  Optimizing k-space sampling trajectories is a challenging topic for fast
magnetic resonance imaging (MRI). This work proposes to optimize a
reconstruction algorithm and sampling trajectories jointly concerning image
reconstruction quality. We parameterize trajectories with quadratic B-spline
kernels to reduce the number of parameters and enable multi-scale optimization,
which may help to avoid sub-optimal local minima. The algorithm includes an
efficient non-Cartesian unrolled neural network-based reconstruction and an
accurate approximation for backpropagation through the non-uniform fast Fourier
transform (NUFFT) operator to accurately reconstruct and back-propagate
multi-coil non-Cartesian data. Penalties on slew rate and gradient amplitude
enforce hardware constraints. Sampling and reconstruction are trained jointly
using large public datasets. To correct the potential eddy-current effect
introduced by the curved trajectory, we use a pencil-beam trajectory mapping
technique. In both simulations and in-vivo experiments, the learned trajectory
demonstrates significantly improved image quality compared to previous
model-based and learning-based trajectory optimization methods for 20x
acceleration factors. Though trained with neural network-based reconstruction,
the proposed trajectory also leads to improved image quality with compressed
sensing-based reconstruction.
