# Analysis Plug-and-Play Methods for Imaging Inverse Problems

arXiv: https://arxiv.org/abs/2509.15422 · HTML: https://mlsanity.com/paper/2509.15422/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 22 references that are in the map.
- First posted on arXiv 18 Sep 2025.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imaging](https://mlsanity.com/paper/2203.17061/) (2022)
- [Solving Linear Inverse Problems Using the Prior Implicit in a Denoiser](https://mlsanity.com/paper/2007.13640/) (2020)
- [RARE: Image Reconstruction using Deep Priors Learned without Ground Truth](https://mlsanity.com/paper/1912.05854/) (2019)
- [Stochastic Deep Restoration Priors for Imaging Inverse Problems](https://mlsanity.com/paper/2410.02057/) (2024)
- [Fast Single Image Super-Resolution](https://mlsanity.com/paper/1510.00143/) (2015)
- [FiRe: Fixed-points of Restoration Priors for Solving Inverse Problems](https://mlsanity.com/paper/2411.18970/) (2024)

## Abstract (arXiv)

Plug-and-Play Priors (PnP) is a popular framework for solving imaging inverse problems by integrating learned priors in the form of denoisers trained to remove Gaussian noise from images. In standard PnP methods, the denoiser is applied directly in the image domain, serving as an implicit prior on natural images. This paper considers an alternative analysis formulation of PnP, in which the prior is imposed on a transformed representation of the image, such as its gradient. Specifically, we train a Gaussian denoiser to operate in the gradient domain, rather than on the image itself. Conceptually, this is an extension of total variation (TV) regularization to learned TV regularization. To incorporate this gradient-domain prior in image reconstruction algorithms, we develop two analysis PnP algorithms based on half-quadratic splitting (APnP-HQS) and the alternating direction method of multipliers (APnP-ADMM). We evaluate our approach on image deblurring and super-resolution, demonstrating that the analysis formulation achieves performance comparable to image-domain PnP algorithms.