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SUMMARY:Some approaches to sparse solutions of linear ill-posed problems -
  Elena Resmerita (Alpen-Adria University of Klagenfurt)
DTSTART:20180712T140000Z
DTEND:20180712T150000Z
UID:TALK108013@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:During  the past two decades it has become clear that $lp$ spa
 ces with $p \\in (0\,2)$ and  corresponding (quasi)norms are appropriate  
 settings for dealing with reconstruction of sparse solutions of ill-posed 
 problems. In this context\, the focus of our presentation is twofold. Firs
 tly\, since the question of how to choose the exponent $p$ in such setting
 s has been not only a numerical issue\, but also a philosophical one\, we 
  present a more flexible way of (performing/achieving) sparse regularizati
 on by varying exponents. Rather than using norms or quasinorms\, we employ
   F-norms on infinite dimensional spaces. Secondly\, we approach the ill-p
 osed problem $Au=f$ by  appropriate discretization in the image space. We 
 formulate the so-called  least error method in an $l1$ setting and perform
  the convergence analysis by choosing the discretization level according t
 o both a priori and a posteriori rules.\nConvergence rates   are obtained 
 under source condition (usually) yielding sparsity of the solution.\n\n\nJ
 oint research with Kristian Bredies\, Barbara Kaltenbacher and Dirk Lorenz
LOCATION:MR 14
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