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Shearlets: Theory and Applications to Imaging Science and Inverse Scattering Problems

Kolloquium der Abteilung 8

Many important problem classes are governed by anisotropic features such as edges in images or inhomogeneities of a medium. Among various representation systems, which are capable of reliably capturing and efficiently approximating such anisotropic structures, shearlets are the most widely used today. Main reasons for this are their optimal sparse approximation properties within a model situation in combination with their unified treatment of the continuum and digital realm, leading to faithful implementations. An additional advantage is the availability of stable compactly supported systems for high spatial localization.
In this talk, we will provide an introduction to the system of shearlets, in particular, compactly supported shearlets, and discuss various applications to imaging science and inverse scattering problems with a particular focus on medical diagnosis.