On the computation of directional scale-discretized wavelet transforms on the sphere

Jason D McEwen, Pierre Vandergheynst, Yves Wiaux

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

13 Citations (Scopus)

Abstract

We review scale-discretized wavelets on the sphere, which are directional and allow one to probe oriented structure in data defined on the sphere. Furthermore, scale-discretized wavelets allow in practice the exact synthesis of a signal from its wavelet coefficients. We present exact and efficient algorithms to compute the scale-discretized wavelet transform of band-limited signals on the sphere. These algorithms are implemented in the publicly available S2DW code. We release a new version of S2DW that is parallelized and contains additional code optimizations. Note that scale-discretized wavelets can be viewed as a directional generalization of needlets. Finally, we outline future improvements to the algorithms presented, which can be achieved by exploiting a new sampling theorem on the sphere developed recently by some of the authors.

Original languageEnglish
Title of host publicationWavelets and Sparsity XV
EditorsDimitri Van De Ville, Vivek K. Goyal, Manos Papadakis
PublisherSPIE
Volume8858
ISBN (Print)9780819497086
DOIs
Publication statusPublished - 2013
EventWavelets and Sparsity XV - San Diego, CA, United States
Duration: 26 Aug 201329 Aug 2013

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume8858
ISSN (Print)1996-756X

Conference

ConferenceWavelets and Sparsity XV
CountryUnited States
CitySan Diego, CA
Period26/08/1329/08/13

Keywords

  • Sampling theorem
  • Sphere
  • Wavelet transform

ASJC Scopus subject areas

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

Fingerprint Dive into the research topics of 'On the computation of directional scale-discretized wavelet transforms on the sphere'. Together they form a unique fingerprint.

Cite this