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Due to the linearity of equation 18 the single voxel solutions
derived in the previous section can be added together to give the
total field for the object as
|
(24) |
This takes the form of a discrete convolution of the discrete
susceptibility map, , and the single voxel solution, .
Therefore the calculation can be efficiently implemented by using the
3D Fast Fourier Transform (FFT) as
|
(25) |
where
is the FFT and is a zero-padding
function, used to ensure that there is no period wrap-around in the
convolution.