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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.20304 |
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| _version_ | 1866910848370343936 |
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| author | Solomon, Jack Michael Renaut, Rosemary Chung, Matthias |
| author_facet | Solomon, Jack Michael Renaut, Rosemary Chung, Matthias |
| contents | 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 $\ell_1$ regularization quickly becomes intractable for many solvers, and, despite the reconstruction advantages of $\ell_1$ regularization, $\ell_2$-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 $\ell_1$-regularized inverse problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20304 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fast $\ell_1$-Regularized EEG Source Localization Using Variable Projection Solomon, Jack Michael Renaut, Rosemary Chung, Matthias Machine Learning Numerical Analysis Signal Processing 65F10, 65F22, 65F2, 90C06 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 $\ell_1$ regularization quickly becomes intractable for many solvers, and, despite the reconstruction advantages of $\ell_1$ regularization, $\ell_2$-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 $\ell_1$-regularized inverse problems. |
| title | Fast $\ell_1$-Regularized EEG Source Localization Using Variable Projection |
| topic | Machine Learning Numerical Analysis Signal Processing 65F10, 65F22, 65F2, 90C06 |
| url | https://arxiv.org/abs/2502.20304 |