TY - JOUR
T1 - Bilevel Parameter Learning for Higher-Order Total Variation Regularisation Models
AU - De los Reyes, J. C.
AU - Schonlieb, C. -B.
AU - Valkonen, Tuomo
N1 - KAUST Repository Item: Exported on 2022-06-03
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: This research has been supported by King Abdullah University of Science and Technology (KAUST) Award No. KUK-I1-007-43, EPSRC grants Nr. EP/J009539/1 Sparse & Higher-order Image Restoration and Nr. EP/M00483X/1 Efficient computational tools for inverse imaging problems, Escuela Politecnica Nacional de Quito Award No. PIS 12-14. MATHAmSud project SOCDE Sparse Optimal Control of Differential Equations and the Leverhulme Trust project on Breaking the non-convexity barrier. While in Quito, I Valkonen has moreover been supported by SENESCYT (Ecuadorian Ministry of Higher Education, Science, Technology and Innovation) under a Prometeo Fellowship.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2016/6/1
Y1 - 2016/6/1
N2 - 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 (Formula presented.) and (Formula presented.) is carried out, showing the advantages and shortcomings of both regularisers, depending on the structure of the processed images and their noise level.
AB - 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 (Formula presented.) and (Formula presented.) is carried out, showing the advantages and shortcomings of both regularisers, depending on the structure of the processed images and their noise level.
UR - http://hdl.handle.net/10754/678496
UR - http://link.springer.com/10.1007/s10851-016-0662-8
UR - http://www.scopus.com/inward/record.url?scp=84973115723&partnerID=8YFLogxK
U2 - 10.1007/s10851-016-0662-8
DO - 10.1007/s10851-016-0662-8
M3 - Article
C2 - 32355410
SN - 1573-7683
VL - 57
SP - 1
EP - 25
JO - JOURNAL OF MATHEMATICAL IMAGING AND VISION
JF - JOURNAL OF MATHEMATICAL IMAGING AND VISION
IS - 1
ER -