# Provable Preconditioned Plug-and-Play Approach for Compressed Sensing MRI Reconstruction

arXiv: https://arxiv.org/abs/2405.03854 · HTML: https://mlsanity.com/paper/2405.03854/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 May 2024.

## Built on by (most cited first, 5 of 5)

- [Patch-Based Diffusion Models Beat Whole-Image Models for Mismatched Distribution Inverse Problems](https://mlsanity.com/paper/2410.11730/) (2024)
- [Robust plug-and-play methods for highly accelerated non-Cartesian MRI reconstruction](https://mlsanity.com/paper/2411.01955/) (2024)
- [Solving Imaging Inverse Problems Using Plug-and-Play Denoisers: Regularization and Optimization Perspectives](https://mlsanity.com/paper/2509.03475/) (2025)
- [Normalization Equivariance for Arbitrary Backbones, with Application to Image Denoising](https://mlsanity.com/paper/2605.08193/) (2026)
- [Unsupervised Deep Image Prior for Sparse-View and Limited-Angle Electron Tomography](https://mlsanity.com/paper/2605.27139/) (2026)

## Abstract (arXiv)

Model-based methods play a key role in the reconstruction of compressed sensing (CS) MRI. Finding an effective prior to describe the statistical distribution of the image family of interest is crucial for model-based methods. Plug-and-play (PnP) is a general framework that uses denoising algorithms as the prior or regularizer. Recent work showed that PnP methods with denoisers based on pretrained convolutional neural networks outperform other classical regularizers in CS MRI reconstruction. However, the numerical solvers for PnP can be slow for CS MRI reconstruction. This paper proposes a preconditioned PnP (P^2nP) method to accelerate the convergence speed. Moreover, we provide proofs of the fixed-point convergence of the P^2nP iterates. Numerical experiments on CS MRI reconstruction with non-Cartesian sampling trajectories illustrate the effectiveness and efficiency of the P^2nP approach.