Regularizing Solutions to the MEG Inverse Problem Using Space-Time Separable Covariance Functions
This work addresses source reconstruction in MEG for neuroscience applications, presenting an incremental extension to existing methods.
The paper tackles the underdetermined inverse problem in magnetoencephalography (MEG) source reconstruction by extending the conventional approach with a Gaussian process model using space-time separable covariance functions, achieving computational complexity of O(t^3 + n^3 + m^2n) and demonstrating efficiency and generality on simulated and empirical data.
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.