Equivalent brain source localization exploiting the proper orthogonal decomposition of EEG

A method for the equivalent brain source localization from EEG measured data is proposed herein exploiting the combined advantages of Proper Orthogonal Decomposition (POD) and Finite Element Method (FEM). The current effort is concentrated on solving a fine discretized forward eigenproblem once and applying POD to reduce the problem dimension. The equivalent brain source localization is in turn formulated by setting up a cost function in its least squares means. The involved calculated data sets as well as the sensitivity matrix are evaluated herein exploiting a POD eigenfunction expansion. Explicitly, for each forward problem solution the voltage within a small volume enclosing the source is expressed using FEM, while for the remaining larger volume a POD eigenfunction is adopted. The continuity of the two solutions is enforced following a Dirichlet-to-Neumann map formalism. The proposed method is expected to offer a computationally efficient forward and overally inverse problem solution.