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

## TL;DR

This paper explores plug-and-play algorithms for MRI image reconstruction, emphasizing their iterative denoising approach, equilibrium interpretation, and demonstrating their effectiveness in recovering images from undersampled data.

## Contribution

It introduces a unifying framework for PnP methods in MRI, including convergence analysis and practical examples of image recovery from undersampled datasets.

## Key findings

- PnP methods effectively reconstruct MRI images from undersampled data
- Convergence of PnP algorithms can be analyzed via equilibrium equations
- Illustrative examples demonstrate practical success in MRI recovery

## Abstract

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.