We present a framework for representing and modeling data on graphs. Based on this framework, we study three typical classes of graph signals: smooth graph signals, piecewise-constant graph signals, and piecewise-smooth graph signals. For each class, we provide an explicit definition of the graph signals and construct a corresponding graph dictionary with desirable properties. We then study how such graph dictionary works in two standard tasks: approximation and sampling followed with recovery, both from theoretical as well as algorithmic perspectives. Finally, for each class, we present a case study of a real-world problem by using the proposed methodology.
@article{arxiv.1512.05406,
title = {Signal Representations on Graphs: Tools and Applications},
author = {Siheng Chen and Rohan Varma and Aarti Singh and Jelena Kovačević},
journal= {arXiv preprint arXiv:1512.05406},
year = {2015}
}