title: Gradient shimming based on regularized estimation for B(0)-field and shim functions.
abstract: Mapping B0-field and shim functions spatially is a crucial step in the gradient shimming. The conventional estimation method used in the phase difference imaging technique takes no account for noise and T2(∗) effects, and is prone to create noisy and distorted field maps. This paper describes a new gradient shimming based on the regularized estimation for B0-field and shim functions. Based on a statistical model, the B0-field and shim function maps are estimated by a Penalized Maximum Likelihood method that minimizes two regularized least-squares cost functions, respectively. The first cost function of B0-field exploits the two facts that the noise in the phase difference measurements is Gaussian and the B0-field maps tend to be smooth. And the other one adds an additional fact that each shim function corresponds to a given spherical harmonic of the magnetic field. Significant improvements in the quality of field mapping and in the final shimming results are demonstrated through computer simulations as well as experiments, especially when the magnetic field homogeneity is poor.
authors.affiliation: State Key Laboratory of Magnetic Resonance and Atomic Molecular Physics, Wuhan Center for Magnetic Resonance, Key Laboratory of Magnetic Resonance in Biological Systems, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China; University of Chinese Academy of Sciences, Beijing 100049, China.
authors.forename: Kan
authors.initials: K
authors.lastname: Song
authors.affiliation: State Key Laboratory of Magnetic Resonance and Atomic Molecular Physics, Wuhan Center for Magnetic Resonance, Key Laboratory of Magnetic Resonance in Biological Systems, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China. Electronic address: baoqingjiahaoba@163.com.
authors.forename: Qingjia
authors.initials: Q
authors.lastname: Bao
authors.affiliation: State Key Laboratory of Magnetic Resonance and Atomic Molecular Physics, Wuhan Center for Magnetic Resonance, Key Laboratory of Magnetic Resonance in Biological Systems, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China.
authors.forename: Fang
authors.initials: F
authors.lastname: Chen
authors.affiliation: State Key Laboratory of Magnetic Resonance and Atomic Molecular Physics, Wuhan Center for Magnetic Resonance, Key Laboratory of Magnetic Resonance in Biological Systems, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China.
authors.forename: Chongyang
authors.initials: C
authors.lastname: Huang
authors.affiliation: State Key Laboratory of Magnetic Resonance and Atomic Molecular Physics, Wuhan Center for Magnetic Resonance, Key Laboratory of Magnetic Resonance in Biological Systems, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China.
authors.forename: Jiwen
authors.initials: J
authors.lastname: Feng
authors.affiliation: State Key Laboratory of Magnetic Resonance and Atomic Molecular Physics, Wuhan Center for Magnetic Resonance, Key Laboratory of Magnetic Resonance in Biological Systems, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China. Electronic address: chyliu@wipm.ac.cn.
authors.forename: Chaoyang
authors.initials: C
authors.lastname: Liu
keywords: B(0) inhomogeneity; Field mapping; Gradient shimming; NMR spectrometer; Penalized Maximum Likelihood; Regularized estimation