摘要翻译：
图滤波器是图信号处理的核心工具之一。它们的一个中心方面是它们的直接分布式实现。然而，过滤性能往往与分布式通信和计算节省进行交换。为了改善这种折衷性，本文将目前最先进的分布式图滤波器推广到每个节点用不同的值对其邻居的信号进行加权，同时保持聚合操作的线性化的滤波器。这种新的实现称为边变图滤波器，在保持逼近精度的同时，大大减少了通信轮数。另外，我们刻画了可以用边变递归描述的移不变图滤波器子集。通过使用低维参数化，所提出的图滤波器通过局部算子即固定支持矩阵的连续和组合来逼近线性算子，其应用范围超出了图信号处理领域。一组数值结果显示了边缘变化滤波器比现有方法的优点，并说明了它们比图滤波有更广泛的应用范围。
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英文标题：
《Advances in Distributed Graph Filtering》
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作者：
Mario Coutino, Elvin Isufi and Geert Leus
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最新提交年份：
2018
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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英文摘要：
  Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational savings. To improve this tradeoff, this work generalizes state-of-the-art distributed graph filters to filters where every node weights the signal of its neighbors with different values while keeping the aggregation operation linear. This new implementation, labeled as edge-variant graph filter, yields a significant reduction in terms of communication rounds while preserving the approximation accuracy. In addition, we characterize the subset of shift-invariant graph filters that can be described with edge-variant recursions. By using a low-dimensional parametrization the proposed graph filters provide insights in approximating linear operators through the succession and composition of local operators, i.e., fixed support matrices, which span applications beyond the field of graph signal processing. A set of numerical results shows the benefits of the edge-variant filters over current methods and illustrates their potential to a wider range of applications than graph filtering.
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PDF链接：
https://arxiv.org/pdf/1808.03004