Debiased Estimation and Inference for Spatial-Temporal EEG/MEG Source Imaging

The development of accurate electroencephalography (EEG) and magnetoencephalography (MEG) source imaging algorithm is of great importance for functional brain research and non-invasive presurgical evaluation of epilepsy. In practice, the challenge arises from the fact that the number of measurement channels is far less than the number of candidate source locations, rendering the inverse problem ill-posed. A widely used approach is to introduce a regularization term into the objective function, which inevitably biased the estimated amplitudes towards zero, leading to an inaccurate estimation of the estimator's variance. This study proposes a novel debiased EEG/MEG source imaging (DeESI) algorithm for detecting sparse brain activities, which corrects the estimation bias in signal amplitude, dipole orientation and depth. The DeESI extends the idea of group Lasso by incorporating both the matrix Frobenius norm and the L1-norm, which guarantees the estimators are only sparse over sources while maintains smoothness in time and orientation. We also derived variance of the debiased estimators for standardization and hypothesis testing. A fast alternating direction method of multipliers (ADMM) algorithm is proposed for solving the matrix form optimization problem directly without the need for vectorization. The proposed algorithm is compared with eleven existing ESI methods using simulations and an open source EEG dataset whose stimulation locations are known precisely. The DeESI exhibits the best performance in peak localization and amplitude reconstruction.