  Data-driven optimization of sampling patterns in MRI has recently received a
significant attention.Following recent observations on the combinatorial number
of minimizers in off-the-grid optimization, we propose a framework to globally
optimize the sampling densities using Bayesian optimization. Using a dimension
reduction technique, we optimize the sampling trajectories more than 20 times
faster than conventional off-the-grid methods, with a restricted number of
training samples. This method -- among other benefits -- discards the need of
automatic differentiation.Its performance is slightly worse than
state-of-the-art learned trajectories since it reduces the space of admissible
trajectories, but comes with significant computational advantages.Other
contributions include: i) a careful evaluation of the distance in probability
space to generate trajectories ii) a specific training procedure on families of
operators for unrolled reconstruction networks and iii) a gradient projection
based scheme for trajectory optimization.
