论文标题
基于定向laplacian的单数值分解的图形傅立叶变换
Graph Fourier transform based on singular value decomposition of directed Laplacian
论文作者
论文摘要
图傅立叶变换（GFT）是图形信号处理中的一个基本概念。在本文中，基于Laplacian的单数值分解，我们在有向图上引入了GFT的新颖定义，并使用Laplacian的单数值来携带图频率的概念。拟议的GFT的％。所提出的GFT与无向图设置中的常规GFT一致，并且在有向循环图上，提出的GFT是经典的离散傅立叶变换，直到某些旋转，置换和相位调节。我们表明，可以通过解决一些限制的最小化问题以低计算成本来评估所提出的GFT的频率和频率成分。数值证明表明，所提出的GFT可以有效地表示具有不同变化模式的图形信号。
Graph Fourier transform (GFT) is a fundamental concept in graph signal processing. In this paper, based on singular value decomposition of Laplacian, we introduce a novel definition of GFT on directed graphs, and use singular values of Laplacian to carry the notion of graph frequencies. % of the proposed GFT. The proposed GFT is consistent with the conventional GFT in the undirected graph setting, and on directed circulant graphs, the proposed GFT is the classical discrete Fourier transform, up to some rotation, permutation and phase adjustment. We show that frequencies and frequency components of the proposed GFT can be evaluated by solving some constrained minimization problems with low computational cost. Numerical demonstrations indicate that the proposed GFT could represent graph signals with different modes of variation efficiently.
