  Accelerated MRI shortens acquisition time by subsampling in the measurement
$\kappa$-space. Recovering a high-fidelity anatomical image from subsampled
measurements requires close cooperation between two components: (1) a sampler
that chooses the subsampling pattern and (2) a reconstructor that recovers
images from incomplete measurements. In this paper, we leverage the sequential
nature of MRI measurements, and propose a fully differentiable framework that
jointly learns a sequential sampling policy simultaneously with a
reconstruction strategy. This co-designed framework is able to adapt during
acquisition in order to capture the most informative measurements for a
particular target. Experimental results on the fastMRI knee dataset demonstrate
that the proposed approach successfully utilizes intermediate information
during the sampling process to boost reconstruction performance. In particular,
our proposed method can outperform the current state-of-the-art learned
$\kappa$-space sampling baseline on over 96% of test samples. We also
investigate the individual and collective benefits of the sequential sampling
and co-design strategies.
