Bilevel Parameter Learning for Higher-Order Total Variation Regularisation Models.
Published version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Abstract
We consider a bilevel optimisation approach for parameter learning in higher-order total variation image reconstruction models. Apart from the least squares cost functional, naturally used in bilevel learning, we propose and analyse an alternative cost based on a Huber-regularised TV seminorm. Differentiability properties of the solution operator are verified and a first-order optimality system is derived. Based on the adjoint information, a combined quasi-Newton/semismooth Newton algorithm is proposed for the numerical solution of the bilevel problems. Numerical experiments are carried out to show the suitability of our approach and the improved performance of the new cost functional. Thanks to the bilevel optimisation framework, also a detailed comparison between TGV 2 and ICTV is carried out, showing the advantages and shortcomings of both regularisers, depending on the structure of the processed images and their noise level.
Description
Keywords
Journal Title
Conference Name
Journal ISSN
1573-7683
Volume Title
Publisher
Publisher DOI
Sponsorship
Engineering and Physical Sciences Research Council (EP/N014588/1)
Engineering and Physical Sciences Research Council (EP/J009539/1)
Alan Turing Institute (unknown)
European Commission Horizon 2020 (H2020) Marie Sk?odowska-Curie actions (691070)