论文标题
P-Adic细胞神经网络：图像处理的应用
p-adic Cellular Neural Networks: Applications to Image Processing
论文作者
论文摘要
P-ADIC细胞神经网络（CNN）是Chua和Yang在80年代引入的神经网络的数学概括。在这项工作中，我们介绍了两种新型的CNN类型，可以使用真实数据执行计算，并且几乎可以完全理解其动态。第一种网络是灰度图像的边缘检测器。这些网络的固定状态是在晶格结构中层次组织的。这些网络中的任何一个的动力都包括向晶格中某些最小状态的过渡。第二种类型是一类新的反应扩散网络。我们研究了这些网络的稳定性，并表明它们可以用作降低噪声并保存边缘的滤波器图像中的灰度图像，以降低边缘的过滤器。在此引入的网络是通过实验发现的。它们是在P-Adic单位球中定义的实现函数的空间上的抽象演化方程，用于一些素数p。在实际应用中，素数P取决于图像的大小，因此仅使用少量素数。我们提供了几个数值模拟，以显示这些网络的工作原理。
The p-adic cellular neural networks (CNNs) are mathematical generalizations of the neural networks introduced by Chua and Yang in the 80s. In this work we present two new types of CNNs that can perform computations with real data, and whose dynamics can be understood almost completely. The first type of networks are edge detectors for grayscale images. The stationary states of these networks are organized hierarchically in a lattice structure. The dynamics of any of these networks consists of transitions toward some minimal state in the lattice. The second type is a new class of reaction-diffusion networks. We investigate the stability of these networks and show that they can be used as filters to reduce noise, preserving the edges, in grayscale images polluted with additive Gaussian noise. The networks introduced here were found experimentally. They are abstract evolution equations on spaces of real-valued functions defined in the p-adic unit ball for some prime number p. In practical applications the prime p is determined by the size of image, and thus, only small primes are used. We provide several numerical simulations showing how these networks work.
