EEG dynamic source localization using constrained particle filtering

We consider the dynamic EEG source localization problem with additional constraints on the expected value of the state. In dynamic EEG source localization, the brain sources, also called dipoles, are not stationary but vary over time. Moreover, given our specific EEG experiment, we expect the dipoles to be located within a certain area of the brain (here, the visual cortex). We formulate this constrained dynamic source localization problem as a constrained non-linear state-estimation problem. Particle filters (PFs) are nowadays the state-of-the-art in optimal non-linear and non-Gaussian state estimation. However, PFs cannot handle additional constraints on the state that cannot be incorporated within the system model. In this case, the additional constraint is on the mean of the state, which means that realizations of the state, also called particles within the PF framework, may or may not satisfy the constraint. However, the state must satisfy the constraint on average. This is indeed the case when tracking brain dipoles from EEG experiments that try to target a specific cortex of the brain. Such constraints on the mean of the state are hard to deal with because they reflect global constraints on the posterior density of the state. The popular solution of constraining every particle in the PF may lead either to a stronger condition or to a different (unrelated) condition; both of which result in incorrect estimation of the state. We propose the Iterative Mean Density Truncation (IMeDeT) algorithm, which inductively samples particles that are guaranteed to satisfy the constraint on the mean. Application of IMeDeT on synthetic and real EEG data shows that incorporating a priori constraints on the state improves the tracking accuracy as well as the convergence rate of the tracker.