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Jens Flemming: Theory and examples of variational regularization with non-metric fitting functionals

Jens Flemming: Theory and examples of variational regularization with non-metric fitting functionals

Author(s):
Jens Flemming
Title:
Theory and examples of variational regularization with non-metric fitting functionals
Electronic source:
application/pdf
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 14, 2010
Mathematics Subject Classification:
47J06 []
65J20 []
47J20 []
47A52 []
Abstract:
We describe and analyze a general framework for solving ill-posed operator equations by minimizing Tikhonov-like functionals. The fitting functional may be non-metric and the operator is allowed to be nonlinear and nonsmooth. In comparision to former results on variational regularization with non-metric fitting functionals we significantly weaken the assumptions for proving convergence rates and, in addition, we extend the results to a wider range of rates. Two examples, coming from imaging applications, show that the developed theory is applicable to practically relevant problems.
Keywords:
variational regularization, variational inequalities, convergence rates, Poisson noise
Language:
English
Publication time:
07/2010