For optimal image quality in susceptibility-weighted imaging and accurate quantification of susceptibility, it is necessary to isolate the local field generated by local magnetic sources (such as iron) from the background field that arises from imperfect shimming and variations in magnetic susceptibility of surrounding tissues (including air). We present a nonparametric background field removal method based on projection onto dipole fields in which the background field inside an ROI is decomposed into a field originating from dipoles outside the ROI using the projection theorem in Hilbert space.