Source separation in post-nonlinear mixtures

In this paper, we address the problem of separation of mutually independent sources in nonlinear mixtures. First, we propose theoretical results and p rove that in the general case, it is not possible to separate the sources w ithout nonlinear distortion. Therefore, we focus our work on specific nonli near mixtures known as post-nonlinear mixtures. These mixtures constituted by a linear instantaneous mixture (linear memoryless channel) followed by a n unknown and invertible memoryless nonlinear distortion, are realistic mod els in many situations and emphasize interesting properties i.e., in such n onlinear mixtures, sources can be estimated with the same indeterminacies a s in instantaneous linear mixtures, The separation structure of nonlinear m ixtures is a two-stage system, namely, a nonlinear stage followed by a line ar stage, the parameters of which are updated to minimize an output indepen dence criterion expressed as a mutual information criterion, The minimizati on of this criterion requires knowledge or estimation of source densities o r of their log-derivatives. A first algorithm based on a Gram-Charlier expa nsion of densities is proposed, Unfortunately, it fails for hard nonlinear mixtures. A second algorithm based on an adaptive estimation of the log-der ivative of densities leads to very good performance, even with hard nonline arities. Experiments are proposed to illustrate these results.