introduces a novel independent component analysis (ICA) approach to the separation of nonlinear convolutive mixtures. The proposed model is an extension of the well-known post nonlinear (PNL) mixing model and consists of the convolutive mixing of PNL mixtures. Theoretical proof of existence and uniqueness of the solution under proper assumptions is provided. Feedforward and recurrent demixing architectures based on spline neurons are introduced and compared. Source separation is performed by minimizing the mutual information of the output signals with respect to the network parameters. More specifically, the proposed architectures perform on-line nonlinear compensation and score function estimation by proper use of flexible spline nonlinearities, yielding a significant performance improvement in terms of source pdf matching and algorithm speed of convergence. Experimental tests on different signals are described to demonstrate the effectiveness of the proposed approach.