Abstract
This paper develops an FBP-MAP (Filtered Backprojection, Maximum a Posteriori) algorithm to reconstruct MRI images from under-sampled data. An objective function is first set up for the MRI reconstruction problem with a data fidelity term and a Bayesian term. The Bayesian term is a constraint in the temporal dimension. This objective function is minimized using the calculus of variations. The proposed algorithm is non-iterative. Undersampled dynamic myocardial perfusion MRI data were used to test the feasibility of the proposed technique. It is shown that the non-iterative Fourier reconstruction method effectively incorporates the temporal constraint and significantly reduces the angular aliasing artifacts caused by undersampling. A significant advantage of the proposed non-iterative Fourier technique over the iterative techniques is its fast computation time.
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