Gabor shearlets
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
Original language | English |
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Pages (from-to) | 87-114 |
Journal / Publication | Applied and Computational Harmonic Analysis |
Volume | 38 |
Issue number | 1 |
Online published | 25 Mar 2014 |
Publication status | Published - Jan 2015 |
Link(s)
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.
Research Area(s)
- Cartoon-like functions, Cone-adapted shearlets, Gabor frames, Gabor shearlets, Orthonormal wavelets, Redundancy, Shearlets, Sparse approximation, Tight frames
Citation Format(s)
Gabor shearlets. / Bodmann, Bernhard G.; Kutyniok, Gitta; Zhuang, Xiaosheng.
In: Applied and Computational Harmonic Analysis, Vol. 38, No. 1, 01.2015, p. 87-114.
In: Applied and Computational Harmonic Analysis, Vol. 38, No. 1, 01.2015, p. 87-114.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review