Title: Caulking the Leakage Effect in MEEG Source Connectivity Analysis,
Abstract: Simplistic estimation of neural connectivity in MEEG sensor space is
impossible due to volume conduction. The only viable alternative is to carry
out connectivity estimation in source space. Among the neuroscience community
this is claimed to be impossible or misleading due to Leakage: linear mixing of
the reconstructed sources. To address this problematic we propose a novel
solution method that caulks the Leakage in MEEG source activity and
connectivity estimates: BC-VARETA. It is based on a joint estimation of source
activity and connectivity in the frequency domain representation of MEEG time
series. To achieve this, we go beyond current methods that assume a fixed
gaussian graphical model for source connectivity. In contrast we estimate this
graphical model in a Bayesian framework by placing priors on it, which allows
for highly optimized computations of the connectivity, via a new procedure
based on the local quadratic approximation under quite general prior models. A
further contribution of this paper is the rigorous definition of leakage via
the Spatial Dispersion Measure and Earth Movers Distance based on the geodesic
distances over the cortical manifold. Both measures are extended for the first
time to quantify Connectivity Leakage by defining them on the cartesian product
of cortical manifolds. Using these measures, we show that BC-VARETA outperforms
most state of the art inverse solvers by several orders of magnitude.