The field of medical image analysis continues to expand as magnetic resonance imaging (MRI) technology advances through increases in field strength and the development of new image acquisition and reconstruction methods. The advent of echo planar imaging (EPI) has allowed volumetric data sets to be obtained in a few seconds, making it possible to image dynamic physiological processes in the brain. In order to extract meaningful information from functional and diffusion data, clinicians and neuroscientists typically combine EPI data with high resolution structural images. Image registration is the process of determining the correct correspondence. Registration of EPI and structural images is difficult due to distortions in EPI data. These distortions are caused by magnetic field perturbations that arise from changes in magnetic susceptibility throughout the object of interest. Distortion is typically corrected by acquiring an additional scan called a fieldmap. A fieldmap provides a direct measure of the magnetic perturbations, allowing distortions to be easily computed and corrected. Fieldmaps, however, require additional scan time, may not be reliable in the presence of significant motion or respiration effects, and are often omitted from clinical protocols. In this thesis, we develop a novel method for correcting distortions in EPI data and registering the EPI to structural MRI. A synthetic fieldmap is computed from a tissue/air segmentation of a structural image using a perturbation method and subsequently used to unwarp the EPI data. Shim and other missing parameters are estimated by registration. We obtain results that are similar to those obtained using fieldmnaps, however, neither fieldmaps nor knowledge of shim coefficients is required. In addition, we describe a method for atlas-based segmentation of structural images for calculation of synthetic fieldmaps. CT data sets are used to construct a probabilistic atlas of the head and corresponding MRI is used to train a classifier that segments soft tissue, air, and bone. Synthetic fieldmap results agree well with acquired fieldmaps: 90% of voxel shifts show subvoxel disagreement with those computed from acquired fieldmaps. In addition, synthetic fieldmaps show statistically significant improvement following inclusion of the atlas. In the second part of this thesis, we focus on the inverse problem of reconstructing quantitative magnetic susceptibility maps from acquired fieldmaps. Iron deposits change the susceptibility of tissue, resulting in magnetic perturbations that are detectable with high resolution fieldmaps. Excessive iron deposition in specific regions of the brain is associated with neurodegenerative disorders such as Alzheimer's and Parkinson's disease. In addition, iron is known to accumulate at varying rates throughout the brain in normal aging. Developing a non-invasive method to calculate iron concentration may provide insight into the role of iron in the pathophysiology of neurodegenerative disease. Calculating susceptibility maps from measured fieldmaps is difficult, however, since iron-related field inhomogeneity may be obscured by larger field perturbations, or 'biasfields', arising from adjacent tissue/air boundaries. In addition, the inverse problem is ill-posed, and fieldmap measurements are only valid in limited anatomical regions. In this dissertation, we develop a novel atlas-based susceptibility mapping (ASM) technique that requires only a single fieldmap acquisition and successfully inverts a spatial formulation of the forward field model. We derive an inhomogeneous wave equation that relates the Laplacian of the observed field to the D'Alembertian of susceptibility, and eliminates confounding biasfields. The tissue/air atlas we constructed for susceptibility-based distortion correction is applied to resolve ambiquity in the forward model arising from the ill-posed inversion. We include fourier-based modeling of external susceptibility sources and the associated biasfield in a variational approach, allowing for simultaneous susceptibility estimation and biasfield elimination. Results show qualitative improvement over two methods commonly used to infer underlying susceptibility values and quantitative susceptibility estimates show stronger correlation with postmortem iron concentrations than competing methods.