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REVIEW 3 major objections 8 minor 79 references

Robust multi-coil MRI reconstruction via self-supervised denoising

T0 review · 3 major / 8 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper argues that GSURE-based denoising of MRI training data improves low-SNR diffusion and MoDL reconstruction.

desk verdict Empirically careful study showing GSURE-denoised training targets help at low SNR across two model families, but the 'bypass clean references' claim is untested because no clean-reference oracle is included. read the letter →

arxiv 2411.12919 v4 pith:ERCYGIKX submitted 2024-11-19 eess.IV cs.AIcs.CVcs.LG

Asad Aali , Marius Arvinte , Sidharth Kumar , Yamin I. Arefeen , Jonathan I. Tamir This is my paper · ORCID
classification eess.IVcs.AIcs.CVcs.LG
keywords MRIreconstructionself-superviseddenoisingGSUREdiffusionprobabilisticmodelsMoDLfastlow-SNRimagingparallel
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper asks whether adding a self-supervised denoising step before training makes deep-learning MRI reconstruction better, and argues that it does. Using GSURE, an unbiased loss that estimates the mean-squared error of a denoiser from noisy measurements alone, the authors train a denoiser on noisy multi-coil k-space and use its output as the training target for two reconstruction families: diffusion probabilistic models sampled with diffusion posterior sampling, and the unrolled model-based deep learning network MoDL. On T2-weighted brain and fat-suppressed knee scans from the fastMRI dataset at three SNR levels each and acceleration factors 4 and 8, denoised training targets give lower NRMSE, higher SSIM, and higher PSNR at low SNR, and performance comparable to noisy-data training at native SNR. The authors conclude that denoising can replace the need for noise-free reference scans when training reconstruction networks for low-SNR settings such as low-field MRI.

What carries the argument

The central object is GSURE (Generalized Stein's Unbiased Risk Estimate), a loss that computes an unbiased estimate of the supervised mean-squared-error loss from noisy measurements alone. The authors implement it by adding the divergence of the denoiser network, approximated with a Monte Carlo perturbation, to a data-consistency term, and applying it to pre-whitened, normalized adjoint images scaled by the estimated noise variance. This GSURE loss trains a UNet denoiser to produce MMSE-denoised coil-combined images, which then replace the raw noisy images as the training targets for an EDM diffusion prior and for MoDL.

What would settle it

Acquire real low-field MRI k-space with a noise pre-scan, run the same two-stage pipeline with its measured non-Gaussian or spatially correlated noise, and check whether reconstructions trained on GSURE-denoised data still beat reconstructions trained on noisy data; if they do not, or if the gains vanish when sensitivity maps are estimated from the noisy data itself, the paper's central claim would not transfer beyond the simulated setting.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that GSURE-denoised training targets improve both generative and end-to-end accelerated MRI reconstruction without any clean reference images. Denoised targets yield better priors: unconditional samples from the diffusion model are cleaner, and DPS reconstructions degrade more gracefully as inference SNR drops, including on a knee case with a meniscus tear. The same pattern holds for MoDL, with the largest margins at the lowest simulated SNRs (12 dB brain, 4 dB knee), and GSURE-trained models reach target NRMSE with fewer posterior averages and fewer training examples. The authors interpret the gains as coming from the denoising operation itself, not from the noise level of the training data, because low-SNR GSURE models sometimes beat higher-SNR GSURE models while the equivalent noisy-data models do not.

Load-bearing premise

The pipeline is unbiased only if, after pre-whitening and normalization, the measurement noise is independent Gaussian noise with known variance; if real low-SNR acquisitions violate that, the reported gains may not transfer.

Editorial extensions

If this is right

  • Noise-free reference scans are not required for training low-SNR reconstruction models; noisy fully sampled data plus GSURE denoising can serve as the target.
  • At low inference SNR, both diffusion-based and unrolled reconstructions become more accurate, with the largest gains at the worst noise levels tested.
  • Training and inference become more efficient: fewer posterior samples and fewer training examples reach a given NRMSE after denoising.
  • The two-stage preprocessing pipeline is architecture-agnostic, so new denoisers or new reconstruction networks could be substituted without changing the core idea.
  • In the unrolled case, GSURE-denoised training also outperforms an alternative self-supervised reconstruction loss when the training SNR is low.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If real low-field MRI noise behaves like the simulated Gaussian noise used here, this two-stage recipe could make clinical training pipelines practical at 0.55 T and lower, where clean references are unavailable; the paper only demonstrates the simulated case.
  • Because the gains concentrate at low SNR and are small or negative for some high-SNR SSIM comparisons, the practical value likely depends on how far a deployment is from native SNR rather than on uniform improvement.
  • A single-stage formulation that learns the noisy distribution directly while incorporating denoising is theoretically possible and the paper leaves it open; the reported stability of the two-stage approach is an empirical argument for keeping the steps separate.
  • The core premise about known Gaussian noise could be tested by estimating the noise covariance from a pre-scan on real low-field systems and checking whether GSURE-trained networks still beat noisy-data-trained ones.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 8 minor

Summary. The paper proposes a two-stage pipeline for low-SNR multi-coil MRI reconstruction: pre-whiten and normalize the k-space data, train a UNet denoiser with the GSURE self-supervised loss, and then use the denoised coil-combined images as training targets for two reconstruction methods, diffusion posterior sampling (DPS) with an EDM prior and Model-Based Deep Learning (MoDL). The experiments compare these GSURE-trained models against the same architectures trained on the original noisy targets, across T2-weighted brain and fat-suppressed knee fastMRI data, at three SNR levels per anatomy and acceleration factors R=4 and R=8. The authors report that GSURE training targets yield lower NRMSE and higher SSIM/PSNR at low SNR, with comparable performance at native SNR, and conclude that self-supervised denoising may bypass the need for noise-free reference scans. The paper includes 72 paired Wilcoxon tests with Bonferroni correction, a pathology example, a training-set-size study, and open-source code.

Significance. If the reported effects are genuine, the pipeline is a practically useful preprocessing recipe for low-SNR MRI, particularly for low-field systems, and the head-to-head comparison of DPS and MoDL under identical preprocessing is a useful reference for the community. The paper is strong in its breadth: two reconstruction paradigms, three SNR levels per anatomy, two acceleration factors, statistical testing, qualitative pathology assessment, and a concrete data-efficiency study. The authors are also transparent about the main limitation, namely that all quantitative metrics are computed against inherently noisy native-SNR references, and they explicitly call for NCE-based and radiologist evaluation in future work. The central quantitative claim, however, rests on metrics whose interpretation is confounded by the presence of the same native noise realization in both the measurements and the reference; the missing clean-reference oracle control leaves the strongest conclusion, the bypass of noise-free references, unsupported.

major comments (3)
  1. [Evaluation Metrics; Data; Discussion] The primary quantitative evidence is computed against native-SNR fully sampled images, which the paper itself calls inherently noisy (Evaluation Metrics, Discussion). Writing the reference as r = c + n0 and the estimator as e, the expected squared error is E||e-r||^2 = E||e-c||^2 + sigma0^2 - 2E[(e-c)^T n0]. The low-SNR test measurements are generated by adding Gaussian noise to the same fully sampled k-space that contains n0, and the data-consistency steps in DPS (Eq. 12) and MoDL (Eq. 14) can create dependence between e and n0. Two estimators equally close to c can therefore receive very different NRMSE/PSNR/SSIM scores depending on whether they reproduce components of n0. The cross term has no definite sign, so the reported GSURE-DPS and GSURE-MoDL gains at 12 dB and 4 dB are not directly interpretable as gains in signal fidelity. This is not merely a caveat: the abstract's quantitative claims are stated in these metrics. The paper should add an experiment with known-clean references (e.g., synthetic ground truth with controlled noise) or at least report the NCE metric and show that the conclusion is unchanged.
  2. [Proposed Approach; Conclusion; Abstract] The conclusion that GSURE preprocessing may 'potentially bypass the need for noise-free reference MRI scans' is not supported by the experimental design. The comparisons are exclusively between networks trained on GSURE-denoised targets and networks trained on noisy targets; there is no oracle condition trained on clean or near-clean references. Consequently, the results show only that GSURE-denoised targets are better than noisy targets under the chosen metric, not that they approximate clean targets well enough to substitute for them. A direct control, training the same DPS and MoDL pipelines on simulated clean references from known ground truth or on multi-average low-noise data, would make the surrogate-quality claim testable. Without such a control, the 'bypass' claim should be removed or explicitly labeled as a hypothesis.
  3. [Theory; Eq. (16); Discussion] The theoretical guarantee of GSURE and the validity of the simulated SNR conditioning both rely on the assumption that, after pre-whitening and ACS normalization, the noise is i.i.d. Gaussian with known scalar variance sigma^2_eta* (Eq. 16). The experiments add zero-mean Gaussian noise to already noisy fastMRI k-space, so this assumption is satisfied by construction in the simulated low-SNR conditions. However, the Discussion motivates the method by low-field and real-world acquisitions, where noise can be non-Gaussian, spatially varying, or correlated across coils, and where sensitivity estimation may itself be noise-contaminated. The paper should either restrict the claims to the Gaussian-noise setting or include a robustness experiment with a non-Gaussian or correlated noise model; as written, the extrapolation to real low-SNR MRI is a conjecture.
minor comments (8)
  1. [Proposed Approach] 'Proof-of-principal' should be 'proof-of-principle'.
  2. [Discussion] 'Eluded another limitation' should read 'alluded to another limitation.'
  3. [Experiments] 'These experimentes' is a typo for 'these experiments.'
  4. [Figures S7 and S8] The captions state 'GSURE-MoDL outperforms Naive-DPS'; the comparison is against Naive-MoDL, so the captions should refer to Naive-MoDL.
  5. [Tables 1 and 2] 'Wehighlight' in the table captions should be 'we highlight.'
  6. [Eq. (17)] The SNR definition should explicitly state that the normalizing constant is the 99th percentile of the ACS root-sum-of-squares reconstruction, since that normalization sets the signal scale used in the SNR expression.
  7. [Self-Supervised Denoising] The statement that GSURE 'can handle ... each coil can have different noise levels' is not demonstrated by the implementation, which pre-whitens the data to a scalar noise variance; please rephrase or provide a per-coil experiment.
  8. [Implementation Details] The training durations '200 iterations' for the GSURE network and '3,000 iterations' for the EDM network should be clarified as epochs or iterations with the stated batch size; 200 iterations seems surprisingly short for a 65M-parameter UNet.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: GSURE preprocessing is compared against a noisy-target baseline on held-out validation data, and the central GSURE identity is cited from independent prior work.

full rationale

The paper's central claim is an empirical comparison: models trained on GSURE-denoised targets (GSURE-DPS, GSURE-MoDL) are evaluated against models trained on noisy targets (Naive-DPS, Naive-MoDL) on held-out fastMRI slices, with errors computed against the same native-SNR fully sampled reference for both arms. The GSURE loss (Eq. 6) and its unbiasedness property (Eq. 9) are standard results cited to Eldar 2008 and Ramani et al. 2008; they are not re-derived from the paper's own outputs, and the downstream reconstruction evaluation does not use the GSURE loss as its metric. No parameter is fitted to the evaluation reference, and no reported quantity equals a training target by construction. The self-citations [36], [56], and [57] are prior related work by the same group, but the present gains are measured in this paper's own experiments rather than imported, so the self-citations are not load-bearing. The acknowledged limitation that native-SNR references are noisy ('We emphasize that this evaluation is inherently biased, as native SNR images are inherently noisy', Evaluation Metrics; further discussed under 'hidden noise' in the Discussion) is a metric-validity caveat, not a circular derivation, because both comparison arms share the same reference and the conclusion does not follow by construction from the loss or from the reference definition.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central claim is empirical, not derived, so the ledger captures modeling assumptions and hyperparameters rather than derivation constants. No invented entities are introduced; GSURE, EDM, DPS, and MoDL are all existing methods.

free parameters (6)
  • GSURE denoiser network weights g_phi = not reported (65M-parameter UNet)
    Trained per anatomy and SNR level with GSURE loss; all downstream training targets depend on this network, and its learned denoising behavior is the mechanism behind the reported gains.
  • DPS guidance parameter gamma_t = not reported in text
    Controls the likelihood/guidance strength in Eq. (12); the paper states hyperparameters were fixed across anatomies and SNRs but does not give values, so exact behavior lives in code.
  • EDM and DPS noise schedules sigma_min/sigma_max = 0.002/80 training; 0.004/10 inference
    Chosen by hand following Karras et al.; reconstruction quality depends on these schedule choices.
  • MoDL unroll count and regularization weight lambda = 6 unrolls; lambda not reported
    Unrolled architecture and regularization strength chosen by hand; the MoDL results depend on them.
  • Monte Carlo divergence epsilon = 0.001
    Chosen to balance divergence estimation accuracy and cost in Eq. (8); a standard choice.
  • Per-anatomy/SNR learning rates = brain 1e-4; knee 5e-7 or 5e-6 depending on SNR
    Hand-tuned hyperparameters reported in Implementation Details.
assumptions (6)
  • standard math GSURE loss provides an unbiased estimate of supervised denoising loss without clean targets
    Invoked in Eqs. (6)-(9) via Eldar (2008); the entire self-supervised denoising step rests on this.
  • standard math Monte Carlo single-sample divergence approximation is sufficiently accurate
    Eq. (8) follows Ramani et al.; approximation error is uncontrolled for a single realization b, but this is accepted practice.
  • domain assumption After pre-whitening and ACS normalization, noise is i.i.d. Gaussian with known variance
    Eq. (16) and the SNR definition in Eq. (17); if noise is non-Gaussian or spatially varying, GSURE and the simulated SNR sweeps are not exact.
  • domain assumption ESPIRiT sensitivity maps accurately represent coil sensitivities
    Used for the forward operator A; the Discussion notes this may not match other calibration methods.
  • ad hoc to paper Fully sampled fastMRI k-space with added Gaussian noise is a valid proxy for real low-SNR acquisitions
    The paper's own limitations state fastMRI is high SNR and no noise prescan is available; real low-field noise characteristics remain untested.
  • ad hoc to paper Native-SNR noisy fully sampled images are an acceptable reference for evaluation metrics
    Methods explicitly says evaluation is inherently biased; Discussion highlights hidden noise and recommends NCE/radiologist reads, which were not performed.

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Cite this review

Pith. "Pith review of Robust multi-coil MRI reconstruction via self-supervised denoising." pith.science (2026). https://pith.science/paper/ERCYGIKX

@misc{pith2026241112919,
  author       = {Pith},
  title        = {Pith review of: Robust multi-coil MRI reconstruction via self-supervised denoising},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ERCYGIKX}},
  note         = {Machine review of arXiv:2411.12919}
}
read the original abstract

We study the effect of incorporating self-supervised denoising as a pre-processing step for training deep learning (DL) based reconstruction methods on data corrupted by Gaussian noise. K-space data employed for training are typically multi-coil and inherently noisy. Although DL-based reconstruction methods trained on fully sampled data can enable high reconstruction quality, obtaining large, noise-free datasets is impractical. We leverage Generalized Stein's Unbiased Risk Estimate (GSURE) for denoising. We evaluate two DL-based reconstruction methods: Diffusion Probabilistic Models (DPMs) and Model-Based Deep Learning (MoDL). We evaluate the impact of denoising on the performance of these DL-based methods in solving accelerated multi-coil magnetic resonance imaging (MRI) reconstruction. The experiments were carried out on T2-weighted brain and fat-suppressed proton-density knee scans. We observed that self-supervised denoising enhances the quality and efficiency of MRI reconstructions across various scenarios. Specifically, employing denoised images rather than noisy counterparts when training DL networks results in lower normalized root mean squared error (NRMSE), higher structural similarity index measure (SSIM) and peak signal-to-noise ratio (PSNR) across different SNR levels, including 32dB, 22dB, and 12dB for T2-weighted brain data, and 24dB, 14dB, and 4dB for fat-suppressed knee data. Overall, we showed that denoising is an essential pre-processing technique capable of improving the efficacy of DL-based MRI reconstruction methods under diverse conditions. By refining the quality of input data, denoising enables training more effective DL networks, potentially bypassing the need for noise-free reference MRI scans.

Figures

Figures reproduced from arXiv: 2411.12919 by the authors.

Figure 1
Figure 1. FastMRI Pre-Processing and Deep Learning-Driven MRI Reconstruction Pipeline. a) The pre-processing begins with pre-whitening and normalization of the raw k-space data. The whitened and normalized adjoint AHy of the k-space is passed through the denoiser network gϕ, outputting the MMSE denoised sample x˜MMSE. We show the magnitude of a sample from the fastMRI dataset before and after denoising, including a histogram … view at source ↗
Figure 2
Figure 2. Unconditional T2-Weighted Brain images generated from EDM models trained on two datasets: a) Noisy (Naive￾EDM), and b) GSURE denoised (GSURE-EDM). Across each column, we show prior samples across three different training SNR levels. Across each row, we show different realizations of images generated from the same distribution. We can observe that GSURE-EDM consistently generates qualitatively superior images, notabl… view at source ↗
Figure 3
Figure 3. Unconditional Fat-Suppressed Knee images generated from EDM models trained on two datasets: a) Noisy (Naive￾EDM), and b) GSURE denoised (GSURE-EDM). Across each column, we show prior samples across three different training SNR levels. Across each row, we show different realizations of images generated from the same distribution. We can observe that GSURE-EDM consistently generates qualitatively superior images, nota… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Conditional T2-Weighted Brain images with DPS as the reconstruction method, utilizing EDM models trained on two datasets: a) Noisy (Naive-DPS) and b) GSURE denoised (GSURE-DPS). Across columns, we show reconstructions across three training/inference SNR levels. In the …
Figure 5
Figure 5. Figure 5: Conditional Fat-Suppressed Knee images with DPS as the reconstruction method, utilizing EDM models trained on two datasets: a) Noisy (Naive-DPS) and b) GSURE denoised (GSURE-DPS). Across columns, we show reconstructions across three training/inference SNR levels. In th…
Figure 6
Figure 6. Figure 6: Conditional Fat-Suppressed Knee reconstruction with pathology (lateral meniscus tear) across multiple inference SNR levels, comparing Naive-DPS and GSURE-DPS trained at SNR 14 dB. Across each column, we show reconstructions across inference SNR levels ranging from 24 d…
Figure 7
Figure 7. Figure 7: Zoomed-In conditional Fat-Suppressed Knee reconstruction with pathology (lateral meniscus tear) across multiple inference SNR levels, comparing Naive-DPS and GSURE-DPS trained at SNR 14 dB. In each row, we zoom-in specific parts of the Knee. We can observe that GSURE-D…
Figure 8
Figure 8. Figure 8: Reconstruction speed comparison between Naive-DPS and GSURE-DPS across T2-Weighted Brain and Fat￾Suppressed Knee anatomies and three different SNR levels. Each plot compares Naive-DPS and GSURE-DPS, where each point on the line represents: a) on y-axis the average NRMS…

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.