Rigid Motion Compensated Compressed Sensing MRI with Untrained Neural Networks

At the moment the paper does not seem complete. and so I am leaning towards rejection. A few points for my assessment are below:

1. The paper seems to propose un-trained methods as best for rigid motion-compensated reconstruction, but the SSIM numbers for the modified supervised methods are much higher for modified supervised methods (~0.88 for un-trained from Table 1, 0.92 for modified supervised in the high-data regime of Figure 3). The paper only considers an idealized setting for the supervised method and does not attempt to incorporate estimation of motion parameters for the idealized case. Why not simply propose the modified supervised method instead? In the abstract the paper's conclusion states, "Our approach outperforms untrained and trained optimization-based baselines such as ℓ1-norm minimization and score-based generative models," but this does not seem qualified with the paper own experiments.
2. The review of the motion-compensated reconstruction literature is fairly light, only including a couple of non-deep learning citations, despite this having been a major field in MRI reconstruction for the last few decades (with many products currently in scanners). Many of these methods are highly sophisticated in how they estimate the motion parameters, beyond tacking on a learnable module as done in Eq. (2) of the present paper.
3. Related to the above, the baselines in the paper may not be tailored for FSE acquisitions (particularly that based on generative priors) and as such could be underpowered for comparison.
4. The motion experiments considered in the paper are only simulated. Most MRI reconstruction publication venues would probably prefer to see the method qualified with prospective motion studies with subjects in a scanner.

This idea is easy to follow. My main concerns are on the experimental setup and results.

• The results of E2EVarNet on motion-corrupted data needs more justification. In this paper’s setting, E2EVarNet perfectly knows the motion information, therefore E2EVarNet is equipped with the optimal forward model that can map the intermediate results to the k-space. That being said, the key idea of E2EVarNet, compared with end-to-end UNet, is its ability to compare against the intermediate reconstruction to the raw undersampled measurements. If the E2EVarNet has the optimal forward model, its performance shouldn’t be affected by motion. The forward operator with motion or without motion can both be expressed as a known operator.
• More classification on the score-based method. The score-based method is trained on a huge amount of motion-free MRI data (in general), then sample a new MRI from the learned distribution. From this aspect, it seems unreasonable the score-based method would generate a MRI image with motion artifact (as in Figure 4), as the model has never been trained on such an image. Could author provide more discussion on this aspect. Also, how does the proposed method compared with this score-based method for MRI motion correction: Annealed Score-Based Diffusion Model for MR Motion Artifact Reduction, which doesn’t need to jointly estimate the motion information.
• The experimental setup can be improved. This paper only considered rigid and x4 acceleration factor, both are known to be less challenging. How does this method perform in more challenging case, such as non-rigid (also a common case in MRI) and x8/x10 acceleration factor? Moreover, l1-min baseline has a well-known weak non-learning-based prior. How does this baseline performance if equipped with a stronger learning-based prior, such as pre-trained denoisers?
• Lack of baseline: How does this method performance when comparing against the end-to-end method.

• The experimental comparisons to a deep learning baseline are performed in an artificial simulation setting that ignores rotations, which is highly unrealistic and decreases the difficulty of the task. Rotations are substantively different from translations in MR motion correction; while translations incur only a phase shift on the acquired data, rotations can result in missing “wedges” of the k-space data that yield qualitatively different artifacts. This makes it difficult to tell whether the observed trend of the proposed method outperforming the score-based generative model will hold in the more realistic setting where both rotations and translations are present.

• More detailed results are needed to evaluate the method. Please provide confidence intervals in Table 1 to give context for the differences between methods relative to the variability across the data. Also, the paper is missing a systematic quantification of the error in the estimated motion parameters — while these are shown for a single example in Figure 4, we need to see estimates of the motion parameter errors across the dataset to understand how well the method is learning the motion states (as opposed to just outputting a high-quality image without properly estimating the motion), and how this compares to other methods.

• The realistic experiment on 3D data acquired with motion that does include rotations only compares to a zero-filled reconstruction, a very weak baseline that makes it difficult to understand how well the method is performing. I am glad to see that rotations are modeled in the 3D motion model in section 4.2.2. However, the proposed method here is only compared to a zero-filled reconstruction, which is a very weak baseline, as this method does not even correct undersampling artifacts. At a minimum, the method should be compared to e.g. a GRAPPA reconstruction of the acquired image so the reader can understand the benefit provided by the proposed method compared to a standard reconstruction. 



  I understand that supervised deep learning techniques can’t be compared to here, because large datasets of 3D motion corrupted MRI data are not easily available. But, another good comparison could be to a “grid of pixels” approach which uses the same loss function to optimize both the estimated motion parameters and the reconstruction pixel values themselves (with no network performing the reconstruction). I am guessing the proposed method would outperform such a baseline because of the prior induced by the convolutional architecture, but it’s important to show how much this improves performance or decreases runtime, as this is the core of the proposed method.


• The paper is missing references to a large body of previous work in the ML for MRI motion correction literature. It is worth noting explicitly in the text of Section 1.1 that this literature review focuses on retrospective brain MRI motion correction, as this section does not currently reference significant previous work on motion correction strategies that use motion measurements, prospective motion correction techniques, and non-rigid motion or motion in other commonly studied anatomies (e.g. cardiac imaging). Further, Section 1.1 is missing several references in the retrospective rigid brain MR motion correction literature; please consider reading and citing some subset of the following works. 



  Model-Based: 


  Cordero‐Grande, Lucilio, et al. "Three‐dimensional motion corrected sensitivity encoding reconstruction for multi‐shot multi‐slice MRI: application to neonatal brain imaging." Magnetic resonance in medicine 79.3 (2018): 1365-1376.



  Haskell, Melissa W., Stephen F. Cauley, and Lawrence L. Wald. "TArgeted Motion Estimation and Reduction (TAMER): data consistency based motion mitigation for MRI using a reduced model joint optimization." IEEE transactions on medical imaging 37.5 (2018): 1253-1265.



  Data-Driven:


  Duffy, Ben A., et al. "Retrospective motion artifact correction of structural MRI images using deep learning improves the quality of cortical surface reconstructions." NeuroImage 230 (2021): 117756.



  Johnson, Patricia M., and Maria Drangova. "Conditional generative adversarial network for 3D rigid‐body motion correction in MRI." Magnetic resonance in medicine 82.3 (2019): 901-910.



  Levac, Brett, et al. "FSE Compensated Motion Correction for MRI Using Data Driven Methods." International Conference on Medical Image Computing and Computer-Assisted Intervention. Cham: Springer Nature Switzerland, 2022.


  Data-Driven and Model-Based:


  Haskell, Melissa W., et al. "Network Accelerated Motion Estimation and Reduction (NAMER): Convolutional neural network guided retrospective motion correction using a separable motion model." Magnetic resonance in medicine 82.4 (2019): 1452-1461.
 
 Singh, Nalini M., et al. "Data Consistent Deep Rigid MRI Motion Correction." Medical Imaging with Deep Learning (2023).



• (minor) I think there is a small notation issue in the second line of Equation 1; the T operator previously was applied to image-domain data in the un-numbered equation on page 2, but here is operating on k-space data.

Weakness:

• The main weakness is the limited novelty of the paper. The application of untrained networks to the motion-corrupted regime is appreciated. However, the proposed method is a mere application of an existing technique with limited technical contribution.

• Another minor weakness is the limited scope for experiments. A comparison with a competitive baseline is provided only in the 2D case with a single dataset, and a single acceleration rate which makes it difficult to quantify the generalizability of the results. This weakness could be easily alleviated by adding more testing scenarios (e.g. more undersampling rates, datasets), or by adding a competitive baseline in the 3D case (e.g. l1-min, score-based).