Soft/hard focalization in the EEG inverse problem

We present in this paper a novel statistical based focalized reconstruction method for the underdetermined EEG (electroencephalogram) inverse problem. The algorithm is based on the representation of non-Gaussian distributions as an infinite mixture of Gaussians (IMG) and relies on an iterative procedure consisting out of alternated variance estimation/linear inversion operations. By taking into account noise statistics, it performs implicit spurious data rejection and produces robust focalized solutions allowing for straightforward discrimination of active/non-active brain regions. We apply the proposed reconstruction procedure to average evoked potentials EEG data and compare the reconstruction results with the corresponding known physiological responses