  Compressed Sensing MRI (CS-MRI) aims at reconstructing de-aliased images from
sub-Nyquist sampling k-space data to accelerate MR Imaging, thus presenting two
basic issues, i.e., where to sample and how to reconstruct. To deal with both
problems simultaneously, we propose a novel end-to-end Probabilistic
Under-sampling and Explicable Reconstruction neTwork, dubbed PUERT, to jointly
optimize the sampling pattern and the reconstruction network. Instead of
learning a deterministic mask, the proposed sampling subnet explores an optimal
probabilistic sub-sampling pattern, which describes independent Bernoulli
random variables at each possible sampling point, thus retaining robustness and
stochastics for a more reliable CS reconstruction. A dynamic gradient
estimation strategy is further introduced to gradually approximate the
binarization function in backward propagation, which efficiently preserves the
gradient information and further improves the reconstruction quality. Moreover,
in our reconstruction subnet, we adopt a model-based network design scheme with
high efficiency and interpretability, which is shown to assist in further
exploitation for the sampling subnet. Extensive experiments on two widely used
MRI datasets demonstrate that our proposed PUERT not only achieves
state-of-the-art results in terms of both quantitative metrics and visual
quality but also yields a sub-sampling pattern and a reconstruction model that
are both customized to training data.
