Electroencephalograms (EEG) are invaluable for treating neurological disorders, however, mapping EEG electrode readings to brain activity requires solving a challenging inverse problem. Due to the time series data, the use of ℓ1 regularization quickly becomes intractable for many solvers, and, despite the reconstruction advantages of ℓ1 regularization, ℓ2-based approaches such as sLORETA are used in practice. In this work, we formulate EEG source localization as a graphical generalized elastic net inverse problem and present a variable projected algorithm (VPAL) suitable for fast EEG source localization. We prove convergence of this solver for a broad class of separable convex, potentially non-smooth functions subject to linear constraints and include a modification of VPAL that reconstructs time points in sequence, suitable for real-time reconstruction. Our proposed methods are compared to state-of-the-art approaches including sLORETA and other methods for ℓ1-regularized inverse problems.
Cite
@article{arxiv.2502.20304,
title = {Fast $\ell_1$-Regularized EEG Source Localization Using Variable Projection},
author = {Jack Michael Solomon and Rosemary Renaut and Matthias Chung},
journal= {arXiv preprint arXiv:2502.20304},
year = {2025}
}