Multi-subject MEG/EEG source imaging with sparse multi-task regression.

Magnetoencephalography and electroencephalography (M/EEG) are non-invasive modalities that measure the weak electromagnetic fields generated by neural activity. Estimating the location and magnitude of the current sources that generated these electromagnetic fields is an inverse problem. Although it can be cast as a linear regression, this problem is severely ill-posed as the number of observations, which equals the number of sensors, is small. When considering a group study, a common approach consists in carrying out the regression tasks independently for each subject using techniques such as MNE or sLORETA. An alternative is to jointly localize sources for all subjects taken together, while enforcing some similarity between them. By pooling S subjects in a single joint regression, the number of observations is S times larger, potentially making the problem better posed and offering the ability to identify more sources with greater precision. Here we show how the coupling of the different regression problems can be done through a multi-task regularization that promotes focal source estimates. To take into account intersubject variabilities, we propose the Minimum Wasserstein Estimates (MWE). Thanks to a new joint regression method based on optimal transport (OT) metrics, MWE does not enforce perfect overlap of activation foci for all subjects but rather promotes spatial proximity on the cortical mantle. Besides, by estimating the noise level of each subject, MWE copes with the subject-specific signal-to-noise ratios with only one regularization parameter. On realistic simulations, MWE decreases the localization error by up to 4 ​mm per source compared to individual solutions. Experiments on the Cam-CAN dataset show improvements in spatial specificity in population imaging compared to individual models such as dSPM as well as a state-of-the-art Bayesian group level model. Our analysis of a multimodal dataset shows how multi-subject source localization reduces the gap between MEG and fMRI for brain mapping.