Summary and Contributions: This work investigates the use of a self-supervised task (Patch2Self) for DWI denoising. The task consists in reconstruction missing directions from held-out voxels. The methods therefore exploits the 4D nature of DWI data. By using left-out directions in the prediction the noise of the target is uncorrelated which allows the theory of the Patch2Self to apply.
Strengths: The paper has limited novel contribution in ML but it is well written, illustrated and comes with convincing experiments. Python code is also provided.
Weaknesses: I would simply suggest that alternative denoising strategies based on dictionary learning have been proposed for DWI images such as https://pubmed.ncbi.nlm.nih.gov/24084469/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4679293/ Sparsity is an alternative to low rank structures and the issue of heteroscedastic noise is also mentioned in these works via a whitening step. I would suggest to comment on these and potentially compare these approaches with the proposed one. Very little details are provided on how the models are trained. Is it done with an online algorithm? More details would have been appreciated.
Relation to Prior Work: Pretty good although as pointed out some references are missing.
Summary and Contributions: The paper proposes a patch-based denoising algorithm for diffusion-weighted MRI. It is essentially a patch-regression approach: each component image of a dwMRI acquisition (which usually contains from a few tens to a few hundred separate grayscale imaging each with slightly different contrast) is denoised via a linear patch-model learned from all the other images. The authors compare the approach with the Marchenko-Pastur algorithm, which they identify as state of the art (not sure how true that is, as it does not appear to be standard or even commonly used in diffusion-weighted MRI, yet it does appear a sensible choice of baseline). Simulation results suggest some benefits of the proposed approach of the baseline. Results on brain data sets show qualitatively less noisy maps and output of tractography.
Strengths: It is an important problem. Diffusion weighted images often have very low signal to noise and noise reduction can certainly help in estimating subtle parameters from them and in reducing perturbation for connectivity mapping. The approach seems sensible and novel. Others have used non-local means and self-similarity for noise reduction in diffusion-weighted MRI (Wiest-Daessle et al MICCAI 2008; Manjon JMRI 2010, MedIA 2012) as well as patch-based learning approaches for more general enhancement (Coupe et al NIMG 2013; Alexander MICCAI 2014, NIMG 2017; Tanno MICCAI 2017). Some discussion of these approaches and how they differ to what is proposed would be useful, but I do believe they are not quite the same as what is proposed.
Weaknesses: Comparison with baseline not fair. One key difference between the proposed patch-based approach and the baseline Marchenko-Pastur is the patch-based nature of the former. Is smoother appearance of the images in figure 2 and the less noisy tractograms in figure 3 simply because the patch-based approach introduces more smoothing? That seems very likely to me. A potential big advantage of the Marchenko-Pastur is that it does not smooth so preserves detail. This is not tested in the qualitative evaluations of figures 2 and 3 or mentioned anywhere in the text. Experiments not very meaningful. As mentioned above, the qualitative comparison in figure 2 is hard to make judgement on. The new images are certainly smoother, but does that really mean “better”. The experiment would benefit from independent assessment from experts on both noise level and level of detail. Similarly the tractography result certainly shows a less noisy appearance, but is important detail lost? As for the kurtosis maps, I’m not sure the results make sense at all. Kurtosis mapping is a simple linear estimation problem. It is unclear what degeneracies the authors refer to in figure 4 that lead to the band of dark pixels. The dark pixels are consistent so it doesn't seem like the result of a degeneracy causing a broad set parameter values that offer equally good fit. The proposed approach certainly produces something different, but not clear it is better in any way. Niche application that does not generalise. While this work may prove important for the MRI community, it is unclear what the NeurIPS community would usefully learn. It seems like a bespoke solution for a specific application rather than a technique that potentially informs a wide range of machine learning problems – at least the authors give no clues as to wider applicability.
Correctness: As far as I can tell.
Clarity: Yes reasonably, although there is a lot of jargon relating to both diffusion MRI and noise reduction that is not easy to cut through or verify (for me at least).
Relation to Prior Work: Not particularly – see comments above.
Additional Feedback: I appreciate the authors' rebuttal, which is reasonable on the points I raise, although I remain unconvinced on two points: Smoothness: the proposed method clearly adds more smoothing than the baseline approach. The authors accept that doesn't necessarily mean better. They argue that the metrics they provide account for that, but I don't see that they do. This seems an outstanding issue for me. Also still unconvinced on relevant: does this paper advance or provide insight more generally on the machine learning aspects of the work? Not particularly I don't think. That said, I am not strongly opposed to acceptance if others are more keen.
Summary and Contributions: I have read the author response, read the other reviews, and participated in the discussion with the reviewers and area chair. My score is unchanged. The authors introduce a method for denoising DWI data with very few assumptions about the noise. The method is based on predicting voxel values in one direction from the values of those voxels + surrounding patches in all the other directions. This framework is general enough to support any regression model (as implemented in scikit-learn), though the authors use a simple linear regression. The authors compare their method against the state-of-the-art approach, and evaluate its effect on simulated and standard DWI data, and also on downstream analyses such as tractography and microstructure modelling. The authors state that the code will be released as part of DIPY, a commonly used library for handling diffusion data.
Strengths: strengths: - clearly written - the method is conceptually elegant and simple to understand/implement - evaluation on downstream analyses, not just DWI data
Weaknesses: nothing major
Correctness: The method is very well described, all my questions are in the Clarity section.
Clarity: 2.2) The process you describe in "Extracting 3D patches" uses data from all directions but one in predicting the left out direction j, for each direction in turn. This would be part A in Figure 1, and m = h * l * w. What is the new data that would be used in part B? Or do you mean you will literally replace each direction by its patch-wise prediction from the other directions? 139-144: is it reasonable to assume that images from different directions are different enough that you would have no collinearity in a regression model? (of course you can use regularization, if that's the case) 150: presumably this will also be the case if the dimensionality of the volume increases? 3) Figure 2: it's not really clear that there is any visual difference between one method and the other, in each dataset. Is there some quantitative criterion you can use, in the absence of ground truth?
Relation to Prior Work: Yes, the description of prior work appears very thorough, to the limited extent I know about this literature.
Summary and Contributions: After the rebuttal and discussion, my opinion is still that this is a nice simple idea that seems to work well in practice, but I am also still a bit concerned about the insight that it provides in ML aspects, as well as the validation. ********** This paper presents a general method for denoising diffusion MR in an unsupervised fashion, where one learns to predict one diffusion weighted volume (channel/direction) from the other directions, and replaces the noisy measurement by the prediction. The idea is that, since the noise is independent across channels, predicting the noise is not possible and the method thus yields an unbiased estimator.
Strengths: -Simple method that seems to do a good job. -Good effort to validate on synthetic and real data, both with noise metrics, and on downstream tasks (e.g., tractography).
Weaknesses: -The validation on real data is largely qualitative (including the tractography, where - I totally understand - ground truth is very hard to obtain), and the quantitative part is very indirect (R2, degenerate voxels).
Correctness: Yes. It's a simple method, and it is well described.
Clarity: Yes, the paper is very clearly written.
Relation to Prior Work: The baseline is a good representative method for unsupervised DWI denoising. However, some classical denoising methods are not acknowleged, including (but not limited to): XQ-NLM Lam, Baban, et al Awate & Whitaker Tristan-Vega et al
Additional Feedback: -If I understood correctly: the measured data in a given direction is not used (not directly) to estimate the denoised value. This is pretty interesting and I believe the authors could discuss it further in the manuscript. - The authors should better justify the use of  as primary baseline. - Comparison with supervised methods (as a ceiling for denoising performance would be informative. - Another discussion point: if a very flexible regressor is used (e.g., a very deep neural net), is it possible that it overfits and the method doesn't work? May that be why the linear model performs the best?