Investigations on contrast functions for blind source separation based on non-Gaussianity and sparsity measures

Abstract

In this paper, we provide a systematic method to construct contrast functions through the use of sub- or super- additive functionals. The used sub- or super-additive functionals are applied to the distributions of the extracted sources to quantify the degree of non-Gaussianity or sparsity. In this work, we assume a completely blind scenario where one knows only the observations and the existence of at most one Gaussian independent component in the mixture. However, there is no a priori information about the mixing matrix nor about the source density. Some practical examples of useful contrast functions are introduced and discussed in order to illustrate the usefulness of the proposed approach.