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Title
An adaptive finite element method in L2-TV-based image denoising
AuthorHintermüller, Michael In der Gemeinsamen Normdatei der DNB nachschlagen ; Rincon-Camacho, M. Monserrat
Published in
Inverse Problems and Imaging (IPI), 2014, Vol. 8, Issue 3, page 685-711
PublishedAmerican Institute of Mathematical Sciences (AIMS), 2014
Edition
Accepted version
LanguageEnglish
Document typeJournal Article
Keywords (EN)A posteriori error estimation / elliptic variational inequality of the second kind / adaptive finite elements / total variation / primal-dual method / semismooth Newton method
Project-/ReportnumberSFB-Report 2010-029
ISSN1930-8337
URNurn:nbn:at:at-ubg:3-3681 Persistent Identifier (URN)
DOI10.3934/ipi.2014.8.685 
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 The work is publicly available
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Abstract (English)

The first order optimality system of a total variation regularization based variational model with L2-data-fitting in image denoising (L2-TV problem) can be expressed as an elliptic variational inequality of the second kind. For a finite element discretization of the variational inequality problem, an a posteriori error residual based error estimator is derived and its reliability and (partial) efficiency are established. The results are applied to solve the L2-TV problem by means of the adaptive finite element method. The adaptive mesh refinement relies on the newly derived a posteriori error estimator and on an additional heuristic providing a local variance estimator to cope with noisy data. The numerical solution of the discrete problem on each level of refinement is obtained by a superlinearly convergent algorithm based on Fenchel-duality and inexact semismooth Newton techniques and which is stable with respect to noise in the data. Numerical results justifying the advantage of adaptive finite elements solutions are presented.

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