发帖
雷达卡
摘要翻译：
图信号处理的基本操作是对标在图上的信号进行滤波，从中提取特定的部分，或者改变其表示域，使用更适合表示图中所包含的信息的变换或字典。本章的目的是回顾一般概念的介绍滤波器和图形信号的表示。我们首先回顾了实现这一目标的一般框架，重点是引入一些与图信号相关的谱域来定义图傅立叶变换。我们展示了如何通过观察图形信号的变化来引入频率分析的概念。然后，我们转向图滤波器的介绍，图滤波器的定义类似于一维信号或二维图像的经典等价，作为在信号的每个频率上工作的线性系统。文中给出了滤波器及其实现的一些例子。最后，作为图信号的替代表示，我们重点讨论了由滤波器定义的多尺度变换。综述了图上的谱小波等连续多尺度变换，以及图上滤波器组的通用方法。讨论了结构图和任意图的图过滤库的几种变体，重点讨论了抽取算子和聚集算子选择的中心点。
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英文标题：
《Design of graph filters and filterbanks》
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作者：
Nicolas Tremblay, Paulo Gon\c{c}alves, Pierre Borgnat
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最新提交年份：
2017
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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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一级分类：Computer Science 计算机科学
二级分类：Information Theory 信息论
分类描述：Covers theoretical and experimental aspects of information theory and coding. Includes material in ACM Subject Class E.4 and intersects with H.1.1.
涵盖信息论和编码的理论和实验方面。包括ACM学科类E.4中的材料，并与H.1.1有交集。
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一级分类：Computer Science 计算机科学
二级分类：Social and Information Networks 社会和信息网络
分类描述：Covers the design, analysis, and modeling of social and information networks, including their applications for on-line information access, communication, and interaction, and their roles as datasets in the exploration of questions in these and other domains, including connections to the social and biological sciences. Analysis and modeling of such networks includes topics in ACM Subject classes F.2, G.2, G.3, H.2, and I.2; applications in computing include topics in H.3, H.4, and H.5; and applications at the interface of computing and other disciplines include topics in J.1--J.7. Papers on computer communication systems and network protocols (e.g. TCP/IP) are generally a closer fit to the Networking and Internet Architecture (cs.NI) category.
涵盖社会和信息网络的设计、分析和建模，包括它们在联机信息访问、通信和交互方面的应用，以及它们作为数据集在这些领域和其他领域的问题探索中的作用，包括与社会和生物科学的联系。这类网络的分析和建模包括ACM学科类F.2、G.2、G.3、H.2和I.2的主题；计算应用包括H.3、H.4和H.5中的主题；计算和其他学科接口的应用程序包括J.1-J.7中的主题。关于计算机通信系统和网络协议（例如TCP/IP）的论文通常更适合网络和因特网体系结构（CS.NI）类别。
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一级分类：Mathematics 数学
二级分类：Information Theory 信息论
分类描述：math.IT is an alias for cs.IT. Covers theoretical and experimental aspects of information theory and coding.
它是cs.it的别名。涵盖信息论和编码的理论和实验方面。
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英文摘要：
Basic operations in graph signal processing consist in processing signals indexed on graphs either by filtering them, to extract specific part out of them, or by changing their domain of representation, using some transformation or dictionary more adapted to represent the information contained in them. The aim of this chapter is to review general concepts for the introduction of filters and representations of graph signals. We first begin by recalling the general framework to achieve that, which put the emphasis on introducing some spectral domain that is relevant for graph signals to define a Graph Fourier Transform. We show how to introduce a notion of frequency analysis for graph signals by looking at their variations. Then, we move to the introduction of graph filters, that are defined like the classical equivalent for 1D signals or 2D images, as linear systems which operate on each frequency of a signal. Some examples of filters and of their implementations are given. Finally, as alternate representations of graph signals, we focus on multiscale transforms that are defined from filters. Continuous multiscale transforms such as spectral wavelets on graphs are reviewed, as well as the versatile approaches of filterbanks on graphs. Several variants of graph filterbanks are discussed, for structured as well as arbitrary graphs, with a focus on the central point of the choice of the decimation or aggregation operators.
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PDF链接：
https://arxiv.org/pdf/1711.02046
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