Trajectory optimization based on the signal-to-noise ratio for spatial encoding with nonlinear encoding fields

Purpose Multiple nonlinear gradient fields offer many potential benefits for spatial encoding including reduced acquisition time, fewer artefacts and region‐specific imaging, although designing a suitable trajectory for such a setup is difficult. This work aims to optimize encoding trajectories for multiple nonlinear gradient fields based on the image signal‐to‐noise ratio. Theory and Methods Image signal‐to‐noise ratio is directly linked to the covariance of the reconstructed pixels, which can be calculated recursively for each projection of the trajectory under a Bayesian formulation. An evolutionary algorithm is used to find the higher‐dimensional projections that minimize the pixel covariance, incorporating receive coil profiles, intravoxel dephasing, and reconstruction regularization. The resulting trajectories are tested through simulations and experiments. Results The optimized trajectories produce images with higher resolution and fewer artefacts compared with traditional approaches, particularly for high undersampling. However, higher‐dimensional projection experiments strongly depend on accurate hardware and calibration. Conclusion Computer‐based optimization provides an efficient means to explore the large trajectory space created by the use of multiple nonlinear encoding fields. The optimization framework, as presented here, is necessary to fully exploit the advantages of nonlinear fields. Magn Reson Med 76:104–117, 2016. © 2015 Wiley Periodicals, Inc.