The collective response of an ensemble of leaky integrate-and-fire neurons induced by local correlated noise is investigated theoretically. Based on the linear response theory, we derive the analytic expression of signal-to-noise ratio (SNR). Numerical results show that the amplitude of internal noise can be increased up to an optimal value where the output SNR reaches a maximum value. Interestingly, we find that the correlated noise between the nearest neurons could lead to the obvious SNR gain. We also show that the SNR can reach unity under condition that the correlated noise between the nearest neurons is negative. This nonlinear amplification of SNR gain in an ensemble of noisy neurons can be related to the array stochastic resonance (SR) phenomenon. Furthermore, we also show that the SNR gain can also be optimized by tuning the number of neuron units, frequency and amplitude of the weak periodic signal.

中文翻译：

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通过噪声神经元集合中相关噪声的信噪比增益

从理论上研究了由局部相关噪声引起的一组泄漏的集成和激发神经元的集体响应。基于线性响应理论，我们推导出信噪比（SNR）的解析表达式。数值结果表明，内部噪声的幅度可以增加到输出信噪比达到最大值的最佳值。有趣的是，我们发现最近神经元之间的相关噪声可能导致明显的 SNR 增益。我们还表明，在最近的神经元之间的相关噪声为负的情况下，SNR 可以达到统一。这种噪声神经元集合中 SNR 增益的非线性放大可能与阵列随机共振 (SR) 现象有关。此外，