  In compressed sensing MRI (CS-MRI), k-space measurements are under-sampled to
achieve accelerated scan times. CS-MRI presents two fundamental problems: (1)
where to sample and (2) how to reconstruct an under-sampled scan. In this
paper, we tackle both problems simultaneously for the specific case of 2D
Cartesian sampling, using a novel end-to-end learning framework that we call
LOUPE (Learning-based Optimization of the Under-sampling PattErn). Our method
trains a neural network model on a set of full-resolution MRI scans, which are
retrospectively under-sampled on a 2D Cartesian grid and forwarded to an
anti-aliasing (a.k.a. reconstruction) model that computes a reconstruction,
which is in turn compared with the input. This formulation enables a
data-driven optimized under-sampling pattern at a given sparsity level. In our
experiments, we demonstrate that LOUPE-optimized under-sampling masks are
data-dependent, varying significantly with the imaged anatomy, and perform well
with different reconstruction methods. We present empirical results obtained
with a large-scale, publicly available knee MRI dataset, where LOUPE offered
superior reconstruction quality across different conditions. Even with an
aggressive 8-fold acceleration rate, LOUPE's reconstructions contained much of
the anatomical detail that was missed by alternative masks and reconstruction
methods. Our experiments also show how LOUPE yielded optimal under-sampling
patterns that were significantly different for brain vs knee MRI scans. Our
code is made freely available at https://github.com/cagladbahadir/LOUPE/.
