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Title
Subspace correction methods for a class of nonsmooth and nonadditive convex variational problems with mixed L1/L2 data-fidelity in image processing
AuthorHintermüller, Michael In der Gemeinsamen Normdatei der DNB nachschlagen ; Langer, Andreas
Published in
SIAM Journal on Imaging Sciences, Philadelphia, Pa., 2013, Vol. 6, Issue 4, page 2134-2173
PublishedSIAM
LanguageEnglish
Document typeJournal Article
Keywords (EN)subspace correction / domain decomposition / total variation minimization / convex optimization / image restoration / combined L1/L2 data-fidelity / convergence analysis / impulse noise / Gaussian noise / mixed noise
URNurn:nbn:at:at-ubg:3-592 Persistent Identifier (URN)
DOIdoi:10.1137/120894130 
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 The work is publicly available
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Subspace correction methods for a class of nonsmooth and nonadditive convex variational problems with mixed L1/L2 data-fidelity in image processing [1.72 mb]
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Abstract (English)

The minimization of a functional composed of a nonsmooth and nonadditive regularization term and a combined L1 and L2 data-fidelity term is proposed. It is shown analytically and numerically that the new model has noticeable advantages over popular models in image processing tasks. For the numerical minimization of the new objective, subspace correction methods are introduced which guarantee the convergence and monotone decay of the associated energy along the iterates. Moreover, an estimate of the distance between the outcome of the subspace correction method and the global minimizer of the nonsmooth objective is derived. This estimate and numerical experiments for Image denoising, inpainting, and deblurring indicate that in practice the proposed subspace correction methods indeed approach the global solution of the underlying minimization problem.

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