compendium

S. Chen, T. Li, R. Varma, A. Singh, and J. Kovačević. Signal representations on graphs: Tools and applications. IEEE Trans. Signal Process., Mar. 2016. Submitted.

[ pdf | @ arXiv | bibtex]

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.

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