# Learning optimal spatially-dependent regularization parameters in total variation image restoration

arXiv: https://arxiv.org/abs/1603.09155 · HTML: https://mlsanity.com/paper/1603.09155/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2016.

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

- [DEALing with Image Reconstruction: Deep Attentive Least Squares](https://mlsanity.com/paper/2502.04079/) (2025)
- [Stability of Data-Dependent Ridge-Regularization for Inverse Problems](https://mlsanity.com/paper/2406.12289/) (2024)
- [Iteratively Refined Image Reconstruction with Learned Attentive Regularizers](https://mlsanity.com/paper/2407.06608/) (2024)
- [Bilevel Imaging Learning Problems as Mathematical Programs with Complementarity Constraints: Reformulation and Theory](https://mlsanity.com/paper/2110.02273/) (2021)

## Abstract (arXiv)

We consider a bilevel optimization approach in function space for the choice of spatially dependent regularization parameters in TV image restoration models. First- and second-order optimality conditions for the bilevel problem are studied, when the spatially-dependent parameter belongs to the Sobolev space H1(Omega). A combined Schwarz domain decomposition-semismooth Newton method is proposed for the solution of the full optimality system and local superlinear convergence of the semismooth Newton method is analyzed. Exhaustive numerical computations are finally carried out to show the suitability of the approach.