# Inpainting in discrete Sobolev spaces: structural information for uncertainty reduction

arXiv: https://arxiv.org/abs/2211.03711 · HTML: https://mlsanity.com/paper/2211.03711/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 67 references that are in the map.
- First posted on arXiv 7 Nov 2022.

## Builds on (most cited first, 2 of 2)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)

## Abstract (arXiv)

In this article, using an exemplar-based approach, we investigate the inpainting problem, introducing a new mathematical functional, whose minimization determines the quality of the reconstructions. The new functional expression takes into account of fnite differences terms, in a similar fashion to what happens in the theoretical Sobolev spaces. Moreover, we introduce a new priority index to determine the scanning order of the points to inpaint, prioritizing the uncertainty reduction in the choice. The achieved results highlight important theoretical-connected aspects of the inpainting by patch procedure.