Nonlinear blind source separation for sparse sources

Blind Source Separation (BSS) is the problem of separating signals which are mixed through an unknown function from a number of observations, without any information about the mixing model. Although it has been mathematically proven that the separation can be done when the mixture is linear, there is not any proof for the separability of nonlinearly mixed signals. Our contribution in this paper is performing nonlinear BSS for sparse sources. It is shown in this case, sources are separable even if the problem is under-determined (the number of observations is less than the number of source signals). However in the most general case (when the nonlinear mixing model can be of any kind and there is no side-information about that), an unknown nonlinear transformation of each source is reconstructed. It is shown why the problem reconstructing the exact sources is severely ill-posed and impossible to do without any other information.