# Imaging with Kantorovich-Rubinstein discrepancy

arXiv: https://arxiv.org/abs/1407.0221 · HTML: https://mlsanity.com/paper/1407.0221/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2014.

## Built on by (most cited first, 10 of 10)

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- [Optimal Transport for Super Resolution Applied to Astronomy Imaging](https://mlsanity.com/paper/2202.05354/) (2022)
- [An Efficient Orlicz-Sobolev Approach for Transporting Unbalanced Measures on a Graph](https://mlsanity.com/paper/2502.00739/) (2025)

## Abstract (arXiv)

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.