Applied and Computational Harmonic Analysis ( IF 2.6 ) Pub Date : 2020-04-21 , DOI: 10.1016/j.acha.2020.04.001 Lihua Yang , Anna Qi , Chao Huang , Jianfeng Huang
The definition of graph Fourier transform is a fundamental issue in graph signal processing. Conventional graph Fourier transform is defined through the eigenvectors of the graph Laplacian matrix, which minimize the norm signal variation. In this paper, we propose a generalized definition of graph Fourier transform based on the norm variation minimization. We obtain a necessary condition satisfied by the Fourier basis, and provide a fast greedy algorithm to approximately construct the Fourier basis. Numerical experiments are also provided to compare the differences between the Laplacian basis, basis and greedy basis.
中文翻译:
图傅立叶变换基于ℓ 1个范变差最小化
图傅立叶变换的定义是图信号处理中的一个基本问题。传统的图傅立叶变换是通过图拉普拉斯矩阵的特征向量定义的,该特征向量使规范信号变化。在本文中,我们提出了基于图的傅立叶变换的广义定义规范变化最小化。我们获得了满足以下条件的必要条件: 傅立叶基础,并提供一种快速贪婪算法来近似构造 傅立叶基础。还提供了数值实验来比较拉普拉斯算子之间的差异, 基础和贪婪的基础。