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Shearlets: Theory and Applications
Author(s) -
Kutyniok Gitta,
Lim WangQ,
Steidl Gabriele
Publication year - 2014
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.201410012
Subject(s) - shearlet , wavelet , gravitational singularity , anisotropy , implementation , computer science , representation (politics) , theoretical computer science , algorithm , mathematics , artificial intelligence , statistical physics , mathematical analysis , physics , optics , politics , law , political science , programming language
Many important problem classes are governed by anisotropic features such as singularities concentrated on lower dimensional embedded manifolds, for instance, edges in images or shock fronts in solutions of transport dominated equations. While the ability to reliably capture and sparsely represent anisotropic structures is obviously the more important the higher the number of spatial variables is, the principal difficulties arise already in two spatial dimensions. Since it was shown that the well‐known wavelets are not capable of efficiently encoding such anisotropic features, various directional representation systems were suggested during the last years. Of those, shearlets are the most widely used today due to their optimal sparse approximation properties in combination with their unified treatment of the continuum and digital realm, leading to faithful implementations. This article shall serve as an introduction to and a survey about shearlets. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)