The separation of water and fat from multi-echo images is a classic problem in magnetic resonance imaging (MRI) with a wide range of important clinical applications. For example, removal of fat signal can provide better visualization of other signal of interest in MRI scans. In other cases, the fat distribution map can be of great importance in diagnosis. Although many methods have been proposed over the past three decades, robust fat water separation remains a challenge as radiological technology and clinical expectation continue to grow. The problem presents three key difficulties: a) the presence of B0 field inhomogeneities, often large in the state-of-the-art research and clinical settings, which makes the problem non-linear and ill-posed; b) the ambiguity of signal modeling in locations with only one metabolite (either fat or water), which can manifest as spurious fat water swaps in the separation; c) the computational expenditure in fat water separation as the size of the data is increasing along with evolving MRI hardware, which hampers the clinical applicability of the fat water separation. The main focus of this thesis is to develop novel graph based algorithms to estimate the B0 field inhomogeneity maps and separate fat water signals with global accuracy and computational efficiency. We propose a new smoothness constrained framework for the GlObally Optimal Surface Estimation (GOOSE), in which the spatial smoothness of the B0 field is modeled as a finite constraint between adjacent voxels in a uniformly discretized graph. We further develop a new non-equidistant graph model that enables a Rapid GlObally Optimal Surface Estimation (R-GOOSE) in a subset of the fully discretized graph in GOOSE. Extensions of the above frameworks are also developed to achieve high computational efficiency for processing large 3D datasets. Global convergence of the optimization formulation is proven in all frameworks. The developed methods have also been extensively compared to the existing state-of-the-art fat water separation methods on a variety of datasets with consistent performance of high accuracy and efficiency.

People with cerebral palsy (CP) may develop muscle contractures, which are defined as a loss of joint range due to an increase in passive muscle stiffness [1]. Computer models suggest that intramuscular fat can increase muscle stiffness [2]. There is evidence that children with spastic CP have elevated intramuscular fat fractions, but quantitative estimations of the intramuscular fat fraction are variable [1]. Therefore, a reliable method for in vivo quantification of intramuscular fat is required. The aim of this thesis was to compare two- and three-point Dixon fat-water separation methods, as well as the IDEAL algorithm for intramuscular fat quantification of the gastrocnemius medialis, for both children with CP and typically developed peers. As a reference standard, the water- and fat-only maps resulting from the Philips mDIXONXD turbo-spin-echo sequence were used (Ingenia CX, Philips Healthcare, The Netherlands). It was found that neither of the methods can compare to the reference standard, which is probably due to poor performance of the phase unwrapping algorithm applied on this data. Further studies need to be done in order to better quantify the phase error in multi-echo Dixon MRI.

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