论文标题
拓扑SLEPIAN：信号的最大局部表示形式
Topological Slepians: Maximally Localized Representations of Signals over Simplicial Complexes
论文作者
论文摘要
本文介绍了拓扑SLEPIAN，即，在拓扑空间（例如，简单的复合物）上定义了一类新的信号，这些信号最大程度地集中在拓扑结构域（例如，在一组节点，边缘，三角形，三角形等）上，并且在双重域上局部化，并在双重域（例如，频率设置）。这些信号作为由适当的定位运算符构建的基质的主要特征向量获得，该矩阵构建了拓扑和频域的作用。然后，我们建议一种原则上的程序来构建拓扑slepians的字典，从理论上讲，该词典提供了非分类框架。最后，我们评估了提出的拓扑Slepian词典在两种应用中的有效性，即稀疏信号表示和边缘流的降解。
This paper introduces topological Slepians, i.e., a novel class of signals defined over topological spaces (e.g., simplicial complexes) that are maximally concentrated on the topological domain (e.g., over a set of nodes, edges, triangles, etc.) and perfectly localized on the dual domain (e.g., a set of frequencies). These signals are obtained as the principal eigenvectors of a matrix built from proper localization operators acting over topology and frequency domains. Then, we suggest a principled procedure to build dictionaries of topological Slepians, which theoretically provide non-degenerate frames. Finally, we evaluate the effectiveness of the proposed topological Slepian dictionary in two applications, i.e., sparse signal representation and denoising of edge flows.
