Signal Representations on Graphs: Tools and Applications

Understand

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.