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Abstract
Sodium MRI can non-invasively measure tissue sodium concentration (TSC), a key biomarker for stroke, tumor, cartilage degeneration, and other diseases, but severely suffers from intrinsically low signal-to-noise ratio and long scan times. Existing methods typically perform denoising on conventionally reconstructed images and then conduct TSC quantification separately, leading to oversmooth reconstruction for highly accelerated acquisition and prohibiting end-to-end concentration quantification. To fill this gap, we propose the first deep unrolling framework in sodium MRI, termed SoReCon, that takes gridded radial k-space as input and simultaneously performs sodium MRI reconstruction and TSC quantification. To this end, we for the first time craft a sharpness-enhanced training data tailored to obtaining vendor-style sodium MRI reconstruction, such that the reconstructed image achieves an appearance consistent with the vendor-reconstructed image without requiring any post-processing. Besides, we devise a differentiable concentration mapping module containing B1 inhomogeneity correction, automatic phantom detection, and linear transformation to convert the reconstructed image into a TSC map. Experiments on 107 subjects show that our method outperforms the existing representative methods by 7.19 dB in PSNR for image reconstruction and 2.54 mM in MAE for TSC quantification. Prospective evaluation on three additional subjects demonstrates the feasibility of SoReCon under real-world four-fold acceleration, reducing the primary sodium acquisition time from 15 min to 3.75 min and highlighting its potential for clinical translation.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/4553_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
N/A
Link to the Dataset(s)
N/A
BibTex
@InProceedings{CaoYil_A3D_MICCAI2026,
author = { Cao, Yilin AND Duan, Caohui AND Shen, Dinggang AND Lou, Xin AND Sun, Kaicong},
title = { { A 3D Unrolling Framework for Joint Sodium MRI Reconstruction and Concentration Quantification } },
booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026},
year = {2026},
publisher = {Springer Nature Switzerland},
volume = {LNCS 16888},
month = {September},
page = {pending}
}
Reviews
Review #1
- Please describe the contribution of the paper
The authors present a deep-learning based reconstruction method for accelerated sodium MRI. The networks enable end-to-end total sodium concentration (TSC) mapping from raw k-space data. In-vivo studies show that the proposed method preserves both reconstruction fidelity and quantitative accuracy at a fourfold acceleration factor.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
1.The proposed method directly produces TSC images, which is of most interest in sodium MRI. In the current practice, deriving TSC from sodium MRI relies on simple (linear model) but tedious post-processing, often including manual masking for calibration phantoms. This work achieve automation for the post-processing step. 2.This work also implemented bilateral filter-based reconstruction for use as the reference. The reference seemingly suppresses noise while preserving edges. 3.Prospective study shows that the proposed method outperformed scanner’s reconstruction pipeline.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
1.p4: What is “clinical DICOM reconstruction”? Is it named after the image format? This is a very confusing nomenclature. 2.The results are unconvincing and the mechanisms of the proposed method is not fully explored. Please refer to the comments below.
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission does not provide sufficient information for reproducibility.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
1.The authors claim that non-uniform FFT (NUFFT) reconstruction produced blur images. However, NUFFT as a Fourier transform variant does not inherently cause blurring (c. f. Behl et. al. , 2016, Magnetic Resonance in Medicine for clear 23Na images by NUFFT). Instead, the blurring might be rooted from density compensation. Authors should describe how the density compensation weighting was performed during NUFFT. Additionally, the acronym should be defined at its first occurrence in the manuscript. 2.The authors should explain how the retrospective data set was divided into train/test sets. 3.The effect of extra B1 correction was not fully discussed. (1) Please introduce NAA/NAV with a bit more details. (2) How much time does the extra scan cost? 4.The CMM is not justified based on the presented evidence. The ablation study shows that the proposed CMM leads to lower PSNR and SSIM. Also, the authors should provide the performance in the case of 2x acceleration. 5.Fig 5: It would be interesting to compare the proposed method compared with the bilateral filtered reconstruction on the undersampled k-space data.
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(3) Weak Reject — marginally below the acceptance threshold, but would not mind if accepted, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
While this work presents an interesting method, the experiment design is probably flawed and there lacks critical evidence supporting authors’ claim.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
Reject
- [Post rebuttal] Please justify your final decision from above.
The authors have provided responses to questions regarding the soundness of results. However, I am afraid extra work is required to understand and verify the proposed design, particularly: (1) the improvment seen after adding CMM and the effect of incorporating data from prolonged auxilliary scans; (2) seemingly incoherent ablation study results; (3) unexplained lower performance on prospective data when compared to the test set.
Review #2
- Please describe the contribution of the paper
The main contributions include: 1) The first end-to-end framework from undersampled k-space to quantitative sodium maps by jointly performing sodium MRI reconstruction and sodium concentration quantification; 2) Construction of a k-space training set for sodium MRI reconstruction with enhanced sharpness; 3) Integrating a concentration mapping module and concentration loss into network training to enable concentration error backpropagation; 4) Evaluated on a relatively large in-house data containing 110 patients including a prospective study, reducing scan time from 15 minutes to 3.75 minutes (4×) while preserving reconstruction quality.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
This paper presents several notable strengths. First, it addresses a clinically important problem in sodium MRI by tackling both low SNR and long acquisition time through a unified framework. Second, the proposed end-to-end approach that jointly performs image reconstruction and concentration quantification from undersampled k-space is well-motivated and represents a meaningful departure from conventional two-stage pipelines. Third, the integration of a differentiable concentration mapping module incorporating B1 correction and phantom calibration enhances the physiological relevance of the method. In addition, the study is supported by a relatively large in-house dataset and includes prospective validation, which strengthens its practical significance. Finally, the demonstrated acceleration with preserved reconstruction fidelity highlights the potential for real clinical translation.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
The limited prospective validation restricts evidence of generalizability. Additionally, the ablation study does not fully justify the contribution of individual components.
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission does not mention open access to source code or data, but provides a clear and detailed description of the algorithm to ensure reproducibility.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(5) Accept — should be accepted, independent of rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The first end-to-end framework from undersampled k-space to quantitative sodium maps; Evaluated on a relatively large in-house data; A prospective study, demonstrating the reduction of scan time from 15 minutes to 3.75 minutes.
- Reviewer confidence
Confident but not absolutely certain (3)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
Accept
- [Post rebuttal] Please justify your final decision from above.
The first end-to-end framework from undersampled k-space to quantitative sodium maps; Evaluated on a relatively large in-house data; A prospective study, demonstrating the reduction of scan time from 15 minutes to 3.75 minutes.
Review #3
- Please describe the contribution of the paper
The paper proposes a new learning technique for 23Na reconstruction.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
*The approach is new *Evaluations are performed with real prospective data
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
*The paper does not compare against reasonable baseline techniques.
*The paper focuses on PSNR, SSIM, and MAE without identifying limitations. This approach has been recently criticized. (DOI:10.1002/mrm.70377)
*The literature review has a major omission with respect to sodium reconstruction methods that use 1H reference images for denoising and edge preservation:
Atkinson IC, Thulborn KR, Lu A, Haldar J, Zhou XJ, Claiborne T, Liang ZP. Quantitative 23-sodium and 17-oxygen MR imaging in human brain at 9.4 Tesla enhanced by constrained k-space reconstruction. In Proceedings of the 16th Annual Meeting of ISMRM, Toronto 2008 (p. 335).
Gnahm, C., Bock, M., Bachert, P., Semmler, W., Behl, N.G.R. and Nagel, A.M. (2014), Iterative 3D projection reconstruction of 23Na data with an 1H MRI constraint. Magn. Reson. Med., 71: 1720-1732. Gnahm C, Nagel AM. Anatomically weighted second-order total variation reconstruction of 23Na MRI using prior information from 1H MRI. Neuroimage. 2015 Jan 15;105:452-61. Lachner S, Zaric O, Utzschneider M, Minarikova L, Zbýň Š, Hensel B, Trattnig S, Uder M, Nagel AM. Compressed sensing reconstruction of 7 Tesla 23Na multi-channel breast data using 1H MRI constraint. Magnetic resonance imaging. 2019 Jul 1;60:145-56. Zhao Y, Guo R, Li Y, Thulborn KR, Liang ZP. High-resolution sodium imaging using anatomical and sparsity constraints for denoising and recovery of novel features. Magnetic Resonance in Medicine. 2021 Aug;86(2):625-36.
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission does not provide sufficient information for reproducibility.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(3) Weak Reject — marginally below the acceptance threshold, but would not mind if accepted, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The novelty is borderline, the results are hard to interpret, and the paper has cited almost none of the relevant 23Na reconstruction methods.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
Accept
- [Post rebuttal] Please justify your final decision from above.
The authors responded well to comments
Author Feedback
We thank the meta-reviewer and reviewers for your constructive feedback and positive recognition of our work on end-to-end sodium MRI reconstruction and quantitative concentration mapping. Below we clarify the major concerns.
(1) Novelty, related work, and baseline positioning (R1, R3, MR). We thank R3 for highlighting prior 1H-constrained methods (e.g., Gnahm et al.), which use external anatomical priors. Since our method relies on multi-coil k-space data for reconstruction rather than on T1w priors for postprocessing (denoising), our protocol did not acquire 1H data and we cannot use these 1H-constrained methods for comparison. Instead, we selected three baselines: NUFFT, compressed sensing, and 3D U-Net, covering both traditional and learning-based approaches and allowing fair comparison. We will add the 1H-constrained methods in the related work. We thank R1 for suggesting the bilateral-filtered reconstruction and will add it into comparison in our journal version.
(2) Clarification of NUFFT/regridding and terminology (R1, MR). We apologize for the previous unclarity. For NUFFT, we used Pipe-Menon algorithm for density compensation and chose the best parameters (e.g., iteration number) for the highest PSNR/SSIM, yielding relatively blurred reconstruction. For training data preparation, we used regridding on raw data without density compensation and took it as input for our sharpening procedure, which balances noise suppression and structural visibility. We will release the code upon acceptance. We agree that “clinical DICOM reconstruction” is confusing and will replace it with “scanner-provided reconstruction”. We will clarify the above issues in revised version.
(3) Justification of CMM and evaluation metrics (R1, R2, R3, MR). Our end-to-end framework aims to obtain both accurate sodium quantification and reconstruction fidelity. At 4× acceleration, CMM substantially improves TSC MAE (9.17→6.16 mM) with slight PSNR/SSIM changes, indicating 1) TSC is easier to recover than image reconstruction for high acceleration, and the model balances both; 2) reconstruction improvement does not always align with TSC [Haldar et al.,2026]. Both show the importance of end-to-end learning. At 2× acceleration, CMM improves both MAE (7.79→6.20 mM) and PSNR (39.55→40.16 dB). We did not show the results due to page limits. Besides PSNR/SSIM, we included TSC error, prospective validation, and visual comparison. Prospective images were reviewed by experienced radiologists and rated as excellent compared to scanner-provided images, showing its clinical potential. We will discuss metric limitations and refer to [Haldar et al.,2026] in the revised manuscript.
(4) Experimental protocol and B1 correction (R1, MR). The retrospective dataset contains 110 cases. 3 were excluded due to quality control. The remaining 107 cases were split at subject level into 77/10/20 for training/validation/test. For B1 calibration, due to B1+ transmit field inhomogeneity, image intensity may not accurately reflect the underlying sodium concentration. Therefore, we acquired high-SNR NAA and homogeneous NAV acquisitions and the voxel-wise NAA/NAV ratio estimates the relative transmit sensitivity map for quantitative bias correction. Our protocol includes two NAA scans for improved SNR (1 min each) and one NAV scan (6 min). These scans are part of our standard workflow. We will add these details to the revised version.
(5) Prospective validation and practical feasibility (R2, MR). We acknowledge that the prospective data is limited due to high cost and long acquisition time. Nevertheless, we performed quantitative and visual evaluation on these prospective acquisitions and will collect more data in future to strengthen the clinical utility. From our empirical results, we found end-to-end learning brings the largest gain and CMM the second. Due to page limits, this was omitted but will be added in the revised version.
Meta-Review
Meta-review #1
- Your recommendation
Invite for Rebuttal
- Please justify your decision. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. In case of an invitation for rebuttal, clarify which points are important to address in the rebuttal.
There seems to be concerns around interpretability of the results, innovation, and literature review, resulting in mixed reviews.
Strengths: The work addresses an important sodium MRI problem by proposing an end-to-end 3D unrolled framework that jointly reconstructs undersampled k-space and produces total sodium concentration maps, incorporating B1 correction, phantom calibration, a relatively large in-house dataset, and prospective validation. Weaknesses: Reviewers found the experimental evidence uneven, with limited prospective validation, incomplete ablation of components, unclear or possibly flawed experimental design, missing comparisons to strong or relevant sodium reconstruction baselines, and an insufficient literature review that makes the novelty hard to assess. The authors therefore be invited for the rebuttal.
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
The authors are advised to address the reviewers’ remaining concerns and do what they promise to do in their rebuttal.
Meta-review #2
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
This paper proposes a 3D unrolling framework for joint sodium MRI reconstruction and concentration quantification, aiming to reconstruct accelerated sodium MRI from undersampled k-space while directly producing quantitative total sodium concentration maps.
The reviewers recognized the clinical importance of accelerated sodium MRI, the value of an end-to-end framework from k-space to quantitative sodium maps, and the inclusion of B1 correction, phantom calibration, a relatively large in-house dataset, and prospective validation. They also appreciated the potential reduction of scan time from 15 minutes to 3.75 minutes.
The reviewers raised concerns about unclear experimental design, limited prospective validation, incomplete ablation, missing sodium MRI baseline comparisons, and insufficient discussion of related 1H-constrained sodium reconstruction methods. In the rebuttal, the authors clarified the NUFFT/regridding setup, dataset split, B1 calibration protocol, the role of the concentration mapping module, and the rationale for selected baselines. They also committed to improving the related-work discussion and terminology.
Although some limitations remain, especially the limited prospective data and the need for clearer ablation presentation, the rebuttal sufficiently addressed the main concerns, and most reviewers supported acceptance after rebuttal. Therefore, I recommend acceptance.
Meta-review #3
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
Post-rebuttal consensus is 2 accept and 1 reject, with R3 moving from weak reject to weak accept. The paper is not a clear accept because R1’s technical objections remain meaningful, but the rebuttal improved the balance. I would recommend accept, emphasizing that the final version must include the promised clarifications, related work, metric limitations, and prospective validation caveats.
Meta-review #4
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
This paper rebuilds undersampled sodium MRI and outputs tissue sodium concentration maps in one trained pass. The main worry at review was that the ablation made no sense, since the concentration module lowers PSNR and SSIM. The rebuttal clears this up. The panel’s reconstruction expert read the same point and moved from reject to accept. The rest holds up from the submitted paper. There are three real baselines, and the extra methods one reviewer asked for need 1H scans this study never collects. PSNR and SSIM are weak metrics, but they are not the headline. The real number is concentration error in mm, which is the right thing to measure and it improves.
The work also has real clinical weight, with a large in-house dataset and a prospective study rated by radiologists. What is left is fixable at camera-ready: the 3.75 minute figure leaves out about 8 minutes of calibration scans and should be given as total time, the prospective set is weaker than the test set and needs a line of explanation, and the “first” claim is only true because it is limited to sodium, since the joint reconstruct-and-quantify idea itself comes from proton qMRI.
It is a sound, clinically useful paper at borderline accept bar.