  The discovery of the theory of compressed sensing brought the realisation
that many inverse problems can be solved even when measurements are
"incomplete". This is particularly interesting in magnetic resonance imaging
(MRI), where long acquisition times can limit its use. In this work, we
consider the problem of learning a sparse sampling pattern that can be used to
optimally balance acquisition time versus quality of the reconstructed image.
We use a supervised learning approach, making the assumption that our training
data is representative enough of new data acquisitions. We demonstrate that
this is indeed the case, even if the training data consists of just 7 training
pairs of measurements and ground-truth images; with a training set of brain
images of size 192 by 192, for instance, one of the learned patterns samples
only 35% of k-space, however results in reconstructions with mean SSIM 0.914 on
a test set of similar images. The proposed framework is general enough to learn
arbitrary sampling patterns, including common patterns such as Cartesian,
spiral and radial sampling.
