<title>Regularized two-step brain activity reconstruction from spatiotemporal EEG data</title>

We are aiming at using EEG source localization in the framework of a Brain Computer Interface project. We propose here a new reconstruction procedure, targeting source (or equivalently mental task) differentiation. EEG data can be thought of as a collection of time continuous streams from sparse locations. The measured electric potential on one electrode is the result of the superposition of synchronized synaptic activity from sources in all the brain volume. Consequently, the EEG inverse problem is a highly underdetermined (and ill-posed) problem. Moreover, each source contribution is linear with respect to its amplitude but non-linear with respect to its localization and orientation. In order to overcome these drawbacks we propose a novel two-step inversion procedure. The solution is based on a double scale division of the solution space. The first step uses a coarse discretization and has the sole purpose of globally identifying the active regions, via a sparse approximation algorithm. The second step is applied only on the retained regions and makes use of a fine discretization of the space, aiming at detailing the brain activity. The local configuration of sources is recovered using an iterative stochastic estimator with adaptive joint minimum energy and directional consistency constraints