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SUMMARY:Convex regularization of discrete-valued inverse problems - Christ
 ian Clason (Universität Duisburg-Essen)
DTSTART:20170907T151000Z
DTEND:20170907T160000Z
UID:TALK78271@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We consider inverse problems where  where a distributed  param
 eter is known a priori to only take on values from a given discrete  set. 
 This property can be promoted in Tikhonov regularization with the  aid of 
 a suitable convex but nondifferentiable regularization term. This  allows 
 applying standard approaches to show well-posedness and  convergence rates
  in Bregman distance. Using the specific properties of  the regularization
  term\, it can be shown that convergence (albeit  without rates) actually 
 holds pointwise. Furthermore\, the resulting  Tikhonov functional can be m
 inimized efficiently using a semi-smooth  Newton method. Numerical example
 s illustrate the properties of the  regularization term and the numerical 
 solution. <br> <br>This is joint work with Thi Bich Tram Do\, Florian Krus
 e\, and Karl Kunisch.<br>
LOCATION:Seminar Room 1\, Newton Institute
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