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/

翻译：加速磁共振成像旨在通过低于奈奎斯特率采集数据来缩短采集时间。作为一个不适定逆问题，存在多种可行解，然而大多数深度学习方法仅生成单一解。我们转而关注从后验分布中采样，这能为下游推理任务提供更全面的信息。为此，我们设计了一种新颖的条件归一化流，它推断测量算子零空间中的信号分量，随后与测量数据结合形成完整图像。利用fastMRI脑部和膝盖数据，我们展示了快速推理和超越最新MRI后验采样技术的精度。代码见https://github.com/jwen307/mri_cnf/