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Reconstruction of Hidden States in Stochastic Neural Field Equations with Infinite Signal Transmission Rate

Due to a growing interest in using dynamic neural field models for solving practical applications, a special interest lies in developing efficient estimation methods for accurate restoration of hidden processes of mathematical models at hand. In this paper, we first propose a constructive way of setting up the nonlinear Bayesian filtering problem arisen in Galerkin-type spectral approximations applied to dynamic neural fields. Next, we propose the efficient numerical scheme for reconstructing the neural population activity over the spatial and time domains from incomplete measurements in both domains. The proposed numerical scheme is designed using the Galerkin approximation and the continuous-discrete extended Kalman filter. The accuracy of the estimation procedure is evaluated by using artificial data through exhaustive numerical tests.