论文标题
用于图形上信号处理的Gabor型帧
Gabor-type frames for signal processing on graphs
论文作者
论文摘要
在过去的十年中，已经取得了重大进展来从傅立叶分析中概括经典工具，以分析和过程信号在网络上定义。在本文中，我们提出了一个新的框架，用于构建图形上的信号的Gabor型帧。我们的方法使用线性操作员的一般和灵活的家庭，将其作为翻译。与文献中的先前工作相比，我们的方法在概括了几种现有构造的广泛环境中产生了相关框架的急剧界限。我们还研究了Gabor型框架如何通过利用基础群体的表示理论来为Cayley图所定义的信号行为。我们探讨了如何为Cayley图构建自然的翻译类别，以及特征性的选择如何显着影响所得的翻译运算符和图上框架的属性。
In the past decade, significant progress has been made to generalize classical tools from Fourier analysis to analyze and process signals defined on networks. In this paper, we propose a new framework for constructing Gabor-type frames for signals on graphs. Our approach uses general and flexible families of linear operators acting as translations. Compared to previous work in the literature, our methods yield the sharp bounds for the associated frames, in a broad setting that generalizes several existing constructions. We also examine how Gabor-type frames behave for signals defined on Cayley graphs by exploiting the representation theory of the underlying group. We explore how natural classes of translations can be constructed for Cayley graphs, and how the choice of an eigenbasis can significantly impact the properties of the resulting translation operators and frames on the graph.
