Optimal trajectory design for higher-dimensional encoding

PURPOSE Spatial encoding magnetic fields (SEMs) that vary nonlinearly over the field-of-view have the potential to accelerate image acquisition and overcome safety limitations. Recent work has demonstrated that the spatially varying resolution, characteristic of this type of encoding, can be controlled with combinations of linear and nonlinear fields with an appropriate trajectory. In addition to challenging reconstuction, trajectory design for these systems is difficult since the familiar k-space is insufficient to represent the higher dimensional encoding space. To date, trajectories have been designed based on traditional sampling schemes such as Cartesian, radial or EPI. Trajectories based on optimizing spatial bases have also been proposed. In this work, we propose a method to optimize the trajectory based on the theoretical variance of the reconstructed image.