Synthetic Magnetic Resonance (MR) imaging predicts images at new design parameter settings from a few observed MR scans. Model-based methods, or methods that use both the physical and statistical properties underlying the MR signal and its acquisition, can predict images at any setting from as few as three scans, allowing it to be used in individualized patient- and anatomy-specific contexts. However, the estimation problem in model-based synthetic MR imaging is ill-posed and so regularization, in the form of correlated Gaussian Markov Random Fields, is imposed on the voxel-wise spin-lattice relaxation time, spin-spin relaxation time and the proton density underlying the MR image. We develop theoretically sound but computationally practical matrix-free estimation methods for synthetic MR imaging. Our evaluations show excellent ability of our methods to synthetize MR images in a clinical framework. An added strength of our model-based approach, also developed and illustrated here, is the accurate estimation of standard errors of regional means in the predicted images.
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