基于SVD的有向积图的图傅立叶变换

IF 3 3区 计算机科学 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC IEEE Transactions on Signal and Information Processing over Networks Pub Date : 2023-07-27 DOI:10.1109/TSIPN.2023.3299511
Cheng Cheng;Yang Chen;Yeon Ju Lee;Qiyu Sun
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引用次数: 0

摘要

图形傅立叶变换(GFT)是图形信号处理中的基本工具之一,它可以将图形信号分解为不同的频率分量,并通过不同的变化模式有效地表示具有强相关性的图形信号。无向图上的GFT已经得到了很好的研究,并提出了几种定义有向图上GFT的方法。本文基于一些图拉普拉斯算子的奇异值分解,在两个有向图的笛卡尔乘积图上提出了两个GFT。我们证明了所提出的GFT可以有效地表示具有强相关性的有向图上的时空数据集,并且在无向图设置中,它们本质上是文献中的联合GFT。在本文中,我们还考虑了所提出的GFT在频域中的带限过程,并展示了它们在对布雷斯特(法国)地区32个气象站和美国218个地点收集的每小时温度数据集进行去噪方面的性能。
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SVD-Based Graph Fourier Transforms on Directed Product Graphs
Graph Fourier transform (GFT) is one of the fundamental tools in graph signal processing to decompose graph signals into different frequency components and to represent graph signals with strong correlation by different modes of variation in an effective way. The GFT on undirected graphs has been well studied and several approaches have been proposed to define GFTs on directed graphs. In this article, based on the singular value decompositions of some graph Laplacians, we propose two GFTs on the Cartesian product graph of two directed graphs. We show that the proposed GFTs could represent spatial-temporal data sets on directed graphs with strong correlation efficiently, and in the undirected graph setting they are essentially the joint GFT in the literature. In this article, we also consider the bandlimiting procedure in frequency domains of the proposed GFTs, and demonstrate their performances on denoising the hourly temperature data sets collected at 32 weather stations in the region of Brest (France) and at 218 locations in the United States.
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来源期刊
IEEE Transactions on Signal and Information Processing over Networks
IEEE Transactions on Signal and Information Processing over Networks Computer Science-Computer Networks and Communications
CiteScore
5.80
自引率
12.50%
发文量
56
期刊介绍: The IEEE Transactions on Signal and Information Processing over Networks publishes high-quality papers that extend the classical notions of processing of signals defined over vector spaces (e.g. time and space) to processing of signals and information (data) defined over networks, potentially dynamically varying. In signal processing over networks, the topology of the network may define structural relationships in the data, or may constrain processing of the data. Topics include distributed algorithms for filtering, detection, estimation, adaptation and learning, model selection, data fusion, and diffusion or evolution of information over such networks, and applications of distributed signal processing.
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