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