Gabor shearlets

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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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: tiey combine elements from Gabor and wavelet frames in their construction. As a consequence, they can be imnplemnented with standard filters fromn wavelet theory in comnbmation with standard Gabor wmdows. Unlike the usual shearlets the new construction can achieve a redundancy as close to one as desired. Our constniction follows the general strategy for shearlets. First we define group-based Gabor shearlets and then mnodify themn to a cone-adapted version. In comnbination with Meyer filters, the cone-adapted Gabor shearlets constitute a tight framne and provide low-redundancy sparse approximnations of the comnmnon mnodel 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 Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review