Handbook of Blind Source Separation

Chapter 4

Likelihood

J.-F. Cardoso

This chapter is devoted to studying instantaneous mixtures of independent components. It is not intended to cover all existing methods described in the literature; rather, it focuses on elucidating the main statistical aspects of the problem by carefully analyzing the structure of the likelihood.

We examine successively three basic features of the ICA model: first, the idea of linear mixture which is associated with the equivariance property; second, the assumption of independence between components which, together with equivariance, determines the statistical structure of ICA; third, the specific models which can be designed for approximating the probability distribution of each component.

Each one of these three ...