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DOI: 10.4230/DagSemProc.08492.9
URN: urn:nbn:de:0030-drops-19216
URL: https://drops.dagstuhl.de/opus/volltexte/2009/1921/
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Dahlke, Stephan ; Steidl, Gabriele ; Teschke, Gerd

The Continuous Shearlet Transform in Arbitrary Space Dimensions

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08492.DahlkeStephan.Paper.1921.pdf (0.2 MB)


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: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/opus/volltexte/2009/1921},
  URN =		{urn:nbn:de:0030-drops-19216},
  doi =		{10.4230/DagSemProc.08492.9},
  annote =	{Keywords: }
}

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


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