Resolution of the MEG inverse problem by Markov Chain Monte Carlo methods : Algorithm comparison and 3-dimensional visualization tools

Markov Chain Monte Carlo methods are statistical tools that have been recently proposed for the resolution of the MEG inverse problem [1]. Their main advantages are easy incorporation of a priori knowledge, and an adequate response to the ambiguity of the ill-posed MEG inverse problem. However, since simpler MCMC schemes might have difficulties in escaping from local modes, adequate research is needed to assess the most efficient MCMC algorithms for the resolution of the MEG inverse problem [2,3]. We present here both our results concerning MCMC scheme comparison, and the imaging tools we have developed for source computation and display. We first describe the probabilistic MEG model and the MCMC algorithms we have used (Parallel Tempering [4] and Reversible Jump [5]). In a first simulation study with a spherical head model, the combination of these MCMC schemes is shown to be superior to Simulated Annealing, both in accuracy and in its ability to estimate an unknown number of sources. We then apply Parallel Tempering to simulated data in a real head model obtained from MRI data. We describe how the MRI data are automatically processed to extract the brain, so that the source positions can be restricted to the cortex layer. We then compare Parallel Tempering with Simulated Annealing and show that PT exhibits a better robustness to noise level. We then use the 3-dimensional information previously extracted from the MRI images to display the MCMC results with this 3-dimensional morphological information. This further demonstrates how MCMC answers the MEG inverse problem by giving it a probabilistic solution.