顶点频率图信号处理综述
Vertex-Frequency Graph Signal Processing: A review
摘要：
图形信号处理处理在不规则图形域上观察到的信号。虽然在经典图论中已经开发了许多方法来以信号无关的方式聚类顶点和分割大型图，但基于信号定位的图上数据分析方法代表了一个新的研究方向，这也是图上大数据分析的关键。为此，在图形和图形信号的基本定义的概述后，我们提出并讨论了局部形式的图形傅里叶变换。为了建立与经典信号处理的类比，接下来给出定位窗口的谱域和顶点域定义。然后，频谱和顶点本地化内核相关的小波变换，其次是本地化图傅里叶变换的滤波和反演的研究。为了严格，能量表示和帧的局部图傅里叶变换的分析扩展到能量形式的顶点频率分布，甚至不需要应用本地化窗口。与经典信号处理的另一个联系是通过局部平滑度的概念建立的，该概念随后与图上信号平滑度的特定范例相关。这一切都代表了一般的点频分析与经典的时间-频率分析的关系的全面帐户，重要的，但缺少的环节，更先进的应用程序的图形信号处理。该理论得到了说明性和实际相关的例子的支持。
英文摘要：
Graph signal processing deals with signals which are observed on an irregular graph domain. While many approaches have been developed in classical graph theory to cluster vertices and segment large graphs in a signal independent way, signal localization based approaches to the analysis of data on graph represent a new research direction which is also a key to big data analytics on graphs. To this end, after an overview of the basic definitions in graphs and graph signals, we present and discuss a localized form of the graph Fourier transform. To establish an analogy with classical signal processing, spectral- and vertex-domain definitions of the localization window are given next. The spectral and vertex localization kernels are then related to the wavelet transform, followed by a study of filtering and inversion of the localized graph Fourier transform. For rigour, the analysis of energy representation and frames in the localized graph Fourier transform is extended to the energy forms of vertex-frequency distributions, which operate even without the need to apply localization windows. Another link with classical signal processing is established through the concept of local smoothness, which is subsequently related to the particular paradigm of signal smoothness on graphs. This all represents a comprehensive account of the relation of general vertex-frequency analysis with classical time-frequency analysis, and important but missing link for more advanced applications of graphs signal processing. The theory is supported by illustrative and practically relevant examples.
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