Source localization with MEG data: A beamforming approach based on covariance thresholding

Reconstructing neural activities using non-invasive sensor arrays outside the brain is an ill-posed inverse problem since the observed sensor measurements could result from an infinite number of possible neuronal sources. The sensor covariance-based beamformer mapping represents a popular and simple solution to the above problem. In this article, we propose a family of beamformers by using covariance thresholding. A general theory is developed on how their spatial and temporal dimensions determine their performance. Conditions are provided for the convergence rate of the associated beamformer estimation. The implications of the theory are illustrated by simulations and a real data analysis.