Imaging with Kantorovich-Rubinstein discrepancy

TL;DR

This paper introduces a novel imaging regularization method using the Kantorovich-Rubinstein norm from optimal transport, demonstrating its effectiveness in denoising and image decomposition tasks.

Contribution

It develops a new variational model combining Kantorovich-Rubinstein discrepancy with total variation, linking it to existing methods and providing a convex optimization framework.

Findings

Effective denoising performance demonstrated

Successful cartoon-texture decomposition shown

Connections to other regularization methods established

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.