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

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 proceeding › Conference contribution

4 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 language	English
Title of host publication	Proceedings of SPIE - The International Society for Optical Engineering
Subtitle of host publication	Wavelets and Sparsity XIV
Editors	Manos Papadakis, Dimitri Van De Ville, Vivek K. Goyal
Volume	8138
DOIs	https://doi.org/10.1117/12.893481
Publication status	Published - 2011
Event	Wavelets and Sparsity XIV - San Diego, CA, United States Duration: 21 Aug 2011 → 24 Aug 2011

Publication series

Name	Proceedings of SPIE--the International Society for Optical Engineering
Volume	8138
ISSN (Print)	1996-756X
ISSN (Electronic)	0277-786X

Conference

Conference	Wavelets and Sparsity XIV
Country/Territory	United States
City	San Diego, CA
Period	21/08/11 → 24/08/11

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

Access to Document

10.1117/12.893481

Cite this

McEwen, J. D., Puy, G., Thiran, J.-P., Vandergheynst, P., Van De Ville, D., & Wiaux, Y. (2011). Sampling theorems and compressive sensing on the sphere. In M. Papadakis, D. Van De Ville, & V. K. Goyal (Eds.), Proceedings of SPIE - The International Society for Optical Engineering: Wavelets and Sparsity XIV (Vol. 8138). Article 81381F (Proceedings of SPIE--the International Society for Optical Engineering; Vol. 8138). https://doi.org/10.1117/12.893481

McEwen, Jason D ; Puy, Gilles ; Thiran, Jean-Philippe et al. / Sampling theorems and compressive sensing on the sphere. Proceedings of SPIE - The International Society for Optical Engineering: Wavelets and Sparsity XIV. editor / Manos Papadakis ; Dimitri Van De Ville ; Vivek K. Goyal. Vol. 8138 2011. (Proceedings of SPIE--the International Society for Optical Engineering).

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title = "Sampling theorems and compressive sensing on the sphere",

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.",

keywords = "compressive sensing, sampling theorem, Sphere, spherical harmonics",

author = "McEwen, {Jason D} and Gilles Puy and Jean-Philippe Thiran and Pierre Vandergheynst and {Van De Ville}, Dimitri and Yves Wiaux",

year = "2011",

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booktitle = "Proceedings of SPIE - The International Society for Optical Engineering",

note = "Wavelets and Sparsity XIV ; Conference date: 21-08-2011 Through 24-08-2011",

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McEwen, JD, Puy, G, Thiran, J-P, Vandergheynst, P, Van De Ville, D & Wiaux, Y 2011, Sampling theorems and compressive sensing on the sphere. in M Papadakis, D Van De Ville & VK Goyal (eds), Proceedings of SPIE - The International Society for Optical Engineering: Wavelets and Sparsity XIV. vol. 8138, 81381F, Proceedings of SPIE--the International Society for Optical Engineering, vol. 8138, Wavelets and Sparsity XIV, San Diego, CA, United States, 21/08/11. https://doi.org/10.1117/12.893481

Sampling theorems and compressive sensing on the sphere. / McEwen, Jason D; Puy, Gilles; Thiran, Jean-Philippe et al.
Proceedings of SPIE - The International Society for Optical Engineering: Wavelets and Sparsity XIV. ed. / Manos Papadakis; Dimitri Van De Ville; Vivek K. Goyal. Vol. 8138 2011. 81381F (Proceedings of SPIE--the International Society for Optical Engineering; Vol. 8138).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Sampling theorems and compressive sensing on the sphere

AU - McEwen, Jason D

AU - Puy, Gilles

AU - Thiran, Jean-Philippe

AU - Vandergheynst, Pierre

AU - Van De Ville, Dimitri

AU - Wiaux, Yves

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N2 - 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.

AB - 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.

KW - compressive sensing

KW - sampling theorem

KW - Sphere

KW - spherical harmonics

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T3 - Proceedings of SPIE--the International Society for Optical Engineering

BT - Proceedings of SPIE - The International Society for Optical Engineering

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A2 - Van De Ville, Dimitri

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McEwen JD, Puy G, Thiran JP, Vandergheynst P, Van De Ville D, Wiaux Y. Sampling theorems and compressive sensing on the sphere. In Papadakis M, Van De Ville D, Goyal VK, editors, Proceedings of SPIE - The International Society for Optical Engineering: Wavelets and Sparsity XIV. Vol. 8138. 2011. 81381F. (Proceedings of SPIE--the International Society for Optical Engineering). doi: 10.1117/12.893481

Sampling theorems and compressive sensing on the sphere

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Keywords

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