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

A new machine-learning framework for solving inverse problems preserves the descent guarantees of classical optimization while learning a structured curvature majorant, its authors report, with initial tests focused on electroencephalography source imaging [1]. The method, described in a paper by Le Minh Triet Tran and colleagues, reformulates the Majorization-Minimization (MM) algorithm inside a bilevel optimization setting. Rather than learning a complete optimizer, the framework learns a majorant that governs each MM step and is explicitly constrained to satisfy valid MM conditions [1][2]. The majorant is parameterized by a lightweight recurrent neural network [1][2]. Inverse problems such as EEG source imaging are often ill-posed and demand optimization schemes with strong stability and convergence guarantees [2]. EEG records voltage fluctuations along the scalp that originate from postsynaptic potentials of pyramidal neurons in the neocortex and allocortex [3]. The signal is distorted by intermediary tissues and bones, and deep structures such as the hippocampus, thalamus, and brain stem do not contribute directly to the scalp recording [3]. Reconstructing the underlying brain sources from these surface measurements is therefore a challenging inverse problem. When a cosine-similarity loss is used, the authors derive explicit curvature bounds that yield diagonal majorants. For cases where analytic bounds are unavailable, the framework relies on efficient Hessian-vector product-based spectral estimation to automatically upper-bound local curvature without forming the Hessian explicitly [1][2]. The paper reports that experiments on EEG source imaging show improved accuracy, stability, and cross-dataset generalization compared with deep-unrolled and meta-learning baselines [1][2]. EEG remains widely used as a clinical diagnostic tool, particularly in epilepsy, and as a research tool in neuroscience, despite its limited spatial resolution compared with MRI and CT [3]. Quantitative EEG analysis can serve as an adjunct to visual inspection, which is subject to inter-rater and intra-rater variability [3]. The work contributes to a broader effort in network neuroscience, which studies the brain at multiple scales to explain brain systems, behavior, and dysfunction in psychiatric and neurological diseases [4]. The learned-MM approach differs from earlier strategies such as extreme learning machines, where hidden-node parameters can be randomly assigned and never updated [5], by maintaining explicit descent control throughout optimization [1][2].