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Main Title: Gabor Shearlets
Author(s): Bodmann, Bernhard G.
Kutyniok, Gitta
Zhuang, Xiaosheng
Type: Research Paper
Abstract: In this paper, we introduce Gabor shearlets, a variant of shearlet systems, which are based on a different group representation than previous shearlet constructions: they combine elements from Gabor and wavelet frames in their construction. As a consequence, they can be implemented with standard filters from wavelet theory in combination with standard Gabor windows. Unlike the usual shearlets, the new construction can achieve a redundancy as close to one as desired. Our construction follows the general strategy for shearlets. First we define group-based Gabor shearlets and then modify them to a cone-adapted version. In combination with Meyer filters, the cone-adapted Gabor shearlets constitute a tight frame and provide low-redundancy sparse approximations of the common model class of anisotropic features which are cartoon-like functions.
Subject(s): Gabor shearlets
cartoon-like functions
cone-adapted shearlets
Gabor frames
orthonormal wavelets
sparse approximation
tight frames
Issue Date: 10-Oct-2014
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 42C40 Wavelets
42C15 Series of general orthogonal functions, generalized Fourier expansions, nonorthogonal expansions
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2014, 18
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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