Sampling theorems and compressive sensing on the sphere

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.


Published in:
Proceedings of SPIE, Wavelets and Sparsity XIV, 8138 81381F-1
Presented at:
Conference on Wavelets and Sparsity XIV, San Diego, CA, August 21-25, 2011
Year:
2011
Publisher:
Spie-Int Soc Optical Engineering, Po Box 10, Bellingham, Wa 98227-0010 Usa
Keywords:
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 Record created 2011-02-13, last modified 2018-09-13

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