Signal Representations on Graphs: Tools and Applications
This work addresses the problem of signal processing on graphs for researchers and practitioners, but it appears incremental as it builds on existing graph signal concepts.
The authors developed a framework for representing and modeling data on graphs, defining three classes of graph signals and constructing corresponding dictionaries, and applied it to approximation and sampling tasks with case studies on real-world problems.
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.