Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.03855 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913164999786496 |
|---|---|
| author | Tran, Le Minh Triet Reynaud, Sarah Fablet, Ronan Merlini, Adrien Rousseau, François Pham, Mai Quyen |
| author_facet | Tran, Le Minh Triet Reynaud, Sarah Fablet, Ronan Merlini, Adrien Rousseau, François Pham, Mai Quyen |
| contents | Inverse problems are often ill-posed and require optimization schemes with strong stability and convergence guarantees. While learning-based approaches such as deep unrolling and meta-learning achieve strong empirical performance, they typically lack explicit control over descent and curvature, limiting robustness. We propose a learned Majorization-Minimization (MM) framework for inverse problems within a bilevel optimization setting. Instead of learning a full optimizer, we learn a structured curvature majorant that governs each MM step while preserving classical MM descent guarantees. The majorant is parameterized by a lightweight recurrent neural network and explicitly constrained to satisfy valid MM conditions. For cosine-similarity losses, we derive explicit curvature bounds yielding diagonal majorants. When analytic bounds are unavailable, we rely on efficient Hessian-vector product-based spectral estimation to automatically upper-bound local curvature without forming the Hessian explicitly. Experiments on EEG source imaging demonstrate improved accuracy, stability, and cross-dataset generalization over deep-unrolled and meta-learning baselines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03855 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Majorization-Minimization Networks for Inverse Problems: An Application to EEG Imaging Tran, Le Minh Triet Reynaud, Sarah Fablet, Ronan Merlini, Adrien Rousseau, François Pham, Mai Quyen Signal Processing Machine Learning Inverse problems are often ill-posed and require optimization schemes with strong stability and convergence guarantees. While learning-based approaches such as deep unrolling and meta-learning achieve strong empirical performance, they typically lack explicit control over descent and curvature, limiting robustness. We propose a learned Majorization-Minimization (MM) framework for inverse problems within a bilevel optimization setting. Instead of learning a full optimizer, we learn a structured curvature majorant that governs each MM step while preserving classical MM descent guarantees. The majorant is parameterized by a lightweight recurrent neural network and explicitly constrained to satisfy valid MM conditions. For cosine-similarity losses, we derive explicit curvature bounds yielding diagonal majorants. When analytic bounds are unavailable, we rely on efficient Hessian-vector product-based spectral estimation to automatically upper-bound local curvature without forming the Hessian explicitly. Experiments on EEG source imaging demonstrate improved accuracy, stability, and cross-dataset generalization over deep-unrolled and meta-learning baselines. |
| title | Majorization-Minimization Networks for Inverse Problems: An Application to EEG Imaging |
| topic | Signal Processing Machine Learning |
| url | https://arxiv.org/abs/2602.03855 |