title: Passive shimming of a superconducting magnet using the L1-norm regularized least square algorithm.
abstract: The uniformity of the static magnetic field B0 is of prime importance for an MRI system. The passive shimming technique is usually applied to improve the uniformity of the static field by optimizing the layout of a series of steel shims. The steel pieces are fixed in the drawers in the inner bore of the superconducting magnet, and produce a magnetizing field in the imaging region to compensate for the inhomogeneity of the B0 field. In practice, the total mass of steel used for shimming should be minimized, in addition to the field uniformity requirement. This is because the presence of steel shims may introduce a thermal stability problem. The passive shimming procedure is typically realized using the linear programming (LP) method. The LP approach however, is generally slow and also has difficulty balancing the field quality and the total amount of steel for shimming. In this paper, we have developed a new algorithm that is better able to balance the dual constraints of field uniformity and the total mass of the shims. The least square method is used to minimize the magnetic field inhomogeneity over the imaging surface with the total mass of steel being controlled by an L1-norm based constraint. The proposed algorithm has been tested with practical field data, and the results show that, with similar computational cost and mass of shim material, the new algorithm achieves superior field uniformity (43% better for the test case) compared with the conventional linear programming approach.
authors.affiliation: Department of Biomedical Engineering, Zhejiang University, Hangzhou, China.
authors.forename: Xia
authors.initials: X
authors.lastname: Kong
authors.affiliation: Department of Biomedical Engineering, Zhejiang University, Hangzhou, China.
authors.forename: Minhua
authors.initials: M
authors.lastname: Zhu
authors.affiliation: Department of Biomedical Engineering, Zhejiang University, Hangzhou, China; State Key Lab of CAD&CG, Zhejiang University, Hangzhou, China. Electronic address: xialing@zju.edu.cn.
authors.forename: Ling
authors.initials: L
authors.lastname: Xia
authors.affiliation: Division of Superconducting Magnet Science and Technology, Institute of Electrical Engineering, Chinese Academy of Sciences, China. Electronic address: qiuliang@mail.iee.ac.cn.
authors.forename: Qiuliang
authors.initials: Q
authors.lastname: Wang
authors.affiliation: Division of Superconducting Magnet Science and Technology, Institute of Electrical Engineering, Chinese Academy of Sciences, China.
authors.forename: Yi
authors.initials: Y
authors.lastname: Li
authors.affiliation: Division of Superconducting Magnet Science and Technology, Institute of Electrical Engineering, Chinese Academy of Sciences, China.
authors.forename: Xuchen
authors.initials: X
authors.lastname: Zhu
authors.affiliation: School of Information Technology and Electrical Engineering, The University of Queensland, Australia.
authors.forename: Feng
authors.initials: F
authors.lastname: Liu
authors.affiliation: School of Information Technology and Electrical Engineering, The University of Queensland, Australia.
authors.forename: Stuart
authors.initials: S
authors.lastname: Crozier
keywords: L(1)-norm regularized least square; MRI (Magnetic Resonance Imaging); Passive shimming