Sampling theorems and compressive sensing on the sphere

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
Subtitle of host publicationWavelets and Sparsity XIV
EditorsManos Papadakis, Dimitri Van De Ville, Vivek K. Goyal
Volume8138
DOIs
Publication statusPublished - 2011
EventWavelets and Sparsity XIV - San Diego, CA, United States
Duration: 21 Aug 201124 Aug 2011

Publication series

NameProceedings of SPIE--the International Society for Optical Engineering
Volume8138
ISSN (Print)1996-756X
ISSN (Electronic)0277-786X

Conference

ConferenceWavelets and Sparsity XIV
CountryUnited States
CitySan Diego, CA
Period21/08/1124/08/11

Keywords

  • compressive sensing
  • sampling theorem
  • Sphere
  • spherical harmonics

ASJC Scopus subject areas

  • Applied Mathematics
  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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