摘要翻译：
图信号处理中最关键的挑战之一是对带限图信号的采样，即在定义良好的图傅里叶域中稀疏的信号。到目前为止，现有技术主要集中在对图形信号的单个快照进行（子）采样，而忽略了它们随时间的演变。然而，时间可以带来新的见解，因为许多真实的信号，如传感器测量、生物、金融和网络信号，在这两个领域都有内在的相关性。本文通过联合考虑图信号的图时性质，将其命名为\emph{graph processes}，填补了这一空白，主要完成了两个任务:\emph{i）}图过程的可观测性；通过Kalman滤波和\emph{ii）}从一个（可能是时变的）节点子集跟踪图进程。详细的数学分析验证了所提出的方法，并提供了不同参与者所起的作用，如图拓扑结构、进程带宽和采样策略。此外，提出了联合利用图结构和图进程性质的（次）最优采样策略。在合成数据和实际数据上的几个数值试验验证了我们的理论发现，并说明了所提出的方法在处理时变图信号方面的性能。
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英文标题：
《Observing and Tracking Bandlimited Graph Processes》
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作者：
Elvin Isufi and Paolo Banelli and Paolo Di Lorenzo 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：
  One of the most crucial challenges in graph signal processing is the sampling of bandlimited graph signals, i.e., signals that are sparse in a well-defined graph Fourier domain. So far, the prior art is mostly focused on (sub)sampling single snapshots of graph signals ignoring their evolution over time. However, time can bring forth new insights, since many real signals like sensor measurements, biological, financial, and network signals in general, have intrinsic correlations in both domains. In this work, {we fill this lacuna} by jointly considering the graph-time nature of graph signals, named \emph{graph processes} for two main tasks: \emph{i)} observability of graph processes; and \emph{ii)} tracking of graph processes via Kalman filtering; both from a (possibly time-varying) subset of nodes. A detailed mathematical analysis ratifies the proposed methods and provides insights into the role played by the different actors, such as the graph topology, the process bandwidth, and the sampling strategy. Moreover, (sub)optimal sampling strategies that jointly exploit the nature of the graph structure and graph process are proposed. Several numerical tests on both synthetic and real data validate our theoretical findings and illustrate the performance of the proposed methods in coping with time-varying graph signals.
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PDF链接：
https://arxiv.org/pdf/1712.00404