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The Continuous Shearlet Transform in Arbitrary Space Dimensions

Authors: Stephan Dahlke, Gabriele Steidl, and Gerd Teschke

Published in: Dagstuhl Seminar Proceedings, Volume 8492, Structured Decompositions and Efficient Algorithms (2009)

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.

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Stephan Dahlke, Gabriele Steidl, and Gerd Teschke. The Continuous Shearlet Transform in Arbitrary Space Dimensions. In Structured Decompositions and Efficient Algorithms. Dagstuhl Seminar Proceedings, Volume 8492, pp. 1-7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{dahlke_et_al:DagSemProc.08492.9,
  author =	{Dahlke, Stephan and Steidl, Gabriele and Teschke, Gerd},
  title =	{{The Continuous Shearlet  Transform in Arbitrary Space Dimensions}},
  booktitle =	{Structured Decompositions and Efficient Algorithms},
  pages =	{1--7},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{8492},
  editor =	{Stephan Dahlke and Ingrid Daubechies and Michal Elad and Gitta Kutyniok and Gerd Teschke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08492.9},
  URN =		{urn:nbn:de:0030-drops-19216},
  doi =		{10.4230/DagSemProc.08492.9},
  annote =	{Keywords: }
}

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The Continuous Shearlet Transform in Arbitrary Space Dimensions

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