Sampling Signals on Graphs: From Theory to Applications
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 is reviewed, focusing on theory and potential applications.
Abstract
The study of sampling signals on graphs, with the goal of building an analog\nof sampling for standard signals in the time and spatial domains, has attracted\nconsiderable attention recently. Beyond adding to the growing theory on graph\nsignal processing (GSP), sampling on graphs has various promising applications.\nIn this article, we review current progress on sampling over graphs focusing on\ntheory and potential applications. Although most methodologies used in graph\nsignal sampling are designed to parallel those used in sampling for standard\nsignals, sampling theory for graph signals significantly differs from the\ntheory of Shannon--Nyquist and shift-invariant sampling. This is due in part to\nthe fact that the definitions of several important properties, such as shift\ninvariance and bandlimitedness, are different in GSP systems. Throughout this\nreview, we discuss similarities and differences between standard and graph\nsignal sampling and highlight open problems and challenges.\n