Source Separation in Nonlinear Mixtures: How and Why?
Résumé
The problem of source separation has been addressed mainly for linear mixtures, either memoryless or convolutive. Methods for solving the problem are based on source assumptions like statistical independence (ICA), time properties (coloration or nonstationarity), positivity or sparsity. However, although linearity is very often a convenient approximation, there are some applications in which the mixing process is clearly nonlinear. In this talk, in a first part, we explain what are the main problems encountered by source separation in nonlinear mixtures and how they can be overcome. Then, in a second part, we will consider actual strongly nonlinear problems: one in image processing and another one in chemical sensor array processing. For each problem, we will derive the nonlinear models, show how source separation can be applied and experiment results which can be achieved.