Abstract

The Blind Source Separation (BSS) problem is defined by a mixture model, a set of source processes, and a set of assumptions. Various types of mixture can be considered, such as instantaneous linear mixtures, convolutive mixtures, or nonlinear mixtures. This chapter proposes several contrast criteria, well matched to various BSS problems. The definition of contrast criteria is based on a noiseless observation model, since no statistical modeling of the noise is supposed to be available. In the real world, blind source estimation and blind mixture identification will be performed in the presence of noise. On the other hand, if statistical properties of noise and sources were known, then it would be preferred to resort to the maximum likelihood criterion. Contrast criteria can be defined, and allow one to separate convolutive mixtures via joint (possibly approximate) diagonalization of a set of matrices or tensors. In order to obtain a criterion corresponding to the joint (approximate) diagonalization of several matrices, one must write the criterion in an efficient manner.

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