Structured Sparsity Regularization Approach to the EEG Inverse Problem

Localization of brain activity involves solving the EEG inverse problem, which is an undetermined ill-posed problem. We propose a novel approach consisting in estimating, using structured sparsity regularization techniques, the Brain Electrical Sources (BES) matrix directly in the spatio-temporal source space. We use proximal splitting optimization methods, which are efficient optimization techniques, with good convergence rates and with the ability to handle large nonsmooth convex problems, which is the typical scenario in the EEG inverse problem. We have evaluated our approach under a simulated scenario, consisting in estimating a synthetic BES matrix with 5124 sources. We report results using ℓ1 (LASSO), ℓ1/ℓ2 (Group LASSO) and ℓ1 + ℓ1/ℓ2 (Sparse Group LASSO) regularizers.