arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2005.04851eess.SP
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子图信号处理

Subgraph Signal Processing

Feng Ji, Wee Peng Tay, Giacomo Kahn

摘要:

图形信号处理,如图形傅里叶变换,需要在图形的每个顶点处的全图形信号。然而,实际上,仅顶点子集处的信号可为可用的。我们提出了一个子图信号处理的框架,涉及一个图形移位运算符或过滤器上的子图与过滤器上的环境图通过运营商损失。它允许我们定义子图信号的移位运算符,这对限制于环境图的不同子图(我们称之为半移位不变)的移位不变滤波器的混合物具有有意义的解释和关系。这导致子图信号的频域概念在某种意义上与全图信号的频域概念一致。我们应用子图信号处理机的几个应用程序,并证明了这个框架的效用的情况下,只有部分图形信号进行观察。

英文摘要:

Graph signal processing, like the graph Fourier transform, requires the full graph signal at every vertex of the graph. However, in practice, only signals at a subset of vertices may be available. We propose a subgraph signal processing framework that relates a graph shift operator or filter on a subgraph with a filter on the ambient graph through an operator loss. It allows us to define shift operators for the subgraph signal, which has a meaningful interpretation and relation to mixtures of shift invariant filters restricted to different subgraphs of the ambient graph (which we call semi shift invariant). This leads to a notion of frequency domain for the subgraph signal consistent in some sense with that of the full graph signal. We apply the subgraph signal processing machinery to several applications and demonstrate the utility of this framework in cases where only partial graph signals are observed.

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