# Inverse problems with second-order Total Generalized Variation constraints

arXiv: https://arxiv.org/abs/2005.09725 · HTML: https://mlsanity.com/paper/2005.09725/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2020.

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

- [VDIP-TGV: Blind Image Deconvolution via Variational Deep Image Prior Empowered by Total Generalized Variation](https://mlsanity.com/paper/2310.19477/) (2023)

## Abstract (arXiv)

Total Generalized Variation (TGV) has recently been introduced as penalty functional for modelling images with edges as well as smooth variations. It can be interpreted as a "sparse" penalization of optimal balancing from the first up to the k-th distributional derivative and leads to desirable results when applied to image denoising, i.e., L2-fitting with TGV penalty. The present paper studies TGV of second order in the context of solving ill-posed linear inverse problems. Existence and stability for solutions of Tikhonov-functional minimization with respect to the data is shown and applied to the problem of recovering an image from blurred and noisy data.