论文标题
伴随模型 - 图形信号处理中的规范模型
The Companion Model -- a Canonical Model in Graph Signal Processing
论文作者
论文摘要
本文介绍了由$ \ textit {canonical} $图形定义的$ \ textit {canonical} $图形信号模型和$ \ textit {canonical} $ shift，$ \ textit {companion} $ graph和$ \ textit {companion} $ shift。这些是规范性的，因为在标准条件下，我们表明任何图形信号处理（GSP）模型都可以转换为规范模型。获得的转换是我们介绍的图形$ z $ -transform（$ \ textrm {g $ z $ t} $）。 GSP规范模型最接近离散信号处理（DSP）时间信号模型：伴侣偏移的结构分解为线路移动和信号延续，就像DSP偏移一样，GSP规范图是有向线图，其终端条件反映了信号延续条件。我们进一步表明，令人惊讶的是，在规范模型中，图形信号的卷积是DSP FFT的快速卷积。
This paper introduces a $\textit{canonical}$ graph signal model defined by a $\textit{canonical}$ graph and a $\textit{canonical}$ shift, the $\textit{companion}$ graph and the $\textit{companion}$ shift. These are canonical because, under standard conditions, we show that any graph signal processing (GSP) model can be transformed into the canonical model. The transform that obtains this is the graph $z$-transform ($\textrm{G$z$T}$) that we introduce. The GSP canonical model comes closest to the discrete signal processing (DSP) time signal models: the structure of the companion shift decomposes into a line shift and a signal continuation just like the DSP shift and the GSP canonical graph is a directed line graph with a terminal condition reflecting the signal continuation condition. We further show that, surprisingly, in the canonical model, convolution of graph signals is fast convolution by the DSP FFT.
