The continuous shearlet transform in arbitrary dimensions

Dahlke, Stephan ; Steidl, Gabriele ; Teschke, Gerd

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URN: urn:nbn:de:bsz:180-madoc-22137
Document Type: Working paper
Year of publication: 2008
The title of a journal, publication series: Preprints / Department of Mathematics
Volume: 08-01
Place of publication: Mannheim
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Preprints
Subject: 510 Mathematics
Subject headings (SWD): Transformation , Dimension
Abstract: This paper 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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Das Dokument wird vom Publikationsserver der Universitätsbibliothek Mannheim bereitgestellt.

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