EEG Extended Source Imaging with Variation Sparsity and Lp-Norm Constraint

Accurately reconstructing the location and extent of cortical sources is crucial for cognitive research and clinical applications. Regularization methods that use the L-1-norm in the spatial variation domain effectively estimate cortical extended sources. However, in the variation domain, employing L-1-norm constraint tends to overestimate the extent of sources. Hence, to achieve more precise estimations of both the location and extent of sources, further sparseness-enforced regularizations are required. In this work, we develop a robust EEG source imaging method, VSSI-L-p, to estimate extended cortical sources. VSSI-L-p employs the L-p-norm (0 < p < 1) in the variation domain to promote sparsity. Using alternating direction method of multipliers (ADMM) and generalized soft-thresholding (GST) algorithm, we can efficiently derive the solution of VSSI-L-p. According to numerical simulations plus real data analysis, VSSI-L-p outperforms both traditional L-2 and L-1-norm-based methods, and the L-1-norm-based method in the variation domain for reconstructing extended sources, validating the outstanding performance of L-p-norm and variation constraint.