KAUST Grant NumberKUK-I1-007-43
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Abstract© 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.
CitationLellmann J, Lorenz DA, Schönlieb C, Valkonen T (2014) Imaging with Kantorovich--Rubinstein Discrepancy. SIAM Journal on Imaging Sciences 7: 2833–2859. Available: http://dx.doi.org/10.1137/140975528.
SponsorsThis 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.
JournalSIAM Journal on Imaging Sciences