Diagram of the nonlinear reconstruction scheme utilized. k-space data are first reconstructed at low resolution and fit to the signal model, producing low-resolution estimates of the B0 heterogeneity, water, fat, and velocity images. k-space data are then reconstructed at high-resolution, using the low-resolution field map for fitting. These high-resolution images are then fit to the signal model without B0 heterogeneity off-resonance, producing high-resolution water, fat, and velocity images.