The nonlinear blind source separation (BSS) problem is a challenging research topic and, differently from the linear case, its development has not reached a general separation framework. Among the reported nonlinear models, we highlight two instances that are crucial for the present project: (i) post-nonlinear (PNL) mixtures and (ii) contexts of separation of colored sources using signal derivatives. In the former case, the assumption of mutual independence among sources can be suitable for solving the PNL problem, but the employment of criteria solely based on independence constrains the nonlinearities to be bijective. Hence, there emerges as an interesting possibility the use of other statistics, such as spatial and/or temporal dependencies, for the adoption of a larger set of nonlinear separation functions. For the second approach, if temporally colored sources are assumed, by computing derivatives of the mixtures, the nonlinear mixing process becomes linear and instantaneous, but time-varying. In that sense, by modeling the probability density function of the derivatives of the sources, a more robust criterion based on the matching of distributions can be applied. The project is intended to be developed at GIPSA-Lab, Grenoble, France, under the supervision of Prof. Christian Jutten, a pioneer in the linear and nonlinear BSS problems.
News published in Agência FAPESP Newsletter about the scholarship: