3-D optimization of magnetic field shimming in MRI by convex programming approach

Spatial uniformity of amplitude and polarization of the RF magnetic field, associate to SAR limitation constitute a crucial problem in the design of advanced Magnetic Resonance Imaging (MRI) equipment. As a result, the issue of shimming the RF magnetic field (i.e. optimizing its space uniformity) has received considerable attention in the recent literature. Recently these authors have introduced and tested in 2D a specialized optimization for this task, where constraints on minimum field, on polarization and SAR limitation have been enforced in an essentially-convex manner by using a convex-under-constraint optimization. Here we discuss the impact of a full 3D scenario, outlining the perceived limits of achievable performance.