INTRODUCTION

Over the past few years, the development of multi-channel sensors has motivated interest in methods for the coherent processing of multivariate data. Areas of application include biomedical engineering, medical imaging, speech processing, astronomical imaging, remote sensing, communication systems, seismology, geophysics, econometrics.

Consider a situation where there is a collection of signals emitted by some physical objects or sources. These physical sources could be, for example, different brain areas emitting electrical signals; people speaking in the same room (the classical cocktail party problem), thus emitting speech signals; or radiation sources emitting their electromagnetic waves. Assume further that there are several sensors or receivers. These sensors are in different positions, so that each records a mixture of the original source signals with different weights. It is assumed that the mixing weights are unknown, since knowledge of that entails knowing all the properties of the physical mixing system, which is not accessible in general. Of course, the source signals are unknown as well, since the primary problem is that they cannot be recorded directly. The blind source separation (BSS) problem is to find the original signals from their observed mixtures, without prior knowledge of the mixing weights, and by knowing very little about the original sources. In the classical example of the cocktail party, the BSS problem amounts to recovering the voices of the different speakers, from the mixtures recorded at several microphones.

There has been much recent research activity on BSS. Some specific issues have already been addressed using a blend of heuristic ideas and rigorous derivations. This is testified to by the extensive literature on the subject. As clearly emphasized by previous work, it is fundamental that the sources to be retrieved present some quantitatively measurable diversity (e.g. decorrelation, independence, morphological diversity, etc.). Recently, sparsity and morphological diversity have emerged as a novel and effective source of diversity for BSS.