We introduce a framework that enables efficient sampling from learned probability distributions for MRI reconstruction. Different from conventional deep learning-based MRI reconstruction techniques, samples are drawn from the posterior distribution given the measured k-space using the Markov chain Monte Carlo (MCMC) method. In addition to the maximum a posteriori (MAP) estimate for the image, which can be obtained with conventional methods, the minimum mean square error (MMSE) estimate and uncertainty maps can also be computed. The data-driven Markov chains are constructed from the generative model learned from a given image database and are independent of the forward operator that is used to model the k-space measurement. This provides flexibility because the method can be applied to k-space acquired with different sampling schemes or receive coils using the same pre-trained models. Furthermore, we use a framework based on a reverse diffusion process to be able to utilize advanced generative models. The performance of the method is evaluated on an open dataset using 10-fold undersampling in k-space.

翻译：我们提出了一种框架，能够从学习到的概率分布中高效采样以实现MRI重建。与传统的基于深度学习的MRI重建技术不同，该方法利用马尔可夫链蒙特卡洛（MCMC）方法从给定k空间测量的后验分布中抽取样本。除了可通过常规方法获得的图像最大后验（MAP）估计外，该方法还可计算最小均方误差（MMSE）估计和不确定性图。数据驱动的马尔可夫链由从给定图像数据库学习到的生成模型构建，且独立于用于建模k空间测量的前向算子。这一特性提供了灵活性，因为该方法可应用于采用不同采样方案或接收线圈获取的k空间数据，且无需重新训练预训练模型。此外，我们采用基于逆向扩散过程的框架，以便利用先进的生成模型。在开放数据集上，该方法在10倍k空间欠采样条件下的性能得到了评估。