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.

中文翻译：

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基于最大熵的顺序方法，用于根据不完整的异常干扰噪声测量快速重建皮层中的神经群体活动


本文继续探索由随机动态神经场（SDNF）方程建模的神经组织中的膜电位重建和模式识别问题。尽管最近的研究提出了通过非线性贝叶斯过滤框架基于状态空间方法的有效解决方案，但忽视SDNF中非高斯不确定性的存在以及神经元群体动态对异常值的稳定性问题变得极其困难。受信号处理和数学神经科学领域最近发生的事件的启发，本文探讨了存在非高斯不确定性的 SDNF，即散粒噪声情况，其中由于传感器损坏可能会出现损坏的数据。我们通过使用顺序处理原理推导了膜电位重建过程的“分布鲁棒”状态估计器，即最大熵准则扩展卡尔曼滤波器（MCC-EKF）及其快速且数值鲁棒（舍入）的实现方法测量向量。提供数值实验来说明新颖估计方法的性能。