SSSI-L2p: An EEG extended source imaging algorithm based on the structured sparse regularization with L2p-Norm

Electroencephalographic (EEG) source imaging (ESI) aims to estimate brain activity locations and extents. ESI is crucial for studying brain functions and detecting epileptic foci. However, accurately reconstructing extended sources remains challenging due to high susceptibility of EEG signals to interference and the underdetermined nature of the ESI problem. In this study, we introduce a new ESI algorithm, Structured Sparse Source Imaging based on $L_{2p}$-norm (SSSI-$L_{2p}$), to estimate potential brain activities. SSSI-$L_{2p}$ utilizes the mixed $L_{2p}$-norm ($0<p<1$) to enforce spatial–temporal constraints within a structured sparsity regularization framework. By leveraging the alternating direction method of multipliers (ADMM) and iteratively reweighted least squares (IRLS) algorithm, the challenging optimization problem of SSSI-$L_{2p}$ can be effectively solved. We showcase the superior performance of SSSI-$L_{2p}$ over benchmark ESI methods through numerical simulations and human clinical data. Our results demonstrate that sources reconstructed by SSSI-$L_{2p}$ exhibit high spatial resolution and clear boundaries, highlighting its potential as a robust and effective ESI technique. Additionally, we have shared the source code of SSSI-$L_{2p}$ at https://github.com/Mashirops/SSSI-L2p.git.