Maximum-correntropy-based sequential method for fast neural population activity reconstruction in the cortex from incomplete abnormally-disturbed noisy measurements

Abstract

This paper continues to explore the membrane potential reconstruction and pattern recognition problem in a neural tissue modeled by Stochastic Dynamic Neural Field (SDNF) equation. Although recent research has suggested an efficient solution based on the state-space approach through nonlinear Bayesian filtering framework, it is becoming extremely difficult to ignore the existence of non-Gaussian uncertainties in the SDNFs as well as the stability problem of neuronal population dynamics to outliers. Motivated by recent events in signal processing and mathematical neuroscience, this paper explores the SDNFs in a presence of non-Gaussian uncertainties, which is the shot noise case, where the corrupted data might appear due to broken sensors. We derive the “distributionally robust” state estimator for the membrane potential reconstruction process that is the Maximum Correntropy Criterion Extended Kalman Filter (MCC-EKF) as well as its fast and numerically robust (to roundoff) implementation method by using the sequential principle of processing the measurement vectors. The numerical experiments are provided to illustrate the performance of the novel estimation methods.