# Constrained Regularization by Denoising with Automatic Parameter Selection

arXiv: https://arxiv.org/abs/2311.03819 · HTML: https://mlsanity.com/paper/2311.03819/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Nov 2023.

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

- [Learning Image Priors through Patch-based Diffusion Models for Solving Inverse Problems](https://mlsanity.com/paper/2406.02462/) (2024)
- [A Diffusion-Based Generative Prior Approach to Sparse-view Computed Tomography](https://mlsanity.com/paper/2602.10722/) (2026)
- [A Unified Plug-and-Play Algorithm with Projected Landweber Operator for Split Convex Feasibility Problems](https://mlsanity.com/paper/2408.12100/) (2024)
- [RELD: Regularization by Latent Diffusion Models for Image Restoration](https://mlsanity.com/paper/2503.22563/) (2025)
- [Automatic regularization parameter choice for tomography using a double model approach](https://mlsanity.com/paper/2602.08528/) (2026)
- [A convergent Plug-and-Play Majorization-Minimization algorithm for Poisson inverse problems](https://mlsanity.com/paper/2603.24156/) (2026)

## Abstract (arXiv)

Regularization by Denoising (RED) is a well-known method for solving image restoration problems by using learned image denoisers as priors. Since the regularization parameter in the traditional RED does not have any physical interpretation, it does not provide an approach for automatic parameter selection. This letter addresses this issue by introducing the Constrained Regularization by Denoising (CRED) method that reformulates RED as a constrained optimization problem where the regularization parameter corresponds directly to the amount of noise in the measurements. The solution to the constrained problem is solved by designing an efficient method based on alternating direction method of multipliers (ADMM). Our experiments show that CRED outperforms the competing methods in terms of stability and robustness, while also achieving competitive performances in terms of image quality.