Wavelets on Graphs: Theory and Applications
Antonio Ortega Signal and Image Processing Institute Department of Electrical Engineering University of Southern California Los Angeles, CA USA
Wavelet transforms have become popular tools for numerous signal processing tasks, from compression to analysis or denoising. These transforms provide a class of signal representations with flexible time (or space) and frequency localization. Recent extensions of these transforms have been targeted to incorporate arbitrary directionality in the transform (e.g., Bandelets, Contourlets).
In this presentation we focus on wavelet-like, multiresolution transforms for datasets that are defined on arbitrary graphs. This is an area that has started to attract some interest only very recently and yet has the potential to have significant impact in a number of applications. Examples of datasets that could be seen as graphs include data distributed in a sensor network, image data traversed in arbitrary fashion, or data available in online social networks.
We first provide an overview of our recent work in the development of wavelets for graphs data. In particular we show constructions based on lifting as well as an example design based simple graph filters. These are among the first critically sampled wavelet representations that have been proposed for arbitrary graph data.
We then provide an overview of two potential applications of these transforms in i) distributed data gathering in a sensor network and ii) image compression.