# A bi-level view of inpainting - based image compression

arXiv: https://arxiv.org/abs/1401.4112 · HTML: https://mlsanity.com/paper/1401.4112/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2014.

## Built on by (most cited first, 4 of 4)

- [Analyzing Inexact Hypergradients for Bilevel Learning](https://mlsanity.com/paper/2301.04764/) (2023)
- [Learning Sparse Masks for Diffusion-based Image Inpainting](https://mlsanity.com/paper/2110.02636/) (2021)
- [Image Inpainting Using Wasserstein Generative Adversarial Imputation Network](https://mlsanity.com/paper/2106.15341/) (2021)
- [A Wasserstein GAN for Joint Learning of Inpainting and Spatial Optimisation](https://mlsanity.com/paper/2202.05623/) (2022)

## Abstract (arXiv)

Inpainting based image compression approaches, especially linear and non-linear diffusion models, are an active research topic for lossy image compression. The major challenge in these compression models is to find a small set of descriptive supporting points, which allow for an accurate reconstruction of the original image. It turns out in practice that this is a challenging problem even for the simplest Laplacian interpolation model. In this paper, we revisit the Laplacian interpolation compression model and introduce two fast algorithms, namely successive preconditioning primal dual algorithm and the recently proposed iPiano algorithm, to solve this problem efficiently. Furthermore, we extend the Laplacian interpolation based compression model to a more general form, which is based on principles from bi-level optimization. We investigate two different variants of the Laplacian model, namely biharmonic interpolation and smoothed Total Variation regularization. Our numerical results show that significant improvements can be obtained from the biharmonic interpolation model, and it can recover an image with very high quality from only 5% pixels.