In fast MR imaging with long readout times, such as echo-planar imaging (EPI) and spiral scans, it is important to correct for the effects of field inhomogeneity to reduce image distortion and blurring. Such corrections require an accurate field map, a map of the off-resonance frequency at each voxel. Standard fieldmap estimation methods yield noisy fieldmaps, particularly in image regions having low spin density. This paper describes regularized methods for fieldmap estimation. These methods exploit the fact that fieldmaps are smooth functions. Efficient convergent algorithms are given even though the problem is highly nonlinear. Results show that the proposed regularized methods significantly improve the quality of fieldmap estimates relative to conventional unregularized methods
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