Blind separation of a class of nonlinear ICA models

In this paper we consider a class of nonlinear ICA models that may be described using the addition theorem (AT). Such models cover a wide variety of nonlinear systems of interest in engineering applications. In general, some nonlinear distortions always remain after performing signal separation using such models. In this paper we find a class of AT models, i.e. nonlinear mixing systems, that may be separated up to conventional scaling ambiguity. A theorem proving the separability is provided as well. A connection between AT models and commonly-used post-nonlinear (PNL) models is established. Furthermore, we extend the proposed AT models to a more general case where the functional form of nonlinearity is parameterized and consider the separability of such systems as well.