  Magnetic Resonance Imaging (MRI) is considered today the golden-standard
modality for soft tissues. The long acquisition times, however, make it more
prone to motion artifacts as well as contribute to the relatively high costs of
this examination. Over the years, multiple studies concentrated on designing
reduced measurement schemes and image reconstruction schemes for MRI, however,
these problems have been so far addressed separately. On the other hand, recent
works in optical computational imaging have demonstrated growing success of the
simultaneous learning-based design of the acquisition and reconstruction
schemes manifesting significant improvement in the reconstruction quality with
a constrained time budget. Inspired by these successes, in this work, we
propose to learn accelerated MR acquisition schemes (in the form of Cartesian
trajectories) jointly with the image reconstruction operator. To this end, we
propose an algorithm for training the combined acquisition-reconstruction
pipeline end-to-end in a differentiable way. We demonstrate the significance of
using the learned Cartesian trajectories at different speed up rates.
