  Optimizing 3D k-space sampling trajectories for efficient MRI is important
yet challenging. This work proposes a generalized framework for optimizing 3D
non-Cartesian sampling patterns via data-driven optimization. We built a
differentiable MRI system model to enable gradient-based methods for sampling
trajectory optimization. By combining training losses, the algorithm can
simultaneously optimize multiple properties of sampling patterns, including
image quality, hardware constraints (maximum slew rate and gradient strength),
reduced peripheral nerve stimulation (PNS), and parameter-weighted contrast.
The proposed method can either optimize the gradient waveform (spline-based
freeform optimization) or optimize properties of given sampling trajectories
(such as the rotation angle of radial trajectories). Notably, the method
optimizes sampling trajectories synergistically with either model-based or
learning-based reconstruction methods. We proposed several strategies to
alleviate the severe non-convexity and huge computation demand posed by the
high-dimensional optimization. The corresponding code is organized as an
open-source, easy-to-use toolbox. We applied the optimized trajectory to
multiple applications including structural and functional imaging. In the
simulation studies, the reconstruction PSNR of a 3D kooshball trajectory was
increased by 4 dB with SNOPY optimization. In the prospective studies, by
optimizing the rotation angles of a stack-of-stars (SOS) trajectory, SNOPY
improved the PSNR by 1.4dB compared to the best empirical method. Optimizing
the gradient waveform of a rotational EPI trajectory improved subjects' rating
of the PNS effect from 'strong' to 'mild.' In short, SNOPY provides an
efficient data-driven and optimization-based method to tailor non-Cartesian
sampling trajectories.
