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.

中文翻译：

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空间分布式网络逆滤波的预处理梯度下降算法

图滤波器及其逆函数已广泛用于去噪、平滑、采样、插值和学习。在空间分布式网络 (SDN) 上实施逆过滤程序是一项重大挑战，因为 SDN 上的每个代理都配备了容量有限的数据处理子系统和由于工程限制而范围有限的通信子系统。在这封信中，我们介绍了一种预处理的梯度下降算法来实现与具有小测地线宽度的图过滤器相关联的逆过滤过程。所提出的算法呈指数收敛，并且可以在顶点级别实现并应用于 SDN 上的时变逆滤波。