Majorization-Minimization Networks for Inverse Problems: An Application to EEG Imaging

• URL: http://arxiv.org/abs/2602.03855v1
• Date: Fri, 23 Jan 2026 10:33:45 GMT
• Title: Majorization-Minimization Networks for Inverse Problems: An Application to EEG Imaging
• Authors: Le Minh Triet Tran, Sarah Reynaud, Ronan Fablet, Adrien Merlini, François Rousseau, Mai Quyen Pham,
• Abstract summary: Inverse problems are often ill-posed and require optimization schemes with strong stability and convergence guarantees.<n>We propose a learned Majorization-Minimization (MM) framework for inverse problems within a bilevel optimization setting.<n>We learn a structured curvature majorant that governs each MM step while preserving classical MM descent guarantees.
• Score: 4.063392865490957
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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