A solution to the dynamical inverse problem of EEG generation using spatiotemporal Kalman filtering.

We present a new approach for estimating solutions of the dynamical inverse problem of EEG generation. In contrast to previous approaches, we reinterpret this problem as a filtering problem in a state space framework; for the purpose of its solution, we propose a new extension of Kalman filtering to the case of spatiotemporal dynamics. The temporal evolution of the distributed generators of the EEG can be reconstructed at each voxel of a discretisation of the gray matter of brain. By fitting linear autoregressive models with neighbourhood interactions to EEG time series, new classes of inverse solutions with improved resolution and localisation ability can be explored. For the purposes of model comparison and parameter estimation from given data, we employ a likelihood maximisation approach. Both for instantaneous and dynamical inverse solutions, we derive estimators of the time-dependent estimation error at each voxel. The performance of the algorithm is demonstrated by application to simulated and clinical EEG recordings. It is shown that by choosing appropriate dynamical models, it becomes possible to obtain inverse solutions of considerably improved quality, as compared to the usual instantaneous inverse solutions.