Nonlinear time varying model identification in ill-posed problems

This work addresses the dynamical inverse problem of EEG source reconstruction by using two main approaches: Dynamic Inverse Problem solution considering Time Varying and Time invariant Constraints, and Weighted Dynamic Inverse Problem solution. Discussed approach of representation comprises two main contributions: Firstly, the introduction of a discrete--time nonlinear model grounded on physiological considerations that explains better the dynamics of the brain neural activity. Secondly, the inclusion of estimation of time varying parameters that allows the enhancement of the nonlinear model, making it suitable for electroencephalographic source localization of such abnormal neuronal activity as epileptic seizures. The estimation that is performed using proposed nonlinear dynamic models with time varying parameters provides an improvement in terms of reconstruction error, if comparing with similar referred linear approximations.