Imaging with Kantorovich-Rubinstein discrepancy

Abstract

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.

References in corpus (3)

• An inertial forward-backward algorithm for monotone inclusions
• A Mass Transportation Model for the Optimal Planning of an Urban Region
• The jump set under geometric regularisation. Part 2: Higher-order approaches

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