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URN: urn:nbn:de:0030-drops-19216
URL: http://drops.dagstuhl.de/opus/volltexte/2009/1921/

Dahlke, Stephan ; Steidl, Gabriele ; Teschke, Gerd

The Continuous Shearlet Transform in Arbitrary Space Dimensions

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Abstract

This note is concerned with the generalization of the continuous shearlet transform to higher dimensions. Similar to the two-dimensional case, our approach is based on translations, anisotropic dilations and specific shear matrices. We show that the associated integral transform again originates from a square-integrable representation of a specific group, the full $n$-variate shearlet group. Moreover, we verify that by applying the coorbit theory, canonical scales of smoothness spaces and associated Banach frames can be derived. We also indicate how our transform can be used to characterize singularities in signals.

BibTeX - Entry

@InProceedings{dahlke_et_al:DSP:2009:1921,
  author =	{Stephan Dahlke and Gabriele Steidl and Gerd Teschke},
  title =	{The Continuous Shearlet  Transform in Arbitrary Space Dimensions},
  booktitle =	{Structured Decompositions and Efficient Algorithms},
  year =	{2009},
  editor =	{Stephan Dahlke and Ingrid Daubechies and Michal Elad and Gitta Kutyniok and Gerd Teschke},
  number =	{08492},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/1921},
  annote =	{Keywords: }
}

Seminar: 08492 - Structured Decompositions and Efficient Algorithms
Issue date: 2009
Date of publication: 10.03.2009


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