Shearlets: From Theory to Deep Learning

Gitta Kutyniok ()
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Gitta Kutyniok: Mathematisches Institut, Ludwig-Maximilians-Universität München

Chapter 30 in Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, 2023, pp 1095-1132 from Springer

Abstract: 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.

Keywords: Deep neural networks; Frames; Shearlets; Sparse approximation; Wavelets (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/978-3-030-98661-2_80

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