A Conditional Normalizing Flow for Accelerated Multi-Coil MR Imaging
Jeffrey Wen Rizwan Ahmad Philip Schniter
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/