Sequential method for fast neural population activity reconstruction in the cortex from incomplete noisy measurements

Abstract

During recent years there has been a growing interest in stochastic dynamic neural fields employed for modeling and predictions in biomedical and technical systems. In this paper, given some incomplete noisy data available from sensors, we propose and explore a state estimation method for fast restorations of membrane potential in the cortex based on such measurements and the Amari equation used for simulations of neural population activity in a stochastic setting. Our novel technique relies upon a Galerkin-type spectral approximation utilized within the conventional state-space approach. Translating a stochastic system into its state-space form creates a straightforward and fruitful way to the data-driven parameter estimation, filtering, prediction and smoothing. The present study is particularly focused on establishing a nonlinear stochastic Galerkin-spectral-approximation-induced system of large size, which is further estimated by the traditional extended Kalman filter (EKF). The efficiency of calculations is the main purpose of our research. That is why the fast filtering solution devised is based on processing the incoming data incrementally, that is, by processing measurements one at a time, rather than handling them as a unified high-dimensional vector. Such sequential filters suit well for dealing with large data sets as well as with real-time on-line computations. Also, their derivation and substantiation is of great interest in the context of neural network training because of large stochastic systems arisen there. In comparison to the batch filtering, our novel algorithm reduces the computational cost of membrane potential reconstructions in terms of the amount of grid nodes N accepted in the underlying spacial discretization, significantly. Apart from its computation efficiency, this sequential method is more robust to round-off errors committed within a computer-based finite precision arithmetics than the classical EKF because of the (N × N)-matrix inversion elimination from such membrane potential calculations. The superior performance of our technique is examined and confirmed in comparison to the batch one on two known scenarios in the dynamic neural field modeling.