A bayesian approach for EEG inverse problem: Spatio-temporal regularization

The famous inverse problem in EEG (electroencephalography) is an ill-posed problem. Its priors or constraints are required to ensure getting an unique solution. Moreover, added to spatial constraints, we impose temporal smoothness priors on dipole magnitude. These constraints are easily included into a Bayesian formalism, through a maximum a posteriori “MAP estimator” of electrical density in the brain. We used a simulated dipole experiment to explore the behavior of our approach with and without temporal constraints.