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Proceedings Paper

On the computation of directional scale-discretized wavelet transforms on the sphere
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Paper Abstract

We review scale-discretized wavelets on the sphere, which are directional and allow one to probe oriented structure in data defined on the sphere. Furthermore, scale-discretized wavelets allow in practice the exact synthesis of a signal from its wavelet coefficients. We present exact and efficient algorithms to compute the scale-discretized wavelet transform of band-limited signals on the sphere. These algorithms are implemented in the publicly available S2DW code. We release a new version of S2DW that is parallelized and contains additional code optimizations. Note that scale-discretized wavelets can be viewed as a directional generalization of needlets. Finally, we outline future improvements to the algorithms presented, which can be achieved by exploiting a new sampling theorem on the sphere developed recently by some of the authors.

Paper Details

Date Published: 26 September 2013
PDF: 13 pages
Proc. SPIE 8858, Wavelets and Sparsity XV, 88580I (26 September 2013); doi: 10.1117/12.2022889
Show Author Affiliations
Jason D. McEwen, Univ. College London (United Kingdom)
Pierre Vandergheynst, Ecole Polytechnique Federale de Lausanne (Switzerland)
Yves Wiaux, Ecole Polytechnique Federale de Lausanne (Switzerland)
Univ. Hospital Lausanne (Switzerland)
Univ. of Geneva (Switzerland)


Published in SPIE Proceedings Vol. 8858:
Wavelets and Sparsity XV
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)

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