# Poisson Inverse Problems by the Plug-and-Play scheme

arXiv: https://arxiv.org/abs/1511.02500 · HTML: https://mlsanity.com/paper/1511.02500/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Nov 2015.

## Built on by (most cited first, 17 of 17)

- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021)
- [Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --](https://mlsanity.com/paper/2301.03362/) (2023)
- [Fixed-Point and Objective Convergence of Plug-and-Play Algorithms](https://mlsanity.com/paper/2104.10348/) (2021)
- [Rotation Equivariant Proximal Operator for Deep Unfolding Methods in Image Restoration](https://mlsanity.com/paper/2312.15701/) (2023)
- [Physics-/Model-Based and Data-Driven Methods for Low-Dose Computed Tomography: A survey](https://mlsanity.com/paper/2203.15725/) (2022)
- [Convergent Bregman Plug-and-Play Image Restoration for Poisson Inverse Problems](https://mlsanity.com/paper/2306.03466/) (2023)
- [Preconditioned Plug-and-Play ADMM with Locally Adjustable Denoiser for Image Restoration](https://mlsanity.com/paper/2110.00493/) (2021)
- [CurvPnP: Plug-and-play Blind Image Restoration with Deep Curvature Denoiser](https://mlsanity.com/paper/2211.07286/) (2022)
- [Bregman Plug-and-Play Priors](https://mlsanity.com/paper/2202.02388/) (2022)
- [How Much Training Data is Memorized in Overparameterized Autoencoders? An Inverse Problem Perspective on Memorization Evaluation](https://mlsanity.com/paper/2310.02897/) (2023)
- [Efficient Bayesian Computation Using Plug-and-Play Priors for Poisson Inverse Problems](https://mlsanity.com/paper/2503.16222/) (2025)
- [Alternative design of DeepPDNet in the context of image restoration](https://mlsanity.com/paper/2202.09810/) (2022)
- [Video Restoration with a Deep Plug-and-Play Prior](https://mlsanity.com/paper/2209.02854/) (2022)
- [PG-DPIR: An efficient plug-and-play method for high-count Poisson-Gaussian inverse problems](https://mlsanity.com/paper/2504.10375/) (2025)
- [Limited-Angle Tomography Reconstruction via Projector Guided 3D Diffusion](https://mlsanity.com/paper/2510.06516/) (2025)
- [A convergent Plug-and-Play Majorization-Minimization algorithm for Poisson inverse problems](https://mlsanity.com/paper/2603.24156/) (2026)

## Abstract (arXiv)

The Anscombe transform offers an approximate conversion of a Poisson random variable into a Gaussian one. This transform is important and appealing, as it is easy to compute, and becomes handy in various inverse problems with Poisson noise contamination. Solution to such problems can be done by first applying the Anscombe transform, then applying a Gaussian-noise-oriented restoration algorithm of choice, and finally applying an inverse Anscombe transform. The appeal in this approach is due to the abundance of high-performance restoration algorithms designed for white additive Gaussian noise (we will refer to these hereafter as "Gaussian-solvers"). This process is known to work well for high SNR images, where the Anscombe transform provides a rather accurate approximation. When the noise level is high, the above path loses much of its effectiveness, and the common practice is to replace it with a direct treatment of the Poisson distribution. Naturally, with this we lose the ability to leverage on vastly available Gaussian-solvers. In this work we suggest a novel method for coupling Gaussian denoising algorithms to Poisson noisy inverse problems, which is based on a general approach termed "Plug-and-Play". Deploying the Plug-and-Play approach to such problems leads to an iterative scheme that repeats several key steps: 1) A convex programming task of simple form that can be easily treated; 2) A powerful Gaussian denoising algorithm of choice; and 3) A simple update step. Such a modular method, just like the Anscombe transform, enables other developers to plug their own Gaussian denoising algorithms to our scheme in an easy way. While the proposed method bares some similarity to the Anscombe operation, it is in fact based on a different mathematical basis, which holds true for all SNR ranges.