Synthetic Magnetic Resonance (MR) imaging predicts images at new design parameter settings from a few observed MR scans. Model-based methods, that use both the physical and statistical properties underlying the MR sig...
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Synthetic Magnetic Resonance (MR) imaging predicts images at new design parameter settings from a few observed MR scans. Model-based 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 demonstrate superior performance of our methods in currently-used clinical settings when compared to existing model-based and deep learning methods. Moreover, unlike deep learning approaches, our fast methodology can synthesize needed images during patient visits, with good estimation and prediction accuracy and consistency. An added strength of our model-based approach, also developed and illustrated here, is the accurate estimation of standard errors of regional contrasts in the synthesized images. A R package symr implements our methodology. Supplementary materials for this article are available online.
Spatial prediction is commonly achieved under the assumption of a Gaussian random field by obtaining maximum likelihood estimates of parameters, and then using the kriging equations to arrive at predicted values. For ...
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Spatial prediction is commonly achieved under the assumption of a Gaussian random field by obtaining maximum likelihood estimates of parameters, and then using the kriging equations to arrive at predicted values. For massive datasets, fixed rank kriging using the expectation-maximizationalgorithm for estimation has been proposed as an alternative to the usual but computationally prohibitive kriging method. The method reduces computation cost of estimation by redefining the spatial process as a linear combination of basis functions and spatial random effects. A disadvantage of this method is that it imposes constraints on the relationship between the observed locations and the knots. We develop an alternative method that utilizes the spatial mixed effects model, but allows for additional flexibility by estimating the range of the spatial dependence between the observations and the knots via an alternating expectation conditional maximization algorithm. Experiments show that our methodology improves estimation without sacrificing prediction accuracy while also minimizing the additional computational burden of extra parameter estimation. The methodology is applied to a temperature dataset archived by the United States National Climate Data Center, with improved results over previous methodology.
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