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. Author manuscript; available in PMC: 2015 Jul 1.
Published in final edited form as: J Magn Reson Imaging. 2014 Oct 1;42(1):23–41. doi: 10.1002/jmri.24768

Figure 3.

Figure 3

Relationship between susceptibility and magnetic field. (a) Each image voxel can be approximated as a magnetic dipole which produces a dipole field that extends beyond the voxel itself. Dipole fields originating from different voxels follow the superposition rule resulting in a convolution relationship between field and susceptibility which can be expressed as a multiplication in the k-space. (b) Solving the inverse problem from field to susceptibility is ill-posed, as the coefficients of the equation become zero on a surface of cone in the k-space when k2 = 3k2z.