  Magnetic Resonance Imaging (MRI) is a widely used medical imaging technique,
but its long acquisition time can be a limiting factor in clinical settings. To
address this issue, researchers have been exploring ways to reduce the
acquisition time while maintaining the reconstruction quality. Previous works
have focused on finding either sparse samplers with a fixed reconstructor or
finding reconstructors with a fixed sampler. However, these approaches do not
fully utilize the potential of joint learning of samplers and reconstructors.
In this paper, we propose an alternating training framework for jointly
learning a good pair of samplers and reconstructors via deep reinforcement
learning (RL). In particular, we consider the process of MRI sampling as a
sampling trajectory controlled by a sampler, and introduce a novel
sparse-reward Partially Observed Markov Decision Process (POMDP) to formulate
the MRI sampling trajectory. Compared to the dense-reward POMDP used in
existing works, the proposed sparse-reward POMDP is more computationally
efficient and has a provable advantage. Moreover, the proposed framework,
called L2SR (Learning to Sample and Reconstruct), overcomes the training
mismatch problem that arises in previous methods that use dense-reward POMDP.
By alternately updating samplers and reconstructors, L2SR learns a pair of
samplers and reconstructors that achieve state-of-the-art reconstruction
performances on the fastMRI dataset. Codes are available at
\url{https://github.com/yangpuPKU/L2SR-Learning-to-Sample-and-Reconstruct}.
