EEG source localization based on multivariate autoregressive models using Kalman filtering

The estimation of current distributions from electroencephalographic recordings poses an inverse problem, which can approximately be solved by including dynamical models as spatio-temporal constraints onto the solution. In this paper, we consider the electrocardiography source localization task, where a specific structure for the dynamical model of current distribution is directly obtained from the data by fitting multivariate autoregressive models to electroencephalographic time series. Whereas previous approaches consider an approximation of the internal connectivity of the sources, the proposed methodology takes into account a realistic structure of the model estimated from the data, such that it becomes possible to obtain improved inverse solutions. The performance of the new method is demonstrated by application to simulated electroencephalographic data over several signal to noise ratios, where the source localization task is evaluated by using the localization error and the data fit error. Finally, it is shown that estimating MVAR models makes possible to obtain inverse solutions of considerably improved quality, as compared to the usual instantaneous inverse solutions, even if the regularized inverse of Tikhonov is used.