Regularized higher-order in vivo shimming

A regularized algorithm is presented for localized in vivo shimming. The technique uses first- (X,Y,Z), second- (Z², ZX, ZY, X²-Y², XY), and third-order (Z³) shim coils, and is robust when applied to arbitrarily-shaped, as well as off-center, regions of interest (ROIs). A single-shot spiral pulse sequence is used for rapid field map acquisition, and a least-squares calculation of the shim currents is performed to minimize the root-meansquare (RMS) value of the B₀ inhomogeneity over a user-selected ROI. The use of a singular value decomposition (SVD) in combination with a regularization algorithm significantly improves the numerical stability of the least-squares fitting procedure. The fully automated shimming package is implemented on a 3 T GE Signa system and its robust performance is demonstrated in phantom and in vivo studies.