Advances in Computational Mathematics

, Volume 5, Issue 1, pp 51–94 | Cite as

Spherical wavelet transform and its discretization

  • Willi Freeden
  • Ulrich Windheuser


A continuous version of spherical multiresolution is described, starting from continuous wavelet transform on the sphere. Scale discretization enables us to construct spherical counterparts to wavelet packets and scale discrete wavelets. The essential tool is the theory of singular integrals on the sphere. It is shown that singular integral operators forming a semigroup of contraction operators of class (C0) (like Abel-Poisson or Gauß-Weierstraß operators) lead in a canonical way to (pyramidal) algorithms.


Spherical continuous wavelet transform scale discretizations wavelet packets Daubechies wavelets (R-)multiresolution analysis 

AMS subject classification

41A58 42C15 44A35 45E99 


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Copyright information

© J.C. Baltzer AG, Science Publishers 1996

Authors and Affiliations

  • Willi Freeden
    • 1
  • Ulrich Windheuser
    • 1
  1. 1.Laboratory of Technomathematics, Geomathematics GroupUniversity of KaiserslauternKaiserslauternGermany

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