Structure-Preserving Correction Learning for Sparse Bayesian Inference in Brain Source Imaging

2026-06-05

AI Summary

This work addresses the limitations of traditional sparse Bayesian brain source imaging methods, which rely on fixed iterative rules and struggle to adaptively optimize their update mechanisms. To overcome this, the authors propose a structure-preserving learnable refinement framework that unfolds a classical joint hyperparameter solver into a neural architecture. By integrating learnable biases, multilayer perceptrons (MLPs), and attention mechanisms, the approach enables adaptive updates while preserving the interpretability inherent in Bayesian inference. The resulting method achieves significantly improved reconstruction accuracy and faster convergence, effectively combining the strengths of model-driven priors with algorithmic transparency.

Abstract

Classical sparse Type-II Bayesian methods for M/EEG brain imaging support joint estimation of source and noise hyperparameters, but rely on fixed iterative update rules. Although these updates are principled and interpretable, their dynamics cannot be adapted from data. We propose to learn the update mechanism itself while preserving the underlying Bayesian structure by unfolding a classical joint hyperparameter-learning solver into a trainable neural architecture whose layers mirror the original iterations. The resulting framework is initialized to recover the classical solver exactly before training and is enriched through progressively more expressive correction-learning mechanisms, ranging from learnable biases to adaptive MLP and attention-based contextual refinements. In this way, training does not replace Bayesian inference with a black-box predictor, but instead learns structured correction terms while retaining the interpretability and model-based character of the original update dynamics. Structured correction learning therefore aims to improve empirical reconstruction performance without replacing the original model-based inference mechanism. Experimental results show that the learned correction variants improve reconstruction performance and convergence behavior over the baseline unfolded solver while preserving its algorithmic transparency.

Problem

• sparse Bayesian inference
• brain source imaging
• hyperparameter learning
• structure-preserving
• iterative update rules

Innovation

• structure-preserving learning
• sparse Bayesian inference
• algorithm unfolding
• correction learning
• brain source imaging