# A Unified Plug-and-Play Algorithm with Projected Landweber Operator for Split Convex Feasibility Problems

arXiv: https://arxiv.org/abs/2408.12100 · HTML: https://mlsanity.com/paper/2408.12100/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 31 references that are in the map.
- First posted on arXiv 22 Aug 2024.

## Builds on (most cited first, 16 of 16)

- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Gradient Step Denoiser for convergent Plug-and-Play](https://mlsanity.com/paper/2110.03220/) (2021)
- [Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularization](https://mlsanity.com/paper/2201.13256/) (2022)
- [Regularization by Denoising via Fixed-Point Projection (RED-PRO)](https://mlsanity.com/paper/2008.00226/) (2020)
- [Performance Analysis of Plug-and-Play ADMM: A Graph Signal Processing Perspective](https://mlsanity.com/paper/1809.00020/) (2018)
- [On the Proof of Fixed-Point Convergence for Plug-and-Play ADMM](https://mlsanity.com/paper/1910.14325/) (2019)
- [Constrained Regularization by Denoising with Automatic Parameter Selection](https://mlsanity.com/paper/2311.03819/) (2023)
- [Multi-resolution Data Fusion for Super-Resolution Electron Microscopy](https://mlsanity.com/paper/1612.00874/) (2016)
- [Regular Sequences of Quasi-Nonexpansive Operators and Their Applications](https://mlsanity.com/paper/1710.00534/) (2017)
- [Weak, Strong and Linear Convergence of the CQ-Method Via the Regularity of Landweber Operators](https://mlsanity.com/paper/1812.07450/) (2018)
- [Strict pseudocontractions and demicontractions, their properties and applications](https://mlsanity.com/paper/2307.07337/) (2023)

## Abstract (arXiv)

In recent years Plug-and-Play (PnP) methods have achieved state-of-the-art performance in inverse imaging problems by replacing proximal operators with denoisers. Based on the proximal gradient method, some theoretical results of PnP have appeared, where appropriate step size is crucial for convergence analysis. However, in practical applications, applying PnP methods with theoretically guaranteed step sizes is difficult, and these algorithms are limited to Gaussian noise. In this paper,from a perspective of split convex feasibility problems (SCFP), an adaptive PnP algorithm with Projected Landweber Operator (PnP-PLO) is proposed to address these issues. Numerical experiments on image deblurring, super-resolution, and compressed sensing MRI experiments illustrate that PnP-PLO with theoretical guarantees outperforms state-of-the-art methods such as RED and RED-PRO.