# Fast ℓ1-Regularized EEG Source Localization Using Variable Projection

arXiv: https://arxiv.org/abs/2502.20304 · HTML: https://mlsanity.com/paper/2502.20304/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 49 references that are in the map.
- First posted on arXiv 27 Feb 2025.

## Builds on (most cited first, 1 of 1)

- [Approximate message-passing for convex optimization with non-separable penalties](https://mlsanity.com/paper/1809.06304/) (2018)

## Built on by (most cited first, 1 of 1)

- [Variational Sparse Paired Autoencoders (vsPAIR) for Inverse Problems and Uncertainty Quantification](https://mlsanity.com/paper/2602.02948/) (2026)

## Abstract (arXiv)

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.