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Proceedings Paper

Sampling theorems and compressive sensing on the sphere
Author(s): Jason D. McEwen; Gilles Puy; Jean-Philippe Thiran; Pierre Vandergheynst; Dimitri Van De Ville; Yves Wiaux
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Paper Abstract

We discuss a novel sampling theorem on the sphere developed by McEwen & Wiaux recently through an association between the sphere and the torus. To represent a band-limited signal exactly, this new sampling theorem requires less than half the number of samples of other equiangular sampling theorems on the sphere, such as the canonical Driscoll & Healy sampling theorem. A reduction in the number of samples required to represent a band-limited signal on the sphere has important implications for compressive sensing, both in terms of the dimensionality and sparsity of signals. We illustrate the impact of this property with an inpainting problem on the sphere, where we show superior reconstruction performance when adopting the new sampling theorem.

Paper Details

Date Published: 27 September 2011
PDF: 9 pages
Proc. SPIE 8138, Wavelets and Sparsity XIV, 81381F (27 September 2011); doi: 10.1117/12.893481
Show Author Affiliations
Jason D. McEwen, Ecole Polytechnique Fédérale de Lausanne (Switzerland)
Gilles Puy, Ecole Polytechnique Fédérale de Lausanne (Switzerland)
Jean-Philippe Thiran, Ecole Polytechnique Fédérale de Lausanne (Switzerland)
Pierre Vandergheynst, Ecole Polytechnique Fédérale de Lausanne (Switzerland)
Dimitri Van De Ville, Ecole Polytechnique Fédérale de Lausanne (Switzerland)
Univ. of Geneva (Switzerland)
Yves Wiaux, Ecole Polytechnique Fédérale de Lausanne (Switzerland)
Univ. of Geneva (Switzerland)


Published in SPIE Proceedings Vol. 8138:
Wavelets and Sparsity XIV
Manos Papadakis; Dimitri Van De Ville; Vivek K. Goyal, Editor(s)

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