Imaging EEG Extended Sources Based on Variation Sparsity with L1-norm Residual

Reconstructing the locations and extents of cortical activities accurately from EEG signals plays an important role in neuroscience research and clinical surgeries. However, due to the ill-posed nature of EEG source imaging problem, there exist no unique solutions for the measured EEG signals. Additionally, evoked EEG is inevitably contaminated by strong background activities and outliers caused by ocular or head movements during recordings. To handle these outliers and reconstruct extended brain sources, in this paper, we have proposed a robust EEG source imaging method, namely \({L_1}\)-norm Residual Variation Sparse Source Imaging (\(L_1\)R-VSSI). \(L_1\)R-VSSI employs the \(L_1\)-loss for the residual error to alleviate the outliers. Additionally, the \(L_1\)-norm constraint in the variation domain of sources is implemented to achieve globally sparse and locally smooth solutions. The solutions of \(L_1\)R-VSSI is obtained by the alternating direction method of multipliers (ADMM) algorithm. Results on both simulated and experimental EEG data sets show that \(L_1\)R-VSSI can effectively alleviate the influences from the outliers during the recording procedure. \(L_1\)R-VSSI also achieves better performance than traditional \({L_2}\)-norm based methods (e.g., wMNE, LORETA) and sparse constraint methods in the original domain (e.g., SBL) and in the variation domain (e.g., VB-SCCD).