Signal Representations on Graphs: Tools and Applications

S. Chen and R. Varma are with the Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213 USA. Email: [email protected], [email protected]. A. Singh is with the Department of Machine Learning, Carnegie Mellon University, Pittsburgh, PA. Email: [email protected]. J. Kovačević is with the Departments of Electrical and Computer Engineering and Biomedical Engineering, Carnegie Mellon University, Pittsburgh, PA. Email: [email protected]. The authors gratefully acknowledge support from the NSF through awards 1130616,1421919, the University Transportation Center grant (DTRT12GUTC11) from the US Department of Transportation, and the CMU Carnegie Institute of Technology Infrastructure Award. VI Representations of Piecewise-smooth Graph Signals 22 VI-A Graph Signal Models . . . . . . . . . . 22 VI-B Graph Dictionary . . . . . . . . . . . . 23 VI-B1 Properties . . . . . . . . . . 23 VI-C Graph Signal Processing Tasks . . . . . 24 VI-C1 Approximation . . . . . . . . 24 VI-C2 Sampling and Recovery . . . 25 VI-D Case Study: Environmental Change Detection . . . . . . . . . . . . . . . . . . 25