# Discontinuities of the minimizers of the weighted or anisotropic total variation for image reconstruction

arXiv: https://arxiv.org/abs/1402.0026 · HTML: https://mlsanity.com/paper/1402.0026/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2014.

## Built on by (most cited first, 1 of 1)

- [Learning spatially varying regularisation parameters of low regularity for image reconstruction](https://mlsanity.com/paper/2608.25127/) (2026)

## Abstract (arXiv)

The study of the regularity of the minimizer of the weighted anisotropic total variation with a general fidelity term is at the heart of this paper. We generalized some recent results on the inclusion of the discontinuities of the minimizer of the image denoising problem. In particular, we proved that for well-chosen weights and anisotropies, it is actually possible to create discontinuities that were not contained in the original image. We also observed a reduced jump property at the discontinuities of the minimizer. To prove these results we used some regularity theorems for minimal surfaces that we had to adapt to our setting. We also illustrated our theoretical results with several numerical simulations.