Probabilistic approach to solving the magnetoencephalography inverse problem

The brain study is the one of the most popular research area in contemporary neuroscience. It accumulates efforts of broad research groups involving different kinds of experts: psychologists, mathematicians, etc. The main problem in this area is how to localize cerebral cortex activity using experimental data. This problem is critical for all neuroimaging methods (functional magnetic resonance imaging, electroencephalography, magnetoencephalography (MEG), etc.). In the paper, MEG data are considered. Magnetoencephalography is a noninvasive neuroimaging technique which allows recording extra weak magnetic fields generated by neurons in human brain. Sources reconstruction using MEG data is an ill-posed inverse problem. The paper considers the Bayesian derivation of the inverse problem solution for MEG data. The main steps are described and necessary calculations are provided. Particular attention was paid to such advantage of the Bayesian approach as universality. It was shown how other popular methods which are widely used in research could be obtained within the unified framework. A generalization to the group-wise experiment is also considered. The paper also provides possible ways of further improvement of the MEG inverse problem solving techniques using the Bayesian approach.