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. Author manuscript; available in PMC: 2013 Mar 1.
Published in final edited form as: Magn Reson Med. 2011 Jun 28;67(3):650–659. doi: 10.1002/mrm.23052

Figure 1.

Figure 1

1D example to illustrate the vectors that span the restricted subspace in which the field map estimate is updated; one can imagine taking an inner product of the field map with each vector to obtain a coefficient in the restricted subspace; further, a backprojection would map the coefficient to image space. (a) one vector that spans the subspace for the first instance of the field map update; (b) three vectors that span the subspace for the next instance of the field map update; (c) seven vectors that span the subspace in the third instance of the field map update; in this example, the step size factor is 0.5 since the vector in (a) has a support size of 256, the vectors in (b) each have a support size of 128, and the vectors in (c) each have a support size of 64; extensions to higher dimensions are made via outer-products of the 1D vectors.