publication . Article . Preprint . 2015

A Novel Sampling Theorem on the Rotation Group

Jason D. McEwen; Boris Leistedt; Martin Büttner; Hiranya V. Peiris; Yves Wiaux;
Open Access English
  • Published: 12 Aug 2015
  • Publisher: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
  • Country: United Kingdom
Abstract
Comment: 5 pages, 2 figures, minor changes to match version accepted for publication. Code available at http://www.sothree.org
Subjects
free text keywords: Science & Technology, Technology, Engineering, Electrical & Electronic, Engineering, Harmonic analysis, rotation group, sampling, spheres, wigner transform, SPHERICAL HARMONIC TRANSFORMS, WAVELETS, GRAVITY, SERIES, Signal Processing, Electrical and Electronic Engineering, Applied Mathematics, Computer Science - Information Theory, Astrophysics - Instrumentation and Methods for Astrophysics, Sampling (statistics), Nyquist–Shannon sampling theorem, Harmonic wavelet transform, Fourier transform, symbols.namesake, symbols, Equiangular polygon, Rotation group SO, Periodic graph (geometry), Mathematics, Discrete mathematics, Discrete Fourier transform
Funded by
RCUK| Signal analysis on the sphere
Project
  • Funder: Research Council UK (RCUK)
  • Project Code: EP/M011852/1
  • Funding stream: EPSRC
,
EC| COSMICDAWN
Project
COSMICDAWN
Understanding the Origin of Cosmic Structure
  • Funder: European Commission (EC)
  • Project Code: 306478
  • Funding stream: FP7 | SP2 | ERC
33 references, page 1 of 3

[1] C. E. Shannon, “Communication in the presence of noise,” Proc. IRE, vol. 37, pp. 10-21, 1949.

[2] J. W. Cooley and J. W. Tukey, “An algorithm for the machine calculation of complex fourier series,” Math. Comp., vol. 19, pp. 297-301, 1965. [OpenAIRE]

[3] Planck Collaboration I, “Planck 2013 results. I. Overview of products and scientific results,” Astron. & Astrophys., vol. 571, no. A1, 2014.

[4] C. P. Ahn, R. Alexandroff, C. Allende Prieto, S. F. Anderson, T. Anderton, B. H. Andrews, E´ . Aubourg, S. Bailey, E. Balbinot, R. Barnes, and et al., “The Ninth Data Release of the Sloan Digital Sky Survey: First Spectroscopic Data from the SDSS-III Baryon Oscillation Spectroscopic Survey,” Astrophys. J. Supp., vol. 203, p. 21, Dec. 2012.

[5] P. Audet, “Directional wavelet analysis on the sphere: Application to gravity and topography of the terrestrial planets,” J. Geophys. Res., vol. 116, no. E1, 2011. [OpenAIRE]

[6] --, “Toward mapping the effective elastic thickness of planetary lithospheres from a spherical wavelet analysis of gravity and topography,” Phys. Earth Planet In., vol. 226, no. 0, pp. 48-82, 2014.

[7] S. Swenson and J. Wahr, “Methods for inferring regional surfacemass anomalies from GRACE measurements of time-variable gravity,” J. Geophys. Res., vol. 107, pp. 2193-278, 2002. [OpenAIRE]

[8] D. S. Tuch, “Q-ball imaging,” Magn. Reson. Med., vol. 52, no. 6, pp. 1358-1372, 2004.

[9] J. R. Driscoll and D. M. J. Healy, “Computing Fourier transforms and convolutions on the sphere,” Adv. Appl. Math., vol. 15, pp. 202-250, 1994.

[10] J. D. McEwen and Y. Wiaux, “A novel sampling theorem on the sphere,” IEEE Trans. Sig. Proc., vol. 59, no. 12, pp. 5876-5887, 2011. [OpenAIRE]

[11] J. D. McEwen, “Fast, exact (but unstable) spin spherical harmonic transforms,” All Res. J. Phys., vol. 1, no. 1, 2011.

[12] K. M. Huffenberger and B. D. Wandelt, “Fast and exact spin-s spherical harmonic transforms,” Astrophys. J. Supp., vol. 189, pp. 255-260, 2010. [OpenAIRE]

[13] Z. Khalid, R. A. Kennedy, and J. D. McEwen, “An optimaldimensionality sampling scheme on the sphere with fast spherical harmonic transforms,” IEEE Trans. Sig. Proc., vol. 62, no. 17, pp. 4597- 4610, 2014.

[14] B. Leistedt and J. D. McEwen, “Exact wavelets on the ball,” IEEE Trans. Sig. Proc., vol. 60, no. 12, pp. 6257-6269, 2012. [OpenAIRE]

[15] J.-P. Antoine and P. Vandergheynst, “Wavelets on the n-sphere and related manifolds,” J. Math. Phys., vol. 39, no. 8, pp. 3987-4008, 1998.

33 references, page 1 of 3
Abstract
Comment: 5 pages, 2 figures, minor changes to match version accepted for publication. Code available at http://www.sothree.org
Subjects
free text keywords: Science & Technology, Technology, Engineering, Electrical & Electronic, Engineering, Harmonic analysis, rotation group, sampling, spheres, wigner transform, SPHERICAL HARMONIC TRANSFORMS, WAVELETS, GRAVITY, SERIES, Signal Processing, Electrical and Electronic Engineering, Applied Mathematics, Computer Science - Information Theory, Astrophysics - Instrumentation and Methods for Astrophysics, Sampling (statistics), Nyquist–Shannon sampling theorem, Harmonic wavelet transform, Fourier transform, symbols.namesake, symbols, Equiangular polygon, Rotation group SO, Periodic graph (geometry), Mathematics, Discrete mathematics, Discrete Fourier transform
Funded by
RCUK| Signal analysis on the sphere
Project
  • Funder: Research Council UK (RCUK)
  • Project Code: EP/M011852/1
  • Funding stream: EPSRC
,
EC| COSMICDAWN
Project
COSMICDAWN
Understanding the Origin of Cosmic Structure
  • Funder: European Commission (EC)
  • Project Code: 306478
  • Funding stream: FP7 | SP2 | ERC
33 references, page 1 of 3

[1] C. E. Shannon, “Communication in the presence of noise,” Proc. IRE, vol. 37, pp. 10-21, 1949.

[2] J. W. Cooley and J. W. Tukey, “An algorithm for the machine calculation of complex fourier series,” Math. Comp., vol. 19, pp. 297-301, 1965. [OpenAIRE]

[3] Planck Collaboration I, “Planck 2013 results. I. Overview of products and scientific results,” Astron. & Astrophys., vol. 571, no. A1, 2014.

[4] C. P. Ahn, R. Alexandroff, C. Allende Prieto, S. F. Anderson, T. Anderton, B. H. Andrews, E´ . Aubourg, S. Bailey, E. Balbinot, R. Barnes, and et al., “The Ninth Data Release of the Sloan Digital Sky Survey: First Spectroscopic Data from the SDSS-III Baryon Oscillation Spectroscopic Survey,” Astrophys. J. Supp., vol. 203, p. 21, Dec. 2012.

[5] P. Audet, “Directional wavelet analysis on the sphere: Application to gravity and topography of the terrestrial planets,” J. Geophys. Res., vol. 116, no. E1, 2011. [OpenAIRE]

[6] --, “Toward mapping the effective elastic thickness of planetary lithospheres from a spherical wavelet analysis of gravity and topography,” Phys. Earth Planet In., vol. 226, no. 0, pp. 48-82, 2014.

[7] S. Swenson and J. Wahr, “Methods for inferring regional surfacemass anomalies from GRACE measurements of time-variable gravity,” J. Geophys. Res., vol. 107, pp. 2193-278, 2002. [OpenAIRE]

[8] D. S. Tuch, “Q-ball imaging,” Magn. Reson. Med., vol. 52, no. 6, pp. 1358-1372, 2004.

[9] J. R. Driscoll and D. M. J. Healy, “Computing Fourier transforms and convolutions on the sphere,” Adv. Appl. Math., vol. 15, pp. 202-250, 1994.

[10] J. D. McEwen and Y. Wiaux, “A novel sampling theorem on the sphere,” IEEE Trans. Sig. Proc., vol. 59, no. 12, pp. 5876-5887, 2011. [OpenAIRE]

[11] J. D. McEwen, “Fast, exact (but unstable) spin spherical harmonic transforms,” All Res. J. Phys., vol. 1, no. 1, 2011.

[12] K. M. Huffenberger and B. D. Wandelt, “Fast and exact spin-s spherical harmonic transforms,” Astrophys. J. Supp., vol. 189, pp. 255-260, 2010. [OpenAIRE]

[13] Z. Khalid, R. A. Kennedy, and J. D. McEwen, “An optimaldimensionality sampling scheme on the sphere with fast spherical harmonic transforms,” IEEE Trans. Sig. Proc., vol. 62, no. 17, pp. 4597- 4610, 2014.

[14] B. Leistedt and J. D. McEwen, “Exact wavelets on the ball,” IEEE Trans. Sig. Proc., vol. 60, no. 12, pp. 6257-6269, 2012. [OpenAIRE]

[15] J.-P. Antoine and P. Vandergheynst, “Wavelets on the n-sphere and related manifolds,” J. Math. Phys., vol. 39, no. 8, pp. 3987-4008, 1998.

33 references, page 1 of 3
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