Learning optimal spatially-dependent regularization parameters in total variation image denoising
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Authors
Van Chung, C
De los Reyes, JC
Schönlieb, CB
Publication Date
2017-06-21Journal Title
Inverse Problems
ISSN
0266-5611
Publisher
IOP Science
Volume
33
Issue
7
Type
Article
This Version
AM
Metadata
Show full item recordCitation
Van Chung, C., De los Reyes, J., & Schönlieb, C. (2017). Learning optimal spatially-dependent regularization parameters in total variation image denoising. Inverse Problems, 33 (7) https://doi.org/10.1088/1361-6420/33/7/074005
Abstract
We consider a bilevel optimization approach in function space for the choice of spatially dependent regularization parameters in TV image denoising models. First- and second-order optimality conditions for the bilevel problem are studied when the spatially-dependent parameter belongs to the Sobolev space H1(Ω). A combined Schwarz domain decomposition-semismooth Newton method is proposed for the solution of the full optimality system and local superlinear convergence of the semismooth Newton method is verified. Exhaustive numerical computations are finally carried out to show the suitability of the approach.
Keywords
optimization-based learning in imaging, bilevel optimization, PDE-constrained optimization, semismooth Newton method, Schwarz domain decomposition method
Sponsorship
Engineering and Physical Sciences Research Council (EP/N014588/1)
Engineering and Physical Sciences Research Council (EP/M00483X/1)
Engineering and Physical Sciences Research Council (EP/J009539/1)
Alan Turing Institute (unknown)
European Commission Horizon 2020 (H2020) Marie Sk?odowska-Curie actions (691070)
Identifiers
External DOI: https://doi.org/10.1088/1361-6420/33/7/074005
This record's URL: https://www.repository.cam.ac.uk/handle/1810/292704
Rights
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http://www.rioxx.net/licenses/all-rights-reserved
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