Learning optimal spatially-dependent regularization parameters in total variation image denoising
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Van Chung, C
De los Reyes, JC
Schönlieb, CB
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.
Description
Keywords
optimization-based learning in imaging, bilevel optimization, PDE-constrained optimization, semismooth Newton method, Schwarz domain decomposition method
Journal Title
Inverse Problems
Conference Name
Journal ISSN
0266-5611
1361-6420
1361-6420
Volume Title
33
Publisher
IOP Science
Publisher DOI
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)
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)