Stochastic and deterministic tensorization for blind signal separation

Abstract

Given an instantaneous mixture of some source signals, the blind signal separation (BSS) problem consists of the identification of both the mixing matrix and the original sources. By itself, it is a non-unique matrix factorization problem, while unique solutions can be obtained by imposing additional assumptions such as statistical independence. By mapping the matrix data to a tensor and by using tensor decompositions afterwards, uniqueness is ensured under certain conditions. Tensor decompositions have been studied thoroughly in literature. We discuss the matrix to tensor step and present tensorization as an important concept on itself, illustrated by a number of stochastic and deterministic tensorization techniques.