Shimming: Theory and Practice - UCLA-DOE

Gradient Shimming
When gradshim is executed, an image (1D or 3D) is taken of the
field using two echo delays (TE 1 and TE 2 ) as before.
The image is compared to the field maps, and the computer calculates
how best the change the shims to make the field homogeneous.;
Heres how the calculation is done:
Optimal shim settings are calculated by solving the following
least-squares problem using singular value decomposition:
S opt = arg. min. (||A . s – b|| 2 )
where
A = matrix of n column vectors, each one a vector of field changes per
unit shim change for m spatial positions. n is the number of shims.
b = vector of current field values for m spatial elements
s = vector of n starting shim settings
S opt = optimal shim settings