The Dual Graph Shift Operator: Identifying the Support of the Frequency Domain
The Dual Graph Shift Operator: Identifying the Support of the Frequency Domain
复制标题
对偶图移位算子：识别频域的支持
DOI：
10.1007/s00041-021-09850-1
复制
发表时间：
2021
影响因子：
1.2
通讯作者：
Marques, Antonio G.
中科院分区：
文献类型：
--
作者：
Leus, Geert;Segarra, Santiago;Ribeiro, Alejandro;Marques, Antonio G.
当代数据通常由不规则结构支持，可以通过图表方便地捕获。考虑到这种图形支持对于分析数据至关重要，从而产生了称为图形信号处理（GSP）的领域。 GSP 中两个最重要的工具是图移位算子 (GSO)，它是一个考虑图拓扑的稀疏矩阵，以及图傅里叶变换 (GFT)，它将图信号映射到由许多与图相关的类傅里叶基向量跨越的频域。图形信号的这种替代表示被命名为图形频率信号。为了解释该图频率信号的支持，已经进行了多次尝试，但它们都导致了一维解释。但是，如果原始信号的支持由图形捕获，为什么图形频率信号会具有简单的一维支持？与现有工作不同，我们提出了对图频率信号的不规则支持，我们将其称为对偶图。双 GSO 可以更好地解释图频率信号及其域，有助于理解不同图频率如何相关和聚类，能够开发更好的图滤波器和滤波器组，并有助于将经典 SP 结果推广到图域。
Contemporary data is often supported by an irregular structure, which can be conveniently captured by a graph. Accounting for this graph support is crucial to analyze the data, leading to an area known as graph signal processing (GSP). The two most important tools in GSP are the graph shift operator (GSO), which is a sparse matrix accounting for the topology of the graph, and the graph Fourier transform (GFT), which maps graph signals into a frequency domain spanned by a number of graph-related Fourier-like basis vectors. This alternative representation of a graph signal is denominated the graph frequency signal. Several attempts have been undertaken in order to interpret the support of this graph frequency signal, but they all resulted in a one-dimensional interpretation. However, if the support of the original signal is captured by a graph, why would the graph frequency signal have a simple one-dimensional support? Departing from existing work, we propose an irregular support for the graph frequency signal, which we coin dual graph. A dual GSO leads to a better interpretation of the graph frequency signal and its domain, helps to understand how the different graph frequencies are related and clustered, enables the development of better graph filters and filter banks, and facilitates the generalization of classical SP results to the graph domain.
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