Source separation in structured nonlinear models

This paper discusses several issues related to blind source separation in nonlinear models. Specifically, separability results show that separation in the general case is impossible, however, for specific nonlinear models the problem does have a solution. A specific set of parametric nonlinear mixtures is considered; this set has the Lie group structure. In the parameter set, a group operation is defined and a relative gradient is defined. The latter is applied to design stochastic algorithms for which the equivariance property is shown.