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

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... 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/.