Statistical control for spatio-temporal MEG/EEG source imaging with desparsified mutli-task Lasso

Detecting where and when brain regions activate in a cognitive task or in a given clinical condition is the promise of non-invasive techniques like magnetoencephalography (MEG) or electroencephalography (EEG). This problem, referred to as source localization, or source imaging, poses however a high-dimensional statistical inference challenge. While sparsity promoting regularizations have been proposed to address the regression problem, it remains unclear how to ensure statistical control of false detections in this setting. Moreover, MEG/EEG source imaging requires to work with spatio-temporal data and autocorrelated noise. To deal with this, we adapt the desparsified Lasso estimator ---an estimator tailored for high dimensional linear model that asymptotically follows a Gaussian distribution under sparsity and moderate feature correlation assumptions--- to temporal data corrupted with autocorrelated noise.