# Automated Parameter Selection for Total Variation Minimization in Image Restoration

arXiv: https://arxiv.org/abs/1509.07442 · HTML: https://mlsanity.com/paper/1509.07442/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Sep 2015.

## Built on by (most cited first, 6 of 6)

- [Learning Regularization Parameters of Inverse Problems via Deep Neural Networks](https://mlsanity.com/paper/2104.06594/) (2021)
- [On Optimal Regularization Parameters via Bilevel Learning](https://mlsanity.com/paper/2305.18394/) (2023)
- [Sequential edge detection using joint hierarchical Bayesian learning](https://mlsanity.com/paper/2302.14247/) (2023)
- [Poissonian Blurred Image Deconvolution by Framelet based Local Minimal Prior](https://mlsanity.com/paper/2206.05283/) (2022)
- [Semi-Blind Image Deblurring Based on Framelet Prior](https://mlsanity.com/paper/2310.00943/) (2023)
- [Total Variation-Based Image Decomposition and Denoising for Microscopy Images](https://mlsanity.com/paper/2505.08843/) (2025)

## Abstract (arXiv)

Algorithms for automatically selecting a scalar or locally varying regularization parameter for total variation models with an Lτ-data fidelity term, τ∈ 1,2, are presented. The automated selection of the regularization parameter is based on the discrepancy principle, whereby in each iteration a total variation model has to be minimized. In the case of a locally varying parameter this amounts to solve a multi-scale total variation minimization problem. For solving the constituted multi-scale total variation model convergent first and second order methods are introduced and analyzed. Numerical experiments for image denoising and image deblurring show the efficiency, the competitiveness, and the performance of the proposed fully automated scalar and locally varying parameter selection algorithms.