Figure 2 Original phase map (a) after N=100 diffusive iterations. It contains smoothly varying background phase error as well as the large phase loop, both to be removed from the original phase map in Fig.1(b). Clean phase map (b) with only desired local susceptibility tissue contrast after phase in Fig.2(a) is removed from that of Fig.1(b).

Figure 3 Compared with Fig.2, (a) is the phase of original complex image after smoothed in real and imaginary parts by a 3x3 sliding window N=100 times. The circled pole was slightly shifted to another location which may cause artifact when this phase map is subtracted from the original. (b) Result after phase in Fig.3(a) was removed from that of Fig.1(b). A phase dipole was created in the circle, which may cause “cusp artifact” after subsequent minimum or maximum intensity projections. The result was also unstable in regions where the background phase changed rapidly (arrows).