Maximum likelihood source separation: Equivariance and adaptivity.

The present paper addresses several issues regarding the source separation problem. It is first recast a multi-dimensional location-scale model, entailing a specific form of parameterization and a specific notion of gradient because location-scale transformations form a group. Within this framework, we consider off-line and on-line maximum likelihood source separation and show that the group structure suggests a class of effective algorithms enjoying a 'uniform performance' property. The Fisher information matrix is also analyzed and is shown to take a simple form: the natural group parameters are largely uncoupled. Finally, we investigate the achievable performance when both the source distributions and the mixing system are jointly estimated. The analysis shows that estimation of the source distributions affects only marginally the achievable performance, even in a non-parametric framework.