1. A method for estimating values of a field map in a magnetic resonance (MR) imaging system, the method comprising: a) applying a magnetic resonance excitation; b) acquiring a set of MR images at multiple echo times based on the magnetic resonance excitation; c) determining a set of feasible field map values for a pixel in a field map from the set of MR images; and d) estimating a value of the field map by choosing a field map value for the pixel from the set of feasible field map values using a combinatorial optimization algorithm that includes a smoothness constraint.