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Proceedings Paper

Higher-order graph wavelets and sparsity on circulant graphs
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Paper Abstract

The notion of a graph wavelet gives rise to more advanced processing of data on graphs due to its ability to operate in a localized manner, across newly arising data-dependency structures, with respect to the graph signal and underlying graph structure, thereby taking into consideration the inherent geometry of the data. In this work, we tackle the problem of creating graph wavelet filterbanks on circulant graphs for a sparse representation of certain classes of graph signals. The underlying graph can hereby be data-driven as well as fixed, for applications including image processing and social network theory, whereby clusters can be modelled as circulant graphs, respectively. We present a set of novel graph wavelet filter-bank constructions, which annihilate higher-order polynomial graph signals (up to a border effect) defined on the vertices of undirected, circulant graphs, and are localised in the vertex domain. We give preliminary results on their performance for non-linear graph signal approximation and denoising. Furthermore, we provide extensions to our previously developed segmentation-inspired graph wavelet framework for non-linear image approximation, by incorporating notions of smoothness and vanishing moments, which further improve performance compared to traditional methods.

Paper Details

Date Published: 24 August 2015
PDF: 9 pages
Proc. SPIE 9597, Wavelets and Sparsity XVI, 95971E (24 August 2015); doi: 10.1117/12.2192003
Show Author Affiliations
Madeleine S. Kotzagiannidis, Imperial College London (United Kingdom)
Pier Luigi Dragotti, Imperial College London (United Kingdom)


Published in SPIE Proceedings Vol. 9597:
Wavelets and Sparsity XVI
Manos Papadakis; Vivek K. Goyal; Dimitri Van De Ville, Editor(s)

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