Localization, Decomposition, and Dictionary Learning of Piecewise-Constant Signals on Graphs

Understand

Motivated by the need to extract meaning from large amounts of complex structured data, we consider three critical problems on graphs: localization, decomposition, and dictionary learning of piecewise-constant signals.

• These graph-based problems are related to many real-world applications, such as localizing stimulus in brain connectivity networks, and mining traffic events in city street networks, where the key issue is to find the supports of localized activated patterns.
• Counterparts of these problems in classical signal/image processing, such as impulse detection and foreground detection, have been studied over the past few decades.
• We use piecewise-constant graph signals to model localized patterns, where each piece indicates a localized pattern that exhibits homogeneous internal behavior and the number of pieces indicates the number of localized patterns.