空间分布网络逆滤波的预条件梯度下降算法
Preconditioned Gradient Descent Algorithm for Inverse Filtering on Spatially Distributed Networks
摘要：
图滤波器及其逆滤波器在去噪、平滑、采样、插值和学习等领域有着广泛的应用。在空间分布式网络（SDN）上实现逆滤波过程是一个显著的挑战，因为SDN上的每个代理都配备有容量有限的数据处理子系统和由于工程限制而具有有限范围的通信子系统。在这封信中，我们介绍了一个预处理的梯度下降算法来实现与具有小测地线宽度的图滤波器相关联的逆滤波过程。该算法具有指数收敛性，可在顶点级实现，并可应用于SDNs上的时变逆滤波。
英文摘要：
Graph filters and their inverses have been widely used in denoising, smoothing, sampling, interpolating and learning. Implementation of an inverse filtering procedure on spatially distributed networks (SDNs) is a remarkable challenge, as each agent on an SDN is equipped with a data processing subsystem with limited capacity and a communication subsystem with confined range due to engineering limitations. In this letter, we introduce a preconditioned gradient descent algorithm to implement the inverse filtering procedure associated with a graph filter having small geodesic-width. The proposed algorithm converges exponentially, and it can be implemented at vertex level and applied to time-varying inverse filtering on SDNs.
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