Space-time variant blind source separation with additive noise

Abstract

We propose a method for solving linear space-time variant blind source separation (BSS) problem with additive noise, x=As+n, on the "pixel-by-pixel" basis i.e. assuming that unknown mixing matrix is different for every space or time location. Solution corresponds with the isothermal-To equilibrium of the free energy H =U-ToS contrast function where U represents the input/output energy exchange and S represents the Shannon entropy. Solution of the inhomogeneous equation (data model with additive noise) is obtained by augmenting inhomogeneous equation into homogeneous "noise free" equation. Consequently, data model with additive noise can be solved by algorithm for the noise free space-time variant BSS problems, [1],[2]. We demonstrate the algorithm capability to perfectly recover images from the space variant mixture of two images with additive noise. © Springer-Verlag 2004.