This works explores the use of data-driven Markov chains that are constructed from generative models for Bayesian MRI reconstruction, where the generative models utilize prior knowledge learned from an existing image database. Given the measured k-space, samples are then drawn from the posterior using Markov chain Monte Carlo (MCMC) method. In addition to the maximum a posteriori (MAP) estimate for the image which is obtained with conventional methods, also a minimum mean square error (MMSE) estimate and uncertainty maps can be computed from these samples.
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