Shearlets pp 1-38 | Cite as

Introduction to Shearlets

Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

Shearlets emerged in recent years among the most successful frameworks for the efficient representation of multidimensional data. Indeed, after it was recognized that traditional multiscale methods are not very efficient at capturing edges and other anisotropic features which frequently dominate multidimensional phenomena, several methods were introduced to overcome their limitations. The shearlet representation stands out since it offers a unique combination of some highly desirable properties: it has a single or finite set of generating functions, it provides optimally sparse representations for a large class of multidimensional data, it is possible to use compactly supported analyzing functions, it has fast algorithmic implementations and it allows a unified treatment of the continuum and digital realms. In this chapter, we present a self-contained overview of the main results concerning the theory and applications of shearlets.

Key words

Affine systems Continuous wavelet transform Image processing Shearlets Sparsity Wavelets 

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Notes

Acknowledgements

G.K. acknowledges support by Deutsche Forschungsgemeinschaft (DFG) Grant KU 1446/14 and DFG Grant SPP-1324 KU 1446/13 and support by the Einstein Foundation Berlin. D.L. acknowledges support by Grant DMS 1008900 and DMS (Career) 1005799. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Institut für MathematikTechnische Universität BerlinBerlinGermany
  2. 2.Department of MathematicsUniversity of HoustonHoustonUSA

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