Solving the MEG Inverse Problem: A Robust Two-Way Regularization Method

Magnetoencephalography (MEG) is a common noninvasive imaging modality for instantly measuring whole brain activities. One challenge in MEG data analysis is how to minimize the impact of the outliers that commonly exist in the images. In this article, we propose a robust two-way regularization approach to solve the important MEG inverse problem, that is, reconstructing neuronal activities using the measured MEG signals. The proposed method is based on the distributed source model and produces a spatio-temporal solution for all the dipoles simultaneously. Unlike the traditional methods that use the squared error loss function, our proposal uses a robust loss function, which improves the robustness of the results against outliers. To impose desirable spatial focality and temporal smoothness, we then penalize the robust loss through appropriate spatial-temporal two-way regularization. Furthermore, an alternating reweighted least-squares algorithm is developed to optimize the penalized model fitting criterion. Extensive simulation studies and a real-world MEG study clearly demonstrate the advantages of the proposed method over three nonrobust methods.