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Variational Methods

In Imaging and Geometric Control

Ed. by Bergounioux, Maïtine / Peyré, Gabriel / Schnörr, Christoph / Caillau, Jean-Baptiste / Haberkorn, Thomas

Series:Radon Series on Computational and Applied Mathematics 18

eBook (PDF)
Publication Date:
January 2017
Copyright year:
2017
ISBN
978-3-11-043039-4
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8. Bilevel approaches for learning of variational imaging models

Calatroni, Luca / Cao, Chung / Carlos De los Reyes, Juan / Schönlieb, Carola-Bibiane / Valkonen, Tuomo

Abstract

We review some recent learning approaches in variational imaging based on bilevel optimization and emphasize the importance of their treatment in function space. The paper covers both analytical and numerical techniques. Analytically, we include results on the existence and structure of minimizers, as well as optimality conditions for their characterization. On the basis of this information, Newton-type methods are studied for the solution of the problems at hand, combining them with sampling techniques in case of large databases. The computational verification of the developed techniques is extensively documented, covering instances with different type of regularizers, several noise models, spatially dependent weights and large image databases.

Citation Information

Variational Methods

In Imaging and Geometric Control

Edited by Bergounioux, Maïtine / Peyré, Gabriel / Schnörr, Christoph / Caillau, Jean-Baptiste / Haberkorn, Thomas

De Gruyter

2016

Pages: 252–290

ISBN (Online): 9783110430394

DOI (Chapter): https://doi.org/10.1515/9783110430394-008

DOI (Book): https://doi.org/10.1515/9783110430394

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