  Brain source imaging is an important method for noninvasively characterizing
brain activity using Electroencephalogram (EEG) or Magnetoencephalography (MEG)
recordings. Traditional EEG/MEG Source Imaging (ESI) methods usually assume
that either source activity at different time points is unrelated, or that
similar spatiotemporal patterns exist across an entire study period. The former
assumption makes ESI analyses sensitive to noise, while the latter renders ESI
analyses unable to account for time-varying patterns of activity. To
effectively deal with noise while maintaining flexibility and continuity among
brain activation patterns, we propose a novel probabilistic ESI model based on
a hierarchical graph prior. Under our method, a spanning tree constraint
ensures that activity patterns have spatiotemporal continuity. An efficient
algorithm based on alternating convex search is presented to solve the proposed
model and is provably convergent. Comprehensive numerical studies using
synthetic data on a real brain model are conducted under different levels of
signal-to-noise ratio (SNR) from both sensor and source spaces. We also examine
the EEG/MEG data in a real application, in which our ESI reconstructions are
neurologically plausible. All the results demonstrate significant improvements
of the proposed algorithm over the benchmark methods in terms of source
localization performance, especially at high noise levels.
