Regularizing Solutions to the MEG Inverse Problem Using Space-Time Separable Covariance Functions

TL;DR

This paper introduces a Bayesian method for MEG source reconstruction that regularizes in space and time using Gaussian processes with separable covariance functions, improving computational efficiency and generality.

Contribution

The paper extends traditional MEG inverse solutions by incorporating space-time regularization with Gaussian processes, enabling more efficient and flexible source reconstruction.

Findings

Efficient computational complexity of $ ext{O}(t^3 + n^3 + m^2n)$ for the proposed model.

Demonstrated effectiveness on both simulated and real MEG data.

Unifies various classical approaches under a Bayesian Gaussian process framework.

Abstract

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.