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Preprint 18-2014

Gabor Shearlets

Source file is available as :   Portable Document Format (PDF)

Author(s) : Bernhard Bodmann , Gitta Kutyniok , Xiaosheng Zhuang

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 18-2014

MSC 2000

42C40 Wavelets
42C15 Series of general orthogonal functions, generalized Fourier expansions, nonorthogonal expansions

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.

Keywords : Gabor shearlets, Cartoon-like functions, Cone-adapted shearlets, Gabor frames, orthonormal wavelets, redundancy, sparse approximation, shearlets, tight frames

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