Bilevel Parameter Learning for Higher-Order Total Variation Regularisation Models

De los Reyes, JC, Schonlieb, C-B and Valkonen, T ORCID: 0000-0001-6683-3572 (2017) Bilevel Parameter Learning for Higher-Order Total Variation Regularisation Models. JOURNAL OF MATHEMATICAL IMAGING AND VISION, 57 (1). pp. 1-25.

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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.

Item Type:	Article
Uncontrolled Keywords:	Bilevel optimisation, Total variation regularisers, Image quality measures
Depositing User:	Symplectic Admin
Date Deposited:	25 Apr 2017 09:32
Last Modified:	20 Jan 2024 08:58
DOI:	10.1007/s10851-016-0662-8
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3007114