Gabor shearlets

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

19 Scopus Citations
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Author(s)

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Detail(s)

Original languageEnglish
Pages (from-to)87-114
Journal / PublicationApplied and Computational Harmonic Analysis
Volume38
Issue number1
Online published25 Mar 2014
Publication statusPublished - Jan 2015

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.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review