DagSemProc.08492.9.pdf
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The Continuous Shearlet Transform in Arbitrary Space Dimensions
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Dagstuhl Seminar Proceedings, Volume 8492
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2009-03-10
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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)
https://doi.org/10.4230/DagSemProc.08492.9
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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