论文标题
子图信号处理
Subgraph Signal Processing
论文作者
论文摘要
图形信号处理，例如图形傅立叶变换，需要图形的每个顶点的完整图信号。但是，实际上，只能在顶点子集中提供信号。我们提出了一个子图信号处理框架，该框架通过操作员损失将图形移动操作员或子图上的过滤器与环境图上的过滤器相关联。它允许我们为子图信号定义移位运算符，该信号具有有意义的解释，并且与仅限于环境图的不同子图（我们称之为半偏移不变的）的不同子图的混合物的关系。从某种意义上说，这导致了子图信号与完整图信号一致的频域的概念。我们将子图信号处理机械应用于几个应用程序，并在仅观察到部分图信号的情况下证明了该框架的实用性。
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.
