Fast and robust design of time-optimal k-space trajectories

Especially 3D parallel selective excitation pulses require the synthesis of fast non-uniform k-space trajectories. Since numerical approaches are usually very time-consuming and impaired by numerical errors, a novel analytic framework on rapidly designing time-optimal trajectories was developed. The trajectory is represented by analytic gradient basis functions that are symbolically solved to traverse given k-space control points. The trajectory is then globally accelerated to fully utilize given hardware constraints Gmax and Smax, yielding time-optimal analytic gradients. Furthermore, this optimization uses an analytically derived Jacobian which guarantees convergence within seconds. Any arbitrarily shaped 2D/3D trajectory can be modeled and optimized using the method.

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