Improving M/EEG source localization with an inter-condition sparse prior

The inverse problem with distributed dipoles models in M/EEG is strongly ill-posed requiring to set priors on the solution. Most common priors are based on a convenient $\ell_2$ norm. However such methods are known to smear the estimated distribution of cortical currents. In order to provide sparser solutions, other norms than $\ell_2$ have been proposed in the literature, but they often do not pass the test of real data. Here we propose to perform the inverse problem on multiple experimental conditions simultaneously and to constrain the corresponding active regions to be different, while preserving the robust $\ell_2$ prior over space and time. This approach is based on a mixed norm that sets a $\ell_1$ prior between conditions. The optimization is performed with an efficient iterative algorithm able to handle highly sampled distributed models. The method is evaluated on two synthetic datasets reproducing the organization of the primary somatosensory cortex (S1) and the primary visual cortex (V1), and validated with MEG somatosensory data.