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Title
Functional-analytic and numerical issues in splitting methods for total variation-based image reconstruction / Michael Hintermüller, Carlos N. Rautenberg, Jooyoung Hahn
AuthorHintermüller, Michael In der Gemeinsamen Normdatei der DNB nachschlagen ; Rautenberg, Carlos N. ; Hahn, Jooyoung
Published in
Inverse Problems, Bristol [u.a.], 2014, Vol. 30, Issue 5
PublishedIOP
LanguageEnglish
Document typeJournal Article
Keywords (EN)Augmented Lagrangian / Bregman iteration / image reconstruction / penalty method / splitting methods / total variation regularization
ISSN1361-6420
URNurn:nbn:at:at-ubg:3-2128 Persistent Identifier (URN)
DOIdoi:10.1088/0266-5611/30/5/055014 
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 The work is publicly available
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Functional-analytic and numerical issues in splitting methods for total variation-based image reconstruction [4.22 mb]
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Abstract (English)

Variable splitting schemes for the function space version of the image reconstruction problem with total variation regularization (TV-problem) in its primal and pre-dual formulations are considered. For the primal splitting formulation, while existence of a solution cannot be guaranteed, it is shown that quasi-minimizers of the penalized problem are asymptotically related to the solution of the original TV-problem. On the other hand, for the pre-dual formulation, a family of parametrized problems is introduced and a parameter dependent contraction of an associated fixed point iteration is established. Moreover, the theory is validated by numerical tests. Additionally, the augmented Lagrangian approach is studied, details on an implementation on a staggered grid are provided and numerical tests are shown.

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