MRI prior computation and parallel tempering algorithm: a probabilistic resolution of the MEG/EEG inverse problem

Since the MEG inverse problem is ill-posed and admits many possible solutions, it is not possible to give it a single "true" answer. Therefore, we propose here to use a specific probabilistic algorithm to map the full probability distribution of the MEG sources with Markov Chain Monte Carlo methods. Using a Bayesian approach, the probability of the MEG solutions is expressed as the product of the likelihood by the prior probability. To compute the prior and constrain the MEG inverse problem resolution, MRI data are also acquired and automatically processed to determine the brain position and volume. We then use Parallel Tempering algorithm to estimate the full posterior probability and determine the likely solutions of the inverse problem. We illustrate the method with results obtained from the analysis of somatosensory data. This illustrates both the MRI processing for the prior computation, and how the knowledge of the full posterior probability distribution can be used to estimate the position of the sources, as well as their likely extension.