Sampling theorems and compressive sensing on the sphere

Jason D. McEwen; Gilles Puy; Jean-Philippe Thiran; Pierre Vandergheynst; Dimitri Van De Ville; Yves Wiaux

doi:10.1117/12.893481

27 September 2011 Sampling theorems and compressive sensing on the sphere

Jason D. McEwen, Gilles Puy, Jean-Philippe Thiran, Pierre Vandergheynst, Dimitri Van De Ville, Yves Wiaux

Proceedings Volume 8138, Wavelets and Sparsity XIV; 81381F (2011) https://doi.org/10.1117/12.893481
Event: SPIE Optical Engineering + Applications, 2011, San Diego, California, United States

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.

Citation Download Citation

Jason D. McEwen, Gilles Puy, Jean-Philippe Thiran, Pierre Vandergheynst, Dimitri Van De Ville, and Yves Wiaux "Sampling theorems and compressive sensing on the sphere", Proc. SPIE 8138, Wavelets and Sparsity XIV, 81381F (27 September 2011); https://doi.org/10.1117/12.893481

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