Thin QR and SVD factorizations for simultaneous blind signal extraction

This paper studies the problem of the simultaneous blind signal extraction of a subset of independent components from a linear mixture. In order to solve it in a robust manner, we consider the optimization of contrast functions that jointly exploit the information provided by several cumulant tensors of the observations. We develop hierarchical and simultaneous ICA extraction algorithms that are able to optimize the proposed contrast functions. These algorithms are based on the thin-QR and thin-SVD factorizations of a matrix of weighted cross-statistics between the observations and outputs. Simulations illustrate the good performance of the proposed methods.