In this work we present an approach for chemical shift based fat/water-separation using variational methods for the estimation of the underlying B0-field inhomogeneity. We show that the fat/water-problem can be solved by the application of total-generalized-variation (TGV) regularization on the underlying B0-field to enforce piecewise smoothness. With this approach we are able to model huge B0-deviations as well as discontinuities in the B0-field at tissue boundaries with different susceptibility parallel to the main-field. This is shown on different datasets, including two of the ISMRM fat/water-challenge of 2012.
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