Multidimensional Wavelets and Generalizations

  • Syed Twareque Ali
  • Jean-Pierre Antoine
  • Jean-Pierre Gazeau
Chapter
Part of the Theoretical and Mathematical Physics book series (TMP)

Abstract

The continuous wavelet transform can be extended to arbitrary dimensions and this is the topic of this chapter. We begin with the general mathematical analysis, with some emphasis on the distinction between isotropic and directional wavelets. Next we particularize to 2-D, the most important case for applications in image analysis, discussing its distinctive properties and some applications. Finally we describe in some detail a number of generalizations, such as multiselective wavelets, ridgelets, curvelets and shearlets.

Keywords

Anisotropy Manifold Covariance Radar Vorticity 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Syed Twareque Ali
    • 1
  • Jean-Pierre Antoine
    • 2
  • Jean-Pierre Gazeau
    • 3
    • 4
  1. 1.Department of Mathematics and StatisticsConcordia UniversityMontréalCanada
  2. 2.Institut de Recherche en Mathématique et Physique (IRMP)Université Catholique de LouvainLouvain-la-NeuveBelgium
  3. 3.Astroparticules et Cosmologie (APC, UMR 7164)Université Paris DiderotSorbonne Paris Cité ParisFrance
  4. 4.Centro Brasileiro de Pesquisas Fisicas (CBPF)Rio de JaneiroBrasil

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