A Conditional Normalizing Flow for Accelerated Multi-Coil MR Imaging
This work addresses the need for more comprehensive information in accelerated MRI for downstream tasks, offering a novel approach to posterior sampling in an incremental domain-specific context.
The paper tackles the problem of accelerated MR imaging by sampling from the posterior distribution to provide multiple plausible solutions, using a conditional normalizing flow to infer missing signal components, and demonstrates fast inference and improved accuracy over recent methods on fastMRI brain and knee data.
Accelerated magnetic resonance (MR) imaging attempts to reduce acquisition time by collecting data below the Nyquist rate. As an ill-posed inverse problem, many plausible solutions exist, yet the majority of deep learning approaches generate only a single solution. We instead focus on sampling from the posterior distribution, which provides more comprehensive information for downstream inference tasks. To do this, we design a novel conditional normalizing flow (CNF) that infers the signal component in the measurement operator's nullspace, which is later combined with measured data to form complete images. Using fastMRI brain and knee data, we demonstrate fast inference and accuracy that surpasses recent posterior sampling techniques for MRI. Code is available at https://github.com/jwen307/mri_cnf/