Patel Ashok, Kosko Bart
Department of Electrical Engineering, Signal and Image Processing Institute, University of Southern California, Los Angeles, CA 90089-2564, USA.
Neural Netw. 2005 Jun-Jul;18(5-6):467-78. doi: 10.1016/j.neunet.2005.06.031.
Two new theorems show that small amounts of additive white noise can improve the bit count or mutual information of several popular models of spiking retinal neurons and spiking sensory neurons. The first theorem gives necessary and sufficient conditions for this noise benefit or stochastic resonance (SR) effect for subthreshold signals in a standard family of Poisson spiking models of retinal neurons. The result holds for all types of finite-variance noise and for all types of infinite-variance stable noise: SR occurs if and only if a sum of noise means or location parameters falls outside a 'forbidden interval' of values. The second theorem gives a similar forbidden-interval sufficient condition for the SR effect for several types of spiking sensory neurons that include the Fitzhugh-Nagumo neuron, the leaky integrate-and-fire neuron, and the reduced Type I neuron model if the additive noise is Gaussian white noise. Simulations show that neither the forbidden-interval condition nor Gaussianity is necessary for the SR effect.
两个新定理表明，少量的加性白噪声可以提高几种流行的视网膜尖峰神经元模型和尖峰感觉神经元模型的比特数或互信息。第一个定理给出了视网膜神经元泊松尖峰模型标准族中亚阈值信号的这种噪声益处或随机共振（SR）效应的充要条件。该结果适用于所有类型的有限方差噪声和所有类型的无限方差稳定噪声：当且仅当噪声均值或位置参数之和落在一个“禁止区间”值之外时，才会发生随机共振。第二个定理给出了一个类似的禁止区间充分条件，用于几种类型的尖峰感觉神经元的随机共振效应，这些神经元包括菲茨休 - 纳古莫神经元、泄漏积分发放神经元以及简化的I型神经元模型，前提是加性噪声为高斯白噪声。模拟表明，对于随机共振效应而言，禁止区间条件和高斯性都不是必要的。
