Bayesian MRI Reconstruction with Joint Uncertainty Estimation using Diffusion Models
This addresses MRI reconstruction for medical imaging by providing flexible, data-driven methods that can handle different sampling schemes, though it is incremental as it builds on existing generative models.
The paper tackles MRI reconstruction by enabling efficient sampling from learned probability distributions using diffusion models, achieving improved reconstruction quality with joint uncertainty estimation, as demonstrated on an open dataset with 10-fold undersampling.
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.