Jump to ContentJump to Main Navigation
Show Summary Details
More options …

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:
See all formats and pricing

8. Bilevel approaches for learning of variational imaging models

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


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

Luca Calatroni, Chung Cao, Juan Carlos De los Reyes, Carola-Bibiane Schönlieb, Tuomo Valkonen (2016). 8. Bilevel approaches for learning of variational imaging models. In Maitine Bergounioux, Gabriel Peyré, Christoph Schnörr, Jean-Baptiste Caillau, Thomas Haberkorn (Eds.), Variational Methods: In Imaging and Geometric Control (pp. 252–290). Berlin, Boston: De Gruyter. https://doi.org/10.1515/9783110430394-008

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

Online ISBN: 9783110430394

© 2016 Walter de Gruyter GmbH, Berlin/Munich/BostonGet Permission

Comments (0)

Please log in or register to comment.
Log in