中文摘要：

目标场方法由Turner于1986年提出，到目前为止该方法已成为核磁共振成像系统中匀场、梯度线圈设计的一种主流方法。各种改进的目标场方法纷纷涌现。为解决线圈设计中的有限尺寸问题，Forbes和Crozier提出了一种新方法，该方法预先通过三角函数来约束线圈面上的电流密度分布，为克服方程求解过程中的病态问题，对电流密度表达式中的待定系数采用最小均方差（least square，LS）和L2范数相结合的方法来进行估计，成功得到了有限长匀场线圈的设计结果。该文采用最小均方差和 L1范数结合的方法来对面电流密度分解表达式中的未知系数进行估计，并将该方法应用于核磁共振成像（magnetic resonance imaging，MRI）系统的匀场线圈设计中。系统主磁体长度为3 m，室温孔直径为1.6 m，目标区域（region of interest，ROI）直径为0.4 m。算例采用Matlab仿真平台，结果表明该文提出的LS-L1目标场方法相比于传统的LS-L2目标场方法磁场偏差更小、效果更好。

英文摘要：

The target field （TF） method proposed by Turner in 1986 has become the mainstream method for both shim coil and gradient coil in magnetic resonance imaging （MRI）. A series of methods based on the original one have been proposed. In order to solve the problem of finite size during coil design, Forbes and Crozier proposed a novel approach which employs the trigonometric functions to expand surface current density. To overcome the ill-posed problem in the equation solving process, the undetermined coefficients are estimated by the combination of the standard least square （LS） with L2 norm regularization （LS-L2）, and good design results are got. This paper proposed to estimate the coefficients of the current density using LS with L1 norm regularization （LS-L1）. This new method was employed to design a set of shim coils for an MRI system. The length of the main magnet used in this system was 3 m;the diameter of room temperature and region of interest （ROI） was 1.6 m, 0.4 m, respectively. Simulation results via Matlab demonstrate that the proposed LS-L1 method performed better than the traditional LS-L2 TF method.