A generic framework for blind source separation in structured nonlinear models

This paper is concerned with blind source separation in nonlinear models. Special attention is paid to separability issues. Results show that separation is impossible in the general case. However, for specific nonlinear models, the problem becomes tractable. A generic set of parametric nonlinear mixtures is considered: This set has the Lie group structure (a group structure with continuous binary operation). In the parameter set, a definition of a relative gradient is given and is used to design both batch and stochastic algorithms. For the latter, it is shown how a proper use of the relative gradient leads to equivariant adaptive algorithms.