Blind identification of under-determined mixtures based on the characteristic function: influence of the knowledge of source PDF's

Abstract

When the number of inputs (sources) is larger than the number of outputs (observations), linear mixtures are referred to as Under-Determined (UDM). The algorithms proposed here aim at identifying UDM using the second characteristic function (c.f.) of observations, without any need of sparsity assumption on sources, but assuming their statistical independence. The first algorithm, already proposed by the authors in P. Comon and M. Rajih (2005), assumes that the source c.f.'s are unknown. In this paper, a variant of the algorithm is described, which allows to take into account the knowledge of source c.f.'s. Performances of both algorithms are compared based on computer simulations