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Shearlets: From Theory to Deep Learning

In: Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

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  • Gitta Kutyniok

    (Mathematisches Institut, Ludwig-Maximilians-Universität München)

Abstract

Many important problem classes are governed by anisotropic features, which typically appear as singularities concentrated on lower-dimensional embedded manifolds. Examples include edges in images or shock fronts in solutions of transport-dominated equations. Shearlets are the first representation system which exhibits optimal sparse approximation properties in combination with a unified treatment of the continuum and digital realm, leading to faithful implementations. A prominent class of applications are inverse problems, foremost in imaging science, where shearlets are utilized for sparse regularization. Recently, shearlet systems have also been used in combination with data-driven approaches, predominately deep neural networks. This chapter shall serve as an introduction to and a survey about the theory of shearlets and their applications.

Suggested Citation

  • Gitta Kutyniok, 2023. "Shearlets: From Theory to Deep Learning," Springer Books, in: Ke Chen & Carola-Bibiane Schönlieb & Xue-Cheng Tai & Laurent Younes (ed.), Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, chapter 30, pages 1095-1132, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-98661-2_80
    DOI: 10.1007/978-3-030-98661-2_80
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