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.
翻译:Fleier变形图(GFT)是图示信号处理的基本工具之一,可以将图形信号分解成不同频率组件,并以不同变化模式有效地代表具有强烈相关性的图形信号。对未定向图形上的GFT进行了仔细研究,并提出了几种方法,在定向图形上定义GFTs。在本文中,根据一些图Laplacians的单值分解,我们提议在两个方向图的Cartesian产品图上使用两个GFTs。我们表明,拟议的GFTs可以代表具有很强相关性的定向网络的空间时空数据集,而在非定向图形设置中,它们基本上是文献中GFT的组合。在本文中,我们还考虑了拟议的GFTs光谱域中的带宽度限制程序,并展示了2014年1月布列斯特(法国)地区温度数据集的性能。