EEG extended source imaging with structured sparsity and L1-norm residual

It is a long-standing challenge to reconstruct the locations and extents of cortical neural activities from electroencephalogram (EEG) recordings, especially when the EEG signals contain strong background activities and outlier artifacts. In this work, we propose a robust source imaging method called L1R-SSSI. To alleviate the effect of outliers in EEG, L1R-SSSI employs the L-1-loss to model the residual error. To obtain locally smooth and globally sparse estimations, L1R-SSSI adopts the structured sparsity constraint, which incorporates the L-1-norm regularization in both the variation and original source domain. The estimations of L1R-SSSI are efficiently obtained using the alternating direction method of multipliers (ADMM) algorithm. Results of simulated and experimental data analysis demonstrate that L1R-SSSI effectively suppresses the effect of the outlier artifacts in EEG. L1R-SSSI outperforms the traditional L-2-norm-based methods (e.g., wMNE, LORETA), and SISSY, which employs L-2-norm loss and structured sparsity, indicated by the larger AUC (average AUC > 0.80), smaller SD (average SD <50 mm), DLE (average DLE <10 mm) and RMSE (average RMSE <1.75) values under all the numerically simulated conditions. L1R-SSSI also provides better estimations of extended sources than the method with L-1-loss and L-p-norm regularization term (e.g., LAPPS).