Gabor shearlets
type: Item
instance of: scholarly article
title: Gabor shearlets
zbMATH Open document ID: 1304.42084
author: Bernhard G. Bodmann
author: Gitta Kutyniok
author: Xiaosheng Zhuang
published in: Applied and Computational Harmonic Analysis
publication date: 2014-11-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/1303.6556
reviewed by: Manfred Tasche
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 6363253
zbMATH Keywords: Gabor shearlets
zbMATH Keywords: Gabor frames
zbMATH Keywords: orthonormal wavelets
zbMATH Keywords: shearlets
zbMATH Keywords: redundancy
zbMATH Keywords: cone-adapted Gabor shearlets
zbMATH Keywords: tight frame
zbMATH Keywords: sparse approximation
zbMATH Keywords: cartoon-like functions
MaRDI profile type: Publication
OpenAlex ID: W4206200052
arXiv ID: 1303.6556
cites work: A quantitative notion of redundancy for finite frames
cites work: New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities
cites work: Ten Lectures on Wavelets
cites work: Painless nonorthogonal expansions
cites work: Foundations of time-frequency analysis
cites work: Parabolic molecules
cites work: Q5486953
cites work: Optimally Sparse Multidimensional Representation Using Shearlets
cites work: Optimally sparse representations of 3D data with \(C^2\) surface singularities using Parseval frames of shearlets
cites work: Adaptive Multiresolution Analysis Structures and Shearlet Systems
cites work: Generalized interpolating refinable function vectors
cites work: Matrix Extension with Symmetry and Its Application to Symmetric Orthonormal Multiwavelets
cites work: Algorithms for matrix extension and orthogonal wavelet filter banks over algebraic number fields
cites work: The nonexistence of shearlet scaling functions
cites work: Construction of compactly supported shearlet frames
cites work: Shearlets. Multiscale analysis for multivariate data.
cites work: Compactly supported shearlets are optimally sparse
cites work: Adaptive Directional Subdivision Schemes and Shearlet Multiresolution Analysis
cites work: Q4705314
cites work: Gabor frames by sampling and periodization
cites work: Q4896587
DOI: 10.1016/J.ACHA.2014.03.006
review text: In this paper, the authors introduce new Gabor shearlets based on a group related to chirp modulations and discuss their frame properties and the associated multiresolution structure. The Gabor shearlets form a unit-norm \(b^{-1}\)-tight frame for \(L^2({\mathbb R}^2)\), where \(b^{-1}\) can be chosen close to 1. Gabor shearlets can achieve a redundancy as close to 1 as desired. Further, the Gabor shearlets have polynomial decay in \({\mathbb R}^2\).NEWLINENEWLINEThen cone-adapted Gabor shearlets are defined by a projection of Gabor shearlets on cones in the frequency domain. The authors show that cone-adapted Gabor shearlets provide optimally sparse approximations of cartoon-like functions.
description: scientific article; zbMATH DE number 6363253