Inverse problem

Iterative reconstruction

Magnetic resonance imaging

Real-time MRI

Mathematics

Computer science

Mathematical optimization

Economics

Computer vision

Medicine

Algorithm

Economic growth

Artificial intelligence

Mathematical analysis

Convergence (economics)

Radiology

Undersampling

Medical imaging

IEEE Signal Processing Magazine

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 reco...

Plug-and-Play Methods for Magnetic Resonance Imaging: Using Denoisers for Image Recovery