IEEE Trans Neural Netw Learn Syst. 2020 Feb;31(2):488-501. doi: 10.1109/TNNLS.2019.2905113. Epub 2019 Apr 11.
The pulse-coupled neural network (PCNN) model is a third-generation artificial neural network without training that uses the synchronous pulse bursts of neurons to process digital images, but the lack of in-depth theoretical research limits its extensive application. By analyzing the working mechanism of the PCNN, we present an expression for the fire-extinguishing time of neurons that fire in the second iteration and an expression for the firing time of neurons that extinguish in the second iteration. In addition, we find a phenomenon of the PCNN and name it mathematically coupled fire extinguishing. Based on the above analysis, we propose a new working mode for the PCNN, where the refiring of fire-extinguishing neurons is only allowed when all firing neurons are extinguished. We also work out the constraint conditions of the parameter settings under this mode. Furthermore, we analyze the relationship between the network parameters and mathematically coupled fire extinguishing, the coupling of neighboring neurons, and the convergence rate of the PCNN, respectively. In addition, we demonstrate the essential regularity of extinguished neuron in the PCNN and then propose an optimal parameter setting to achieve the best comprehensive performance of the PCNN.
脉冲耦合神经网络（PCNN）模型是一种无需训练的第三代人工神经网络，它利用神经元的同步脉冲爆发来处理数字图像，但由于缺乏深入的理论研究，限制了其广泛应用。通过分析 PCNN 的工作机制，我们提出了在第二次迭代中点火的神经元的熄灭时间的表达式和在第二次迭代中熄灭的神经元的点火时间的表达式。此外，我们发现了 PCNN 的一种现象，并对其进行了数学上的耦合熄灭。基于上述分析，我们提出了一种 PCNN 的新工作模式，即在所有点火神经元熄灭的情况下，才允许对熄灭神经元进行重新点火。我们还推导出了在这种模式下参数设置的约束条件。此外，我们分别分析了网络参数与数学上的耦合熄灭、相邻神经元的耦合以及 PCNN 的收敛速度之间的关系。此外，我们还证明了 PCNN 中熄灭神经元的基本规律，然后提出了一个最佳参数设置，以达到 PCNN 的最佳综合性能。
