Dynamic functional graph-Laplacian priors integrated with optimization for EEG source localization

Objective. Electroencephalography (EEG) source localization is an ill-posed inverse problem in which conventional methods often rely on static anatomical or smoothness assumptions and may neglect task-related dynamic functional interactions. This study aims to develop a dynamic graph-regularized EEG source localization framework that incorporates time-varying functional connectivity directly into inverse reconstruction and improves source-space motor imagery (MI) decoding.Approach. We propose DynaGraph-alternating direction method of multipliers (DG-ADMM), a source localization framework that combines linearly constrained minimum variance (LCMV) beamforming, region-of-interest-level dimensionality reduction, dynamic phase synchronization analysis, graph-Laplacian regularization, and efficient optimization. Initial source estimates are obtained using a LCMV beamformer. Region-level source signals are then extracted using principal component analysis and sliding-window phase-locking values with surrogate-based statistical testing are used to construct reliable dynamic functional graphs. The resulting graph Laplacian is mapped back to source space and embedded as a structured prior in an ADMMs optimization problem.Main results. Experiments on the MNE sample dataset showed that DG-ADMM produced spatially concentrated and physiologically plausible source patterns. On the PhysioNet MI dataset, the proposed framework achieved a binary left-versus-right MI classification accuracy of 93.52%, outperforming representative deep learning baselines. In a 320-dataset synthetic benchmark covering single-source, double-source, correlated-source, and dynamic-source conditions at two signal-to-noise ratios, DG-ADMM achieved the lowest mean center-of-mass localization error in five of eight conditions and showed its clearest advantage for dynamic sources.Significance. The results demonstrate that dynamic functional connectivity can serve as an informative graph-structured prior for EEG inverse reconstruction. DG-ADMM provides an interpretable and computationally feasible strategy for improving spatial focus, temporal consistency, and source-space decoding performance in EEG-based brain-computer interfaces.