# Plug and play methods for magnetic resonance imaging (long version)

arXiv: https://arxiv.org/abs/1903.08616 · HTML: https://mlsanity.com/paper/1903.08616/

## Key facts

- Cited by 75 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2019.

## Built on by (most cited first, 30 of 75)

- [Transformers in Medical Imaging: A Survey](https://mlsanity.com/paper/2201.09873/) (2022)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Adaptive Diffusion Priors for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2207.05876/) (2022)
- [Gradient Step Denoiser for convergent Plug-and-Play](https://mlsanity.com/paper/2110.03220/) (2021)
- [Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie](https://mlsanity.com/paper/2103.04715/) (2021)
- [Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors](https://mlsanity.com/paper/2405.18782/) (2024)
- [Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularization](https://mlsanity.com/paper/2201.13256/) (2022)
- [Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --](https://mlsanity.com/paper/2301.03362/) (2023)
- [Provable Probabilistic Imaging using Score-Based Generative Priors](https://mlsanity.com/paper/2310.10835/) (2023)
- [Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging](https://mlsanity.com/paper/2203.12215/) (2022)
- [Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization](https://mlsanity.com/paper/2205.02640/) (2022)
- [Recovery of Continuous 3D Refractive Index Maps from Discrete Intensity-Only Measurements using Neural Fields](https://mlsanity.com/paper/2112.00002/) (2021)
- [Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inference](https://mlsanity.com/paper/2304.11134/) (2023)
- [Imaging with Equivariant Deep Learning](https://mlsanity.com/paper/2209.01725/) (2022)
- [A theoretical framework for self-supervised MR image reconstruction using sub-sampling via variable density Noisier2Noise](https://mlsanity.com/paper/2205.10278/) (2022)
- [Equivariant plug-and-play image reconstruction](https://mlsanity.com/paper/2312.01831/) (2023)
- [Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Condition](https://mlsanity.com/paper/2106.03668/) (2021)
- [Online Deep Equilibrium Learning for Regularization by Denoising](https://mlsanity.com/paper/2205.13051/) (2022)
- [Fixed-Point and Objective Convergence of Plug-and-Play Algorithms](https://mlsanity.com/paper/2104.10348/) (2021)
- [SGD-Net: Efficient Model-Based Deep Learning with Theoretical Guarantees](https://mlsanity.com/paper/2101.09379/) (2021)
- [On Maximum-a-Posteriori estimation with Plug & Play priors and stochastic gradient descent](https://mlsanity.com/paper/2201.06133/) (2022)
- [Graph Signal Restoration Using Nested Deep Algorithm Unrolling](https://mlsanity.com/paper/2106.15910/) (2021)
- [Prior Mismatch and Adaptation in PnP-ADMM with a Nonconvex Convergence Analysis](https://mlsanity.com/paper/2310.00133/) (2023)
- [Deformation-Compensated Learning for Image Reconstruction without Ground Truth](https://mlsanity.com/paper/2107.05533/) (2021)
- [MRI Reconstruction Using Deep Energy-Based Model](https://mlsanity.com/paper/2109.03237/) (2021)
- [Deep Model-Based Architectures for Inverse Problems under Mismatched Priors](https://mlsanity.com/paper/2207.13200/) (2022)
- [Block Coordinate Plug-and-Play Methods for Blind Inverse Problems](https://mlsanity.com/paper/2305.12672/) (2023)
- [MRI Super-Resolution with Deep Learning: A Comprehensive Survey](https://mlsanity.com/paper/2511.16854/) (2025)
- [Deep Algorithm Unrolling for Biomedical Imaging](https://mlsanity.com/paper/2108.06637/) (2021)
- [A Plug-and-Play Approach to Multiparametric Quantitative MRI: Image Reconstruction using Pre-Trained Deep Denoisers](https://mlsanity.com/paper/2202.05269/) (2022)

## Abstract (arXiv)

Magnetic Resonance Imaging (MRI) is a non-invasive diagnostic tool that provides excellent soft-tissue contrast without the use of ionizing radiation. Compared to other clinical imaging modalities (e.g., CT or ultrasound), however, the data acquisition process for MRI is inherently slow, which motivates undersampling and thus drives the need for accurate, efficient reconstruction methods from undersampled datasets. In this article, we describe the use of "plug-and-play" (PnP) algorithms for MRI image recovery. We first describe the linearly approximated inverse problem encountered in MRI. Then we review several PnP methods, where the unifying commonality is to iteratively call a denoising subroutine as one step of a larger optimization-inspired algorithm. Next, we describe how the result of the PnP method can be interpreted as a solution to an equilibrium equation, allowing convergence analysis from the equilibrium perspective. Finally, we present illustrative examples of PnP methods applied to MRI image recovery.