Source Reconstruction of Resting-State MEG and EEG Activity: A Technical Note on the Choice of Noise Covariance

Minimum variance beamforming is widely used to reconstruct neural sources from MEG and EEG data, but results critically depend on the choice of noise covariance. In task-based studies, this is often defined from pre-stimulus baselines, but for resting-state data the problem presents a fundamental challenge. Conventional solutions, such as empty-room recordings or diagonal white sensor noise, are not optimal. They either ignore brain-generated noise or yield artificial, non-uniform source-level baselines that can distort results. Our approach is to define a baseline at the source level as a uniform distribution of uncorrelated, randomly oriented neural dipoles, representing a maximum-entropy "ground state" of brain activity. Projecting this source model through the electromagnetic lead fields yields a sensor-level covariance that captures realistic spatial correlations. A data-driven constraint scales the model to match measured data, ensuring a physically admissible solution. Applied to real human resting-state data, the method produces a structured, non-uniform sensor covariance dictated by participants anatomy, source reconstructions that are smooth and plausible, and free from the artificial peaks induced by diagonal noise models. This source-level approach provides a principled and physiologically grounded baseline for beamforming and improves the reliability of resting-state analyses and interpretation.