An MR magnetic field inhomogeneity compensation system acquires multiple MR data sets representing luminance intensity values of individual image elements comprising corresponding multiple different image versions of at least a portion of a first imaging slice of patient anatomy including fat and water components. The compensation system employs the multiple MR data sets in solving corresponding multiple simultaneous nonlinear equations to calculate local frequency offset associated with magnetic field inhomogeneity at the individual image element location, for an individual image element of the image elements. The local frequency offset comprises a difference between proton spin frequency at the location and a nominal proton spin frequency. The compensation system derives data representing an electrical signal to be applied to magnetic field generation coils to substantially compensate for determined offset frequencies at the plurality of individual locations. A magnetic field generation coil generates a magnetic field in response to applying the electrical signal to substantially compensate for the magnetic field inhomogeneity at the individual image element location.