Compactly Supported Shearlets: Theorie and Applications
Talk by Prof. Dr. Gitta Kutyniok
Date: 16.09.14 Time: 10.15 - 11.15 Room: ETH HG D 16.2
Many important problem classes are governed by anisotropic features such as singularities concentrated on lower dimensional embedded manifolds, for instance, edges in images or shear layers in solutions of transport dominated equations. While the ability to reliably capture and sparsely represent anisotropic structures is obviously the more important the higher the number of spatial variables is, principal difficulties arise already in two spatial dimensions. Since it was shown that the well-known (isotropic) wavelet systems are not capable of efficiently approximating such anisotropic features, the need arose to introduce appropriate anisotropic representation systems.Among various suggestions, 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 anisotropic representation system of shearlets, in particular, compactly supported shearlets, present the main theoretical results, and discuss applications to imaging science and adaptive numerical solution of partial differential equations.