  Deep neural networks have recently been thoroughly investigated as a powerful
tool for MRI reconstruction. There is a lack of research, however, regarding
their use for a specific setting of MRI, namely non-Cartesian acquisitions. In
this work, we introduce a novel kind of deep neural networks to tackle this
problem, namely density compensated unrolled neural networks, which rely on
Density Compensation to correct the uneven weighting of the k-space. We assess
their efficiency on the publicly available fastMRI dataset, and perform a small
ablation study. Our results show that the density-compensated unrolled neural
networks outperform the different baselines, and that all parts of the design
are needed. We also open source our code, in particular a Non-Uniform Fast
Fourier transform for TensorFlow.
