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Convex regularization of discrete-valued inverse problems

Presented by: 
Christian Clason
Thursday 7th September 2017 - 16:10 to 17:00
INI Seminar Room 1
We consider inverse problems where where a distributed parameter 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 minimized efficiently using a semi-smooth Newton method. Numerical examples illustrate the properties of the regularization term and the numerical solution.

This is joint work with Thi Bich Tram Do, Florian Kruse, and Karl Kunisch.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons