  Supervised deep learning methods have shown promise in undersampled Magnetic
Resonance Imaging (MRI) reconstruction, but their requirement for paired data
limits their generalizability to the diverse MRI acquisition parameters.
Recently, unsupervised controllable generative diffusion models have been
applied to undersampled MRI reconstruction, without paired data or model
retraining for different MRI acquisitions. However, diffusion models are
generally slow in sampling and state-of-the-art acceleration techniques can
lead to sub-optimal results when directly applied to the controllable
generation process. This study introduces a new algorithm called
Predictor-Projector-Noisor (PPN), which enhances and accelerates controllable
generation of diffusion models for undersampled MRI reconstruction. Our results
demonstrate that PPN produces high-fidelity MR images that conform to
undersampled k-space measurements with significantly shorter reconstruction
time than other controllable sampling methods. In addition, the unsupervised
PPN accelerated diffusion models are adaptable to different MRI acquisition
parameters, making them more practical for clinical use than supervised
learning techniques.
