Localization properties of an EEG sensor system: Lower bounds and optimality

Most studies concerning the EEG inverse problem focus on the properties of one or another specific inverse solution. Few studies approach the problem of the bounds imposed by the system itself, indifferently of the inversion method used. We are interested in the localization properties of an EEG sensor system using a generic reconstruction procedure in the context of a Brain Computer Interface project. We investigate various perturbations: additive noise, electrode misplacement errors and external sources contributions. The estimation of errors uses the notions of normalized measurements and sensitivity functions in a deterministic framework, but our results closely link to the stochastic CramerRao minimum bound. We propose to modify the system, and more specifically the electrodes configuration, such as to minimize the forecasted errors, thus enhancing the robustness of the system. The configurations obtained through a hybrid Simulated Annealing - Gradient Descent approach show significant improvement when compared to normal setups.