Discrete Signal Processing on Graphs: Frequency Analysis

Aliaksei Sandryhaila, Jose M. F. Moura
2014 IEEE Transactions on Signal Processing  
Signals and datasets that arise in physical and engineering applications, as well as social, genetics, biomolecular, and many other domains, are becoming increasingly larger and more complex. In contrast to traditional time and image signals, data in these domains are supported by arbitrary graphs. Signal processing on graphs extends concepts and techniques from traditional signal processing to data indexed by generic graphs. This paper studies the concepts of low and high frequencies on
more » ... and low-, high-and band-pass graph signals and graph filters. In traditional signal processing, these concepts are easily defined because of a natural frequency ordering that has a physical interpretation. For signals residing on graphs, in general, there is no obvious frequency ordering. We propose a definition of total variation for graph signals that naturally leads to a frequency ordering on graphs and defines low-, high-, and band-pass graph signals and filters. We study the design of graph filters with specified frequency response, and illustrate our approach with applications to sensor malfunction detection and data classification.
doi:10.1109/tsp.2014.2321121 fatcat:co5lmubojra4vca7egk627p5oe