# Whiteness-based bilevel estimation of weighted TV parameter maps for image denoising

arXiv: https://arxiv.org/abs/2503.07814 · HTML: https://mlsanity.com/paper/2503.07814/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 21 references that are in the map.
- First posted on arXiv 10 Mar 2025.

## Builds on (most cited first, 7 of 7)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [UNSURE: self-supervised learning with Unknown Noise level and Stein's Unbiased Risk Estimate](https://mlsanity.com/paper/2409.01985/) (2024)
- [Bilevel parameter learning for higher-order total variation regularisation models](https://mlsanity.com/paper/1508.07243/) (2015)
- [Learning Regularization Parameter-Maps for Variational Image Reconstruction using Deep Neural Networks and Algorithm Unrolling](https://mlsanity.com/paper/2301.05888/) (2023)
- [Techniques for Gradient Based Bilevel Optimization with Nonsmooth Lower Level Problems](https://mlsanity.com/paper/1602.07080/) (2016)
- [Backtracking strategies for accelerated descent methods with smooth composite objectives](https://mlsanity.com/paper/1709.09004/) (2017)
- [Whiteness-based bilevel learning of regularization parameters in imaging](https://mlsanity.com/paper/2403.07026/) (2024)

## Built on by (most cited first, 2 of 2)

- [Self-Tuning Regularization for Image Scanning Microscopy](https://mlsanity.com/paper/2605.31426/) (2026)
- [Learning spatially varying regularisation parameters of low regularity for image reconstruction](https://mlsanity.com/paper/2608.25127/) (2026)

## Abstract (arXiv)

We consider a bilevel optimisation strategy based on normalised residual whiteness loss for estimating the weighted total variation parameter maps for denoising images corrupted by additive white Gaussian noise. Compared to supervised and semi-supervised approaches relying on prior knowledge of (approximate) reference data and/or information on the noise magnitude, the proposal is fully unsupervised. To avoid noise overfitting an early stopping strategy is used, relying on simple statistics of optimal performances on a set of natural images. Numerical results comparing the supervised/unsupervised procedures for scalar/pixel-dependent mboxparameter maps are shown.