Incorporating anatomical connectivity into EEG source estimation via sparse approximation with cortical graph wavelets

The source estimation problem for EEG consists of estimating cortical activity from measurements of electrical potential on the scalp surface. This is a underconstrained inverse problem as the dimensionality of cortical source currents far exceeds the number of sensors. We develop a novel regularization for this inverse problem which incorporates knowledge of the anatomical connectivity of the brain, measured by diffusion tensor imaging. We construct an overcomplete wavelet frame, termed cortical graph wavelets, by applying the recently developed spectral graph wavelet transform to this anatomical connectivity graph. Our signal model is formed by assuming that the desired cortical currents have a sparse representation in these cortical graph wavelets, which leads to a convex ℓ₁-regularized least squares problem for the coefficients. On data from a simple motor potential experiment, the proposed method shows improvement over the standard minimum-norm regularization.