论文标题
在简单复合物上处理信号
Signal processing on simplicial complexes
论文作者
论文摘要
图形信号处理（GSP）的理论发展和应用引起了很多关注。在经典的GSP中，基础结构受维度的限制。图是建模二进制关系的组合对象，并且不会直接建模复杂的N- ARY关系。图形的一个可能的高维概括是简单的复合物。它们是图形约束情况和超图的一般情况之间的一步。在本文中，我们在简单复合物上开发了一个信号处理框架，以便在局限于图表上的信号时恢复传统的GSP理论。值得一提的是，尽管本文的重点是简单的复合物，但该框架的起作用更为普遍。我们演示了如何使用数值示例使用框架执行信号处理。
Theoretical development and applications of graph signal processing (GSP) have attracted much attention. In classical GSP, the underlying structures are restricted in terms of dimensionality. A graph is a combinatorial object that models binary relations, and it does not directly model complex n-ary relations. One possible high dimensional generalization of graphs are simplicial complexes. They are a step between the constrained case of graphs and the general case of hypergraphs. In this paper, we develop a signal processing framework on simplicial complexes, such that we recover the traditional GSP theory when restricted to signals on graphs. It is worth mentioning that the framework works much more generally, though the focus of the paper is on simplicial complexes. We demonstrate how to perform signal processing with the framework using numerical examples.
