Sparse wavelet-based solutions for the M/EEG inverse problem

This paper is concerned with variational and Bayesian approaches to neuro-electromagnetic inverse problems (EEG and MEG). The strong indeterminacy of these problems is tackled by introducing sparsity inducing regularization/priors in a transformed domain, namely a spatial wavelet domain. Sparsity in the wavelet domain allows to reach "data compression" in the cortical sources domain. Spatial wavelets defined on the mesh graph of the triangulated cortical surface are used, in combination with sparse regression techniques, namely LASSO regression or sparse Bayesian learning, to provide localized and compressed estimates for brain activity from sensor data. Numerical results on simulated and real MEG data are provided, which outline the performances of the proposed approach in terms of localization.