Cylindrical-surface shim coil design using target-field method combined with fast L₁ norm minimization algorithm

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.