Cerebral current ?ows are directly related to information transfer in the brain and thus an excellent means for studying the mechanisms of cogni- tive processing. Electro- and Magneto-encephalography, EEG and MEG, are noninvasive measures of these electric currents (EEG) or their respec- tive accompanying magnetic ?elds (MEG). The reconstruction of the cere- bral current density from EEG/MEG measurements is an ill-posed inverse problem. As the forward mapping from the current sources to the external sensors is linear, the inverse problem may be formulated as a highly un- der determined linear system of equations, which has no unique solution. The common strategy to deal with this ambiguity is regularization, i.e. ?t- ting the data with an additional penalization of the sources. Both l2-norm and l1-norm based penalties have been proposed based on the neurophys- iologically motivated assumptions of smoothness and sparsity, respectively.