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Shearlets

  • Reference work entry
  • First Online:
Encyclopedia of Applied and Computational Mathematics

  • 80 Accesses

Mathematics Subject Classification

42C40; 42C15; 65T60

Synonyms

Shearlets; Shearlet system

Short Description

Shearlets are multiscale systems in \(L^{2}(\mathbb{R}^{2})\) which efficiently encode anisotropic features. They extend the framework of wavelets and are constructed by parabolic scaling, shearing, and translation applied to one or very few generating functions. The main application area of shearlets is imaging science, for example, denoising, edge detection, or inpainting. Extensions of shearlet systems to \(L^{2}(\mathbb{R}^{n})\), n ≥ 3 are also available.

Description

Multivariate Problems

Multivariate problem classes are typically governed by anisotropic features such as singularities concentrated on lower dimensional embedded manifolds. Examples are edges in images or shock fronts of transport dominated equations. Since due to their isotropic nature wavelets are deficient to efficiently encode such functions, several directional representation systems were proposed among...

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References

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Berlin, Berlin, Germany

    Gitta Kutyniok

Authors
  1. Gitta Kutyniok
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Editor information

Editors and Affiliations

  1. University of Texas at Austin, Austin, TX, USA

    Björn Engquist

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© 2015 Springer-Verlag Berlin Heidelberg

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Kutyniok, G. (2015). Shearlets. In: Engquist, B. (eds) Encyclopedia of Applied and Computational Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70529-1_558

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