论文标题
图形傅立叶变换在有向产品图上
Graph Fourier transforms on directed product graphs
论文作者
论文摘要
图形傅立叶变换（GFT）是图形信号处理中的基本工具之一，将图形信号分解为不同的频率组件，并通过有效的变化模式来表示具有强相关性的图形信号。已经对无向图上的GFT进行了充分的研究，并提出了几种方法来定义有向图上的GFT。在本文中，基于某些图Laplacians的奇异值分解，我们在两个有向图的笛卡尔产品图上提出了两个GFT。我们表明，所提出的GFT可以在有效相关性的有向网络上代表空间数据集，在无向图设置中，它们本质上是文献中的关节GFT。在本文中，我们还考虑了拟议的GFT的频谱域中的带限制程序，并证明了其性能，以将2014年1月在布雷斯特（法国）地区的温度数据设置降低。
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 effectively. The GFT on undirected graphs has been well studied and several approaches have been proposed to define GFTs on directed graphs. In this paper, 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 networks with strong correlation efficiently, and in the undirected graph setting they are essentially the joint GFT in the literature. In this paper, we also consider the bandlimiting procedure in the spectral domain of the proposed GFTs, and demonstrate its performance to denoise the temperature data set in the region of Brest (France) on January 2014.
