Sampling Signals on Graphs: From Theory to Applications
It addresses the problem of extending sampling theory to graph-based data for researchers and practitioners in graph signal processing, but it is incremental as it reviews existing progress.
This paper reviews the theory and applications of sampling signals on graphs, highlighting how it differs from traditional signal sampling due to differences in properties like shift invariance and bandlimitedness.
The study of sampling signals on graphs, with the goal of building an analog of sampling for standard signals in the time and spatial domains, has attracted considerable attention recently. Beyond adding to the growing theory on graph signal processing (GSP), sampling on graphs has various promising applications. In this article, we review current progress on sampling over graphs focusing on theory and potential applications. Although most methodologies used in graph signal sampling are designed to parallel those used in sampling for standard signals, sampling theory for graph signals significantly differs from the theory of Shannon--Nyquist and shift-invariant sampling. This is due in part to the fact that the definitions of several important properties, such as shift invariance and bandlimitedness, are different in GSP systems. Throughout this review, we discuss similarities and differences between standard and graph signal sampling and highlight open problems and challenges.