Fat-water separation is a classical problem for in vivomagnetic resonance imaging, with multiple applications both in cases where the aim is the removal of fat signal, as well as in cases where the fat signal itself is of diagnostic interest. Although many methods have been proposed, robust fat-water separation remains a challenge. The problem presents two key difficulties: (a) the presence of B0 field inhomogeneities, which makes the problem non-linear and ill-posed; and (b) the difficulty of accurately modeling the acquired signal, which can lead to bias in quantitative fat-water separation applications. The research in this thesis has developed joint estimation methods to address the ill-posedness of the problem by simultaneously estimating the complete fat-water images and field inhomogeneity map. The joint estimation formulation developed in this work is able to overcome the complications of voxel-by-voxel separation, and it allows characterization of the resolution properties of its estimates, but results in a challenging optimization problem.To address this complication, optimization algorithms based on graph cuts have been developed and studied. Additionally, this work addresses the modeling issues of fat-water separation by comparing a set of recently proposed models, demonstrating that accurate spectral modeling of the acquired signal is critical for quantitative applications. Simulation, phantom and in vivo results are included to highlight the properties of the proposed methods and compare them to previous approaches.This thesis also contains example applications of the proposed methods, with an emphasis on the characterization of intramyocardial fat.
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Joint estimation of water and fat images from magnetic resonance signals