Regularizing Solutions to the MEG Inverse Problem Using Space-Time   Separable Covariance Functions
  In magnetoencephalography (MEG) the conventional approach to source reconstruction is to solve the underdetermined inverse problem independently over time and space. Here we present how the conventional approach can be extended by regularizing the solution in space and time by a Gaussian process (Gaussian random field) model. Assuming a separable covariance function in space and time, the computational complexity of the proposed model becomes (without any further assumptions or restrictions) $\mathcal{O}(t^3 + n^3 + m^2n)$, where $t$ is the number of time steps, $m$ is the number of sources, and $n$ is the number of sensors. We apply the method to both simulated and empirical data, and demonstrate the efficiency and generality of our Bayesian source reconstruction approach which subsumes various classical approaches in the literature. 
Arno Solin, Pasi Jyl\"anki, Jaakko Kauram\"aki, Tom Heskes, Marcel A.   J. van Gerven, Simo S\"arkk\"a
stat.AP stat.ML