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Title
A Bilevel Optimization Approach for Parameter Learning in Variational Models
AuthorKunisch, Karl In der Gemeinsamen Normdatei der DNB nachschlagen ; Pock, Thomas
Published in
SIAM journal on imaging sciences, Philadelphia, Pa., 2013, Vol. 6, Issue 2, page 938-983
PublishedSIAM
LanguageEnglish
Document typeJournal Article
Keywords (EN)regularization parameter / image denoising / learning theory / nondifferentiable optimization / bilevel optimization / semismooth Newton algorithm
Keywords (GND)Bildverarbeitung / Newton-Verfahren / Optimierung / Online-Publikation
URNurn:nbn:at:at-ubg:3-255 Persistent Identifier (URN)
DOIdoi:10.1137/120882706 
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 The work is publicly available
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A Bilevel Optimization Approach for Parameter Learning in Variational Models [5.03 mb]
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Abstract (English)

In this work we consider the problem of parameter learning for variational image denoising models.The learning problem is formulated as a bilevel optimization problem, where the lower-level problemis given by the variational model and the higher-level problem is expressed by means of a loss functionthat penalizes errors between the solution of the lower-level problem and the ground truth data.We consider a class of image denoising models incorporating p-normbased analysis priors usinga fixed set of linear operators. We devise semismooth Newton methods for solving the resultingnonsmooth bilevel optimization problems and show that the optimized image denoising models canachieve state-of-the-art performance.

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