  Determining the magnitude and location of neural sources within the brain
that are responsible for generating magnetoencephalography (MEG) signals
measured on the surface of the head is a challenging problem in functional
neuroimaging. The number of potential sources within the brain exceeds by an
order of magnitude the number of recording sites. As a consequence, the
estimates for the magnitude and location of the neural sources will be
ill-conditioned because of the underdetermined nature of the problem. One
well-known technique designed to address this imbalance is the minimum norm
estimator (MNE). This approach imposes an $L^2$ regularization constraint that
serves to stabilize and condition the source parameter estimates. However,
these classes of regularizer are static in time and do not consider the
temporal constraints inherent to the biophysics of the MEG experiment. In this
paper we propose a dynamic state-space model that accounts for both spatial and
temporal correlations within and across candidate intracortical sources. In our
model, the observation model is derived from the steady-state solution to
Maxwell's equations while the latent model representing neural dynamics is
given by a random walk process.
