Interdisciplinary Distinguished Lecturer: Dr. Antonio Ortega

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Wavelets on Graphs: Theory and Applications

Dr. Antonio Ortega, Professor and Associate Chair of EE-Systems
Signal and Image Processing Institute Department of Electrical Engineering University of Southern California

Dr. Antonio Ortega spoke on Friday, November 16th, 2012 at 12:50PM in Engineering Building II, Room 1230

USAWavelet 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.

Along the way we provide an overview of two potential applications of these transforms in i) distributed data gathering in a sensor network and ii) image/video compression.