A Novel Target-Field Method Using LASSO Algorithm for Shim and Gradient Coil Design

Target field (TF) method is very important for design of shim and gradient coils which have been used in magnetic resonance imaging (MRI) and other applications. Many works based on TF have been proposed. To restrict the current distribution on cylindrical coils with a given finite length, the current density is expanded by trigonometric series and the unknown coefficients are estimated based on the standard Least Square (LS) with L2 norm regularization (LS-L2). In this paper, we propose to estimate the coefficients using LS with L1 norm regularization (LS-L1), also named Least Absolute Shrinkage and Selection Operator (LASSO), which is solved via Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). The proposed method can obtain sparse solutions and better approximations, which can be used to design cylindrical shim and gradient coils for MRI. Simulation results show that the proposed LS-L1 method performs better than the LS-L2 TF method.