# Robust plug-and-play methods for highly accelerated non-Cartesian MRI reconstruction

arXiv: https://arxiv.org/abs/2411.01955 · HTML: https://mlsanity.com/paper/2411.01955/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 29 references that are in the map.
- First posted on arXiv 4 Nov 2024.

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

- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Neighbor2Neighbor: Self-Supervised Denoising from Single Noisy Images](https://mlsanity.com/paper/2101.02824/) (2021)
- [Gradient Step Denoiser for convergent Plug-and-Play](https://mlsanity.com/paper/2110.03220/) (2021)
- [MR Image Denoising and Super-Resolution Using Regularized Reverse Diffusion](https://mlsanity.com/paper/2203.12621/) (2022)
- [Learning Maximally Monotone Operators for Image Recovery](https://mlsanity.com/paper/2012.13247/) (2020)
- [Benchopt: Reproducible, efficient and collaborative optimization benchmarks](https://mlsanity.com/paper/2206.13424/) (2022)
- [Equivariant plug-and-play image reconstruction](https://mlsanity.com/paper/2312.01831/) (2023)
- [TFPnP: Tuning-free Plug-and-Play Proximal Algorithm with Applications to Inverse Imaging Problems](https://mlsanity.com/paper/2012.05703/) (2020)
- [Multi-Scale Energy (MuSE) plug and play framework for inverse problems](https://mlsanity.com/paper/2305.04775/) (2023)
- [Memory-efficient model-based deep learning with convergence and robustness guarantees](https://mlsanity.com/paper/2206.04797/) (2022)
- [First AI for deep super-resolution wide-field imaging in radio astronomy: unveiling structure in ESO 137--006](https://mlsanity.com/paper/2207.11336/) (2022)
- [A Plug-and-Play Approach to Multiparametric Quantitative MRI: Image Reconstruction using Pre-Trained Deep Denoisers](https://mlsanity.com/paper/2202.05269/) (2022)
- [Provable Preconditioned Plug-and-Play Approach for Compressed Sensing MRI Reconstruction](https://mlsanity.com/paper/2405.03854/) (2024)
- [The AIRI plug-and-play algorithm for image reconstruction in radio-interferometry: variations and robustness](https://mlsanity.com/paper/2312.07137/) (2023)

## Built on by (most cited first, 2 of 2)

- [A Comprehensive Survey on Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/2503.07097/) (2025)
- [Unsupervised Deep Image Prior for Sparse-View and Limited-Angle Electron Tomography](https://mlsanity.com/paper/2605.27139/) (2026)

## Abstract (arXiv)

Achieving high-quality Magnetic Resonance Imaging (MRI) reconstruction at accelerated acquisition rates remains challenging due to the inherent ill-posed nature of the inverse problem. Traditional Compressed Sensing (CS) methods, while robust across varying acquisition settings, struggle to maintain good reconstruction quality at high acceleration factors (≥ 8). Recent advances in deep learning have improved reconstruction quality, but purely data-driven methods are prone to overfitting and hallucination effects, notably when the acquisition setting is varying. Plug-and-Play (PnP) approaches have been proposed to mitigate the pitfalls of both frameworks. In a nutshell, PnP algorithms amount to replacing suboptimal handcrafted CS priors with powerful denoising deep neural network (DNNs). However, in MRI reconstruction, existing PnP methods often yield suboptimal results due to instabilities in the proximal gradient descent (PGD) schemes and the lack of curated, noiseless datasets for training robust denoisers. In this work, we propose a fully unsupervised preprocessing pipeline to generate clean, noiseless complex MRI signals from multicoil data, enabling training of a high-performance denoising DNN. Furthermore, we introduce an annealed Half-Quadratic Splitting (HQS) algorithm to address the instability issues, leading to significant improvements over existing PnP algorithms. When combined with preconditioning techniques, our approach achieves state-of-the-art results, providing a robust and efficient solution for high-quality MRI reconstruction.