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.

[1]  A. Doucet,et al.  A Tutorial on Particle Filtering and Smoothing: Fifteen years later , 2008 .

[2]  Lakhmi C. Jain,et al.  A Beamformer-Particle Filter Framework for Localization of Correlated EEG Sources , 2016, IEEE Journal of Biomedical and Health Informatics.

[3]  Lyudmila Mihaylova,et al.  EEG dynamic source localization using Marginalized Particle Filtering , 2015, 2015 IEEE International Conference on Bioinformatics and Biomedicine (BIBM).

[4]  Andrew W. Young,et al.  Differential effects of object-based attention on evoked potentials to fearful and disgusted faces , 2008, Neuropsychologia.

[5]  M. Scherg,et al.  Two bilateral sources of the late AEP as identified by a spatio-temporal dipole model. , 1985, Electroencephalography and clinical neurophysiology.

[6]  Moritz Grosse-Wentrup,et al.  Beamforming in Noninvasive Brain–Computer Interfaces , 2009, IEEE Transactions on Biomedical Engineering.

[7]  D. Simon.  Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches , 2006 .

[8]  Biao Huang,et al.  Constrained Bayesian state estimation – A comparative study and a new particle filter based approach , 2010 .

[9]  Robi Polikar,et al.  Constrained state estimation in particle filters , 2015, 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[10]  Moritz Grosse-Wentrup,et al.  Preprint Accepted for Publication in the Ieee Transactions on Biomedical Engineering Beamforming in Non-invasive Brain-computer Interfaces Abstract—spatial Filtering Constitutes an Integral Part of Build- Ing Eeg-based Brain-computer Interfaces (bcis). Algorithms Frequently Used for Spatial Filterin , 2008 .

[11]  Martin Ulmke,et al.  On constraints exploitation for particle filtering based target tracking , 2012, 2012 15th International Conference on Information Fusion.

[12]  Saeid Sanei,et al.  EEG signal processing , 2000, Clinical Neurophysiology.