Imaging with Kantorovich--Rubinstein Discrepancy

Jan Lellmann, Dirk A. Lorenz, Carola Schönlieb, Tuomo Valkonen

Research output: Contribution to journalArticlepeer-review

75 Scopus citations


© 2014 Society for Industrial and Applied Mathematics. We propose the use of the Kantorovich-Rubinstein norm from optimal transport in imaging problems. In particular, we discuss a variational regularization model endowed with a Kantorovich- Rubinstein discrepancy term and total variation regularization in the context of image denoising and cartoon-texture decomposition. We point out connections of this approach to several other recently proposed methods such as total generalized variation and norms capturing oscillating patterns. We also show that the respective optimization problem can be turned into a convex-concave saddle point problem with simple constraints and hence can be solved by standard tools. Numerical examples exhibit interesting features and favorable performance for denoising and cartoon-texture decomposition.
Original languageEnglish (US)
Pages (from-to)2833-2859
Number of pages27
JournalSIAM Journal on Imaging Sciences
Issue number4
StatePublished - Jan 2014
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: This research was supported by King Abdullah University of Science and Technology (KAUST) award KUK-I1-007-43 and EPSRC first grant EP/J009539/1, "Sparse & Higher-order Image Restoration."The research of the first author was supported by Leverhulme Early Career Fellowship ECF-2013-436.The research of this author was supported by a Senescyt (Ecuadorian Ministry of Education, Science, and Technology) Prometeo fellowship.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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