An L0-Norm-Based Method for Passive Shimming Design in MRI: A Simulation-Based Study

In a magnetic resonance imaging (MRI) system, it is highly desirable to achieve superior homogeneity of the static magnetic field (B0) within the imaging region for high-performance imaging. Passive shimming (PS) is a widely used technique that employs ferromagnetic materials to reduce the B0 deviations. However, the PS installation process often involves multiple manual iterations due to system or human errors, causing efficiency and accuracy difficulties. Existing PS solutions usually use L1-norm-based optimization algorithms to minimize the total iron consumption and constrain the peak-to-peak field inhomogeneity within the desired range. This design scheme can lead to substantial modifications to shim pockets in each iteration, making the process time-consuming and prone to induce installation errors and even causing operation failures. This paper proposes a novel approach that utilizes the L0-norm to redesign the PS optimization model. Instead of focusing on reducing the total thickness of iron pieces, as done in conventional PS optimizations, the new design allows the explicit adjustment of the number of shim pockets, enhancing shimming efficiency and reducing manual errors in the installation process. To validate the effectiveness of the proposed method, we conducted several tests on shimming a 3-T superconducting magnet. The results demonstrate that our new scheme consistently generates sparse solutions that improve efficiency and accuracy compared to conventional solutions. Thus, our method offers a favorable solution to streamline the shimming process, addressing the long-standing technical restrictions of the standard LP model. This new PS is expected to achieve high B0 uniformity for various MRI applications.