  Acquisition of Magnetic Resonance Imaging (MRI) scans can be accelerated by
under-sampling in k-space (i.e., the Fourier domain). In this paper, we
consider the problem of optimizing the sub-sampling pattern in a data-driven
fashion. Since the reconstruction model's performance depends on the
sub-sampling pattern, we combine the two problems. For a given sparsity
constraint, our method optimizes the sub-sampling pattern and reconstruction
model, using an end-to-end learning strategy. Our algorithm learns from
full-resolution data that are under-sampled retrospectively, yielding a
sub-sampling pattern and reconstruction model that are customized to the type
of images represented in the training data. The proposed method, which we call
LOUPE (Learning-based Optimization of the Under-sampling PattErn), was
implemented by modifying a U-Net, a widely-used convolutional neural network
architecture, that we append with the forward model that encodes the
under-sampling process. Our experiments with T1-weighted structural brain MRI
scans show that the optimized sub-sampling pattern can yield significantly more
accurate reconstructions compared to standard random uniform, variable density
or equispaced under-sampling schemes. The code is made available at:
https://github.com/cagladbahadir/LOUPE .
