Robust joint estimation of regional brain activity and inter-regional source covariance via full-structure covariance learning

Uncovering the mechanisms underlying cognition and brain disorders requires accurate regional source imaging and reliable characterization of inter-regional statistical dependencies. Traditional methods typically follow a two-stage pipeline that first performs source imaging and then calculates inter-regional dependence measures separately. Such a decoupled framework can propagate source-reconstruction errors to covariance-based network analyses, leading to biased source localization and distorted dependency patterns. To address these limitations, we propose a joint estimation method for regional brain source activity and source covariance via full-structure covariance learning, termed Joint Activity-Covariance Estimation via Full-Structure Covariance Learning (JAC-FS). JAC-FS constructs a Gaussian probabilistic model at the brain-region level and employs a full-structure source covariance matrix to represent regional source variance and inter-regional dependencies. In this covariance representation, diagonal entries encode marginal regional source variance, whereas off-diagonal entries quantify symmetric zero-lag covariance-based dependencies. These estimates are statistical associations and do not by themselves establish direct, directional, or causal physiological communication. A median-weighted covariance statistic suppresses high-energy artifacts, and convex surrogate optimization provides closed-form updates for source activity and source covariance. In addition, constrained noise estimation with diagonal floor protection, low-rank correlation constraints, and phased damped updates limits signal absorption and spurious covariance structure. Simulations showed that JAC-FS outperformed conventional algorithms in regional source localization, temporal recovery, source-covariance recovery against the simulated ground truth, and recovery of predefined short- and long-range covariance edges. In real MEG analyses, JAC-FS produced focal evoked source distributions and representative time courses together with evoked source-covariance patterns. These results establish JAC-FS as a unified framework for regional source imaging and zero-lag source covariance estimation.