  We propose the use of the Kantorovich-Rubinstein norm from optimal transport
in imaging problems. In particular, we discuss a variational regularisation
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 favourable performance for denoising and
cartoon-texture decomposition.

Computer Vision and Pattern Recognition;Numerical Analysis