Compactly Supported Shearlets
Gitta Kutyniok, Jakob Lemvig, Wang-Q Lim

TL;DR
This paper discusses the theory and construction of compactly supported shearlet systems, highlighting their properties, applications in image approximation, and recent advances in 2D and 3D settings.
Contribution
It introduces constructions of compactly supported shearlet frames and analyzes their effectiveness in sparse image approximation, extending results to generalized cartoon-like models.
Findings
Compactly supported shearlet frames can provide optimally sparse approximations.
Shearlet systems effectively analyze anisotropic features in 2D and 3D data.
Recent results show their applicability to generalized cartoon-like images.
Abstract
Shearlet theory has become a central tool in analyzing and representing 2D data with anisotropic features. Shearlet systems are systems of functions generated by one single generator with parabolic scaling, shearing, and translation operators applied to it, in much the same way wavelet systems are dyadic scalings and translations of a single function, but including a precise control of directionality. Of the many directional representation systems proposed in the last decade, shearlets are among the most versatile and successful systems. The reason for this being an extensive list of desirable properties: shearlet systems can be generated by one function, they provide precise resolution of wavefront sets, they allow compactly supported analyzing elements, they are associated with fast decomposition algorithms, and they provide a unified treatment of the continuum and the digital realm.…
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Taxonomy
TopicsImage Processing Techniques and Applications · Image and Signal Denoising Methods · Optical measurement and interference techniques
