Bayesian Magnetic Resonance Image Reconstruction and Uncertainty Quantification

Motivation: Quantification of the effect of sub-sampled k-space data in magnetic resonance image reconstruction by providing joint image reconstruction and uncertainty quantification. Goal(s): Image reconstruction and uncertainty quantification from sub-sampled k-space measurements. Approach: The problem is formulated within a Bayesian framework as an inverse problem, and prior distributions are assigned to the unknown model parameters. A Markov chain Monte Carlo (MCMC) method, based on a split-and-augmented Gibbs sampler, is then used to sample the resulting posterior distribution. Results: The model is demonstrated using a real brain image from the human connectome project (HCP) to reconstruct images and provide uncertainty measures from sub-sampled k-space data. Impact: We introduced an image reconstruction and uncertainty quantification algorithm from under-sampled k-space data. The results showed that the algorithm can quantify the effect of reduced samples, enabling fast imaging. Future work can investigate this approach using low-field MRI.