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SUMMARY:Compactly Supported Shearlets: Theory and Applications - Professor
  Dr Gitta Kutyniok\, Einstein-Professorin\, Technische Universität Berlin
DTSTART:20170919T130000Z
DTEND:20170919T140000Z
UID:TALK78171@talks.cam.ac.uk
CONTACT:June Rix
DESCRIPTION:Many important problem classes are governed by anisotropic fea
 tures such as singularities concentrated on lower dimensional embedded man
 ifolds\, for instance\, edges in images or shear layers in solutions of tr
 ansport dominated equations. While the ability to reliably capture and spa
 rsely 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 s
 uch anisotropic features\, the need arose to introduce appropriate anisotr
 opic representation systems. Among various suggestions\, shearlets are the
  most widely used today. Main reasons for this are their optimal sparse ap
 proximation 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 co
 mpactly supported systems for high spatial localization.\n\nIn this talk\,
  we will first provide an introduction to the anisotropic representation s
 ystem of shearlets\, in particular\, compactly supported shearlets\, and p
 resent the main theoretical results. We will then discuss several applicat
 ions ranging from sparse regularization of inverse problems to the theory 
 of deep neural networks.\n
LOCATION:MR3\,  Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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