# Benchmarking MRI Reconstruction Neural Networks on Large Public Datasets
## 6 Discussion  
In this work, we only considered one scheme of under-sampling. However, it should be interesting to see if the performance obtained on one type of under-sampling generalizes to other types of under-sampling, especially if we do a re-gridding step for non-Cartesian under-sampling schemes. On that specific point, the extension of the networks towards non-Cartesian sampling schemes is not easy because the data consistency cannot be performed in the same way, and the measurement space is no longer similar to an image (except if we re-grid). In a recent work [47], some of the authors of the Cascade-net [11] propose a way to extend their approach to the non-Cartesian case, using a re-gridding step. The PD-net [9] also has a straightforward implementation for the non-Cartesian case even without re-gridding, in what is called the learned Primal. In this case, the network in the k-space is just computing the difference (residual) between the current k-space measurements and the initial k-space measurements. Therefore, there are no parameters to learn, which alleviates the problem of how to learn them.  
We also only considered a single-coil acquisition setting. As parallel imaging is primarily used in CS-MRI to allow higher image quality [3], it is important to see how these networks will behave in the multi-coil setting. The difficult part in the extension of these works to the multi-coil setting will be to understand how to best involve the sensitivity maps (or even not involve them [48]).  
Regarding the networks themselves, the results seem to suggest that for cross-domain networks, the trade-off between a high number of iterations and a richer correction in a certain domain (by having deeper networks) is in favor of having more iterations (i.e., alternating more between domains). It is, however, unclear how to best tackle the reconstruction in the k-space, since the convolutional networks make a shift invariance hypothesis, which is not true in the Fourier space where the coefficients corresponding to the high frequencies should probably not be treated in the same way as with the low frequencies. This leaves room for improvement in the near future.  
Finally, this work has not dealt with recent approaches involving adversarial training for MRI reconstruction networks [18; 49]. It would be very interesting to see how the adversarial training could improve each of the proposed networks.  
Conceptualization, Z.R. and P.C.; methodology, Z.R.; software, Z.R.; validation, Z.R., P.C. and J.-L.S.; formal analysis, Z.R.; investigation, Z.R.; resources, P.C.; data curation, Z.R.; writing--original draft preparation, Z.R.; writing--review and editing, P.C. and J.-L.S.; visualization, Z.R.; supervision, P.C. and J.-L.S.; project administration, P.C. and J.-L.S.; funding acquisition, P.C. and J.-L.S. All authors have read and agree to the published version of the manuscript.  
This research was funded by the Cross-Disciplinary Program on Numerical Simulation (SILICOSMIC project) of CEA, the French Alternative Energies and Atomic Energy Commission.  
We want to thank [PERSON], [PERSON], and [PERSON] for their very useful and benevolent remarks and answers they gave when asked questions about their works.  
The authors declare no conflicts of interest  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} MRI & Magnetic Resonance Imaging \\ CS-MRI & Compressed Sensing MRI \\ GPU & Graphical Processing Unit \\ ReLU & Rectified Linear Unit \\ PReLU & Parametrized ReLU \\ PSNR & Peak Signal-to-Noise Ratio \\ SSIM & Structural SIMilarity index \\ \end{tabular}