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Abstract
We introduce a novel composite total variation (TV) and its solution algorithm with their application to multi-echo, respiratory motion-resolved 5D (3D space + 1D respiratory motion + 1D echo signal evolution) compressed sensing (CS) abdominal MR image reconstruction. The proposed formalism ensures a sparse representation between multi-echo images with varying contrast—a vital feature that needs to be preserved—making it highly suitable for applications in multi-dimensional computational/quantitative imaging. The key idea of the proposed composite TV and its formal definition were inspired by the observation that the spatial gradient of difference images in multi-echo MRI appears sparse. Throughout extensive experiments on a small number of healthy volunteers, we have demonstrated improved performance of the proposed method in 5D motion-resolved CS reconstruction of multi-echo MRI data compared to the state-of-the-art method. We have also demonstrated improved performance of the proposed method in quantitative tissue parameter mapping (such as R2*, proton density fat fraction, and quantitative susceptibility mapping) across a wide range of undersampling factors. In conclusion, the proposed method enables vastly accelerated motion-resolved multi-echo CS-MRI minimally impacting the quantification of downstream tissue parameters.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2025/paper/3082_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{KanMun_Accelerated_MICCAI2025,
author = { Kang, MungSoo and Alus, Or and Kee, Youngwook},
title = { { Accelerated Free-Breathing 5D Multi-Echo Respiratory Motion-Resolved R2*, PDFF, and QSM Using Novel Composite Total Variation } },
booktitle = {proceedings of Medical Image Computing and Computer Assisted Intervention -- MICCAI 2025},
year = {2025},
publisher = {Springer Nature Switzerland},
volume = {LNCS 15962},
month = {September},
page = {23 -- 33}
}
Reviews
Review #1
- Please describe the contribution of the paper
The paper introduces a composite total variation regularization method and applies it to 5D MRI.
- 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.
While this type of regularization has existed for a long time in the MRI reconstruction literature (not as novel as claimed), the application of composite TV to the 5D MRI application is new, and the authors demonstrate results with interesting new 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 has a couple major weaknesses:
- Lack of awareness of related literature. The paper claims that “Note that classical TV and existing generalizations do not account for the notion of sparsity among multi-echo images because the contrast differences between echoes are not inherently sparse and must be preserved.” However, there are several MRI reconstruction papers that impose TV-like joint smoothness constraints among images with major contrast differences, such as
J. P. Haldar, Z.-P. Liang. Joint Reconstruction of Noisy High-Resolution MR Image Sequences. IEEE ISBI, 2008, pp. 752-755.
J. Trzasko, A. Manduca. Group sparse reconstruction of vector-valued images. ISMRM 2011. p. 2839
B. Bilgic, V. K. Goyal, E. Adalsteinsson. Multi-contrast reconstruction with Bayesian compressed sensing. Magn Reson Med 2011;66:1601–15.
J. P. Haldar, V. J. Wedeen, M. Nezamzadeh, G. Dai, M. W. Weiner, N. Schuff, Z.-P. Liang. Improved Diffusion Imaging through SNR-Enhancing Joint Reconstruction. Magn Reson Med 69:277-289, 2013.
There are also similar TV-like regularizers for multicontrast images in the image processing literature:
P. Blomgren and T. F. Chan, “Color TV: Total variation methods for restoration of vector-valued images,” IEEE Trans. Image Process., vol. 7, pp. 304–309, 1998.
R. Molina, J. Mateos, A. K. Katsaggelos, and M. Vega, “Bayesian multichannel image restoration using compound Gauss-Markov random fields,” IEEE Trans. Image Process., vol. 12, pp. 1642–1654, 2003.
X. Bresson and T. F. Chan, “Fast dual minimization of the vectorial total variation norm and applications to color image processing,” Inverse Probl. Imaging, vol. 2, pp. 455–484, 2008.
J. Yang, W. Yin, Y. Zhang, and Y. Wang, “A fast algorithm for edge-preserving variational multichannel image restoration,” SIAM J. Imaging Sci., vol. 2, pp. 569–592, 2009.
There are also several more recent papers that claim to be more powerful than TV-type approaches for this type of problem, including structured low-rank methods (Bilgic et al “Improving Parallel Imaging by Jointly Reconstructing Multi-Contrast Data” 2018), multidimensional low-rank methods (Trzasko “Exploiting local low-rank structure in higher-dimensional MRI applications” 2013, Bustin et al “High-dimensionality undersampled patch-based reconstruction (HD-PROST) for accelerated multi-contrast MRI” 2019), and deep learning methods.
- Writing. The L21 norm used in Eq. (3) is a well known joint-sparsity regularizer, but the fact that it encourages joint sparsity isn’t explained clearly. This means that the proposed “new” contribution isn’t explained very clearly. (Of course, the “new” contribution also isn’t that new as described above).
- Please rate the clarity and organization of this paper
Poor
- 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.
- 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/2025/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 — could be rejected, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The paper needs to be revised to properly acknowledge that the authors are using an existing regularization technique, not something novel. The novelty lies in the application of the new technique to 5D data. If the authors are not allowed to revise the manuscript, then the current manuscript is misleading and should be rejected.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
N/A
- [Post rebuttal] Please justify your final decision from above.
N/A
Review #2
- Please describe the contribution of the paper
The authors proposed a multi-echo sparsity regularization and a primal-dual optimization scheme for free-breathing 5D multi-echo gradient echo (mGRE) image reconstruction, enabling R2*, fat fraction, and quantitative susceptibility mapping. A novel temporal regularization approach leveraging echo-gradient sparsity, along with a rigorous primal-dual optimization framework, was employed. The method demonstrated improved image quality compared to a previous reconstruction approach that did not incorporate echo sparsity.
- 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.
- A 5D tensor processing framework is employed to reconstruct free-breathing 5D multi-echo gradient echo (mGRE) data.
- The proposed primal-dual min-max reconstruction scheme is carefully designed with a solid theoretical foundation.
- Retrospective undersampling and reconstruction were performed, and the results were compared with a previous method that did not use echo regularization.
- A 3D cone MRI sequence was implemented and used to acquire the k-space 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.
- Only three healthy subjects were scanned, with a limited sample size and no reconstruction comparison involving pathological cases.
- An ablation study is missing that evaluates the effects of using only spatial gradients without forward differences along the echo, or only forward differences along the echo without spatial gradients.
- Prospective undersampling and reconstruction are needed in future work to further validate the proposed approach against prior methods.
- 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.
- 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/2025/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 paper presents a well-motivated and technically sound reconstruction framework for free-breathing 5D multi-echo gradient echo imaging. The proposed primal-dual min-max optimization scheme is theoretically grounded and demonstrates clear improvements in image quality over prior methods. The experimental setup is appropriate, and the results support the method’s effectiveness. Despite some limitations in dataset size and ablation depth, the overall contribution is significant and merits acceptance.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
N/A
- [Post rebuttal] Please justify your final decision from above.
N/A
Review #3
- Please describe the contribution of the paper
This paper proposed a 5D multi-echo respiratory motion-resolved MRI compressed sensing reconstruction method. The proposed method was evaluated for 3 healthy subjects and showed excellent reconstruction performance.
- 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 proposed optimization algorithm for 5D MRI reconstruction is promising, as it effectively exploits the redundancy in high-dimensional data. The results presented in the paper demonstrate superior performance compared to conventional 4D reconstruction methods.
- 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.
Although the proposed method demonstrates improved qualitative image quality, the quantitative results are somewhat inconsistent, particularly for R2* and QSM. As shown in Table 1, there is a substantial difference in R2* values between the accelerated and fully sampled images. Compared to the conventional method, the proposed approach yields lower R2* accuracy for Subject 1 and only marginal improvements for Subjects 2 and 3. For QSM, the proposed method shows worse accuracy for Subject 1, and for Subjects 2 and 3, its accuracy varies with the acceleration rate—sometimes better, sometimes worse than the conventional method. Given that the primary application of this method is quantitative imaging, these issues should be carefully addressed.
Although it was published only recently, a relevant paper on 5D image reconstruction should be acknowledged. The authors should consider revising the wording accordingly and include a comparison with this related work. [Kang, MungSoo, et al. “5D image reconstruction exploiting space-motion-echo sparsity for accelerated free-breathing quantitative liver MRI.” Medical Image Analysis (2025): 103532.]
- 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.
- 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/2025/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 paper proposed a 5D image reconstruction method that exploits the redundancy in high-dimensional MRI data and showed superior performance compared to 4D reconstruction. However, the quantification results are not consistently accurate or better than existing methods.
- 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 did not address my concern about the similarity with a recently published paper. [MungSoo Kang, et al, 5D image reconstruction exploiting space-motion-echo sparsity for accelerated free-breathing quantitative liver MRI.]
Author Feedback
We thank the reviewers for their valuable feedback. Below, we address the major concerns raised to improve the current paper.
R1.1. Lack of awareness of related literature. Resp: All suggested relevant literature has now been cited in the revised Introduction. The last sentence of the second paragraph has been updated to: “We note that several MRI reconstruction studies have explored TV-like joint smoothness constraints across images with significant contrast differences (Haldar et al., Trzasko et al., Bilgic et al., Haldar et al.). Related TV-based regularizers for multi-contrast images have also been proposed in the image processing literature (Blomgren and Chan, Molina et al., Bresson and Chan, Yang et al.). Finally, low-rank methods—such as those by Bilgic et al., Trzasko et al., and Bustin et al.—have shown promise. Note that these methods were primarily designed for 2D/3D Cartesian imaging of static organs like the brain with little attention to tissue parameter mapping and have not been extended to 5D non-Cartesian motion-resolved mGRE MRI.”
R1.2. Detailed explanation of Eq. 3, emphasizing the composite TV term is new. Resp: Although joint sparsity regularizers have been studied in the literature cited by the reviewer, we were unable to identify the L21 formulation in Eq. (3) in prior work. Our approach defines an explicit sparsifying transform combining echo-wise differences and spatial gradients into a composite operator within joint regularization, introducing a new regularizer tailored for 5D mGRE reconstruction as well as its solution algorithm; thus, we believe this constitutes a novel technical contribution. We have added the following for clarity: “The composite operator inside the L21 norm extracts a contrast-invariant sparse representation—while contrast changes across echoes are not sparse, image edges remain largely sparse. Noise-like undersampling artifacts (as the difference of two Gaussians is also Gaussian), extracted with sparse edges, are selectively suppressed by the L21 norm, effectively preserving sharp edges.”
R2.1. Dataset size Resp: We acknowledge the limited dataset in this proof-of-concept study. While formal power analysis is needed for systematic comparisons, we have included three patients with liver iron overload. Compared to prior 4D techniques, our method produced more consistent liver parameter maps across various acceleration factors; which is consistent with our initial findings. This will be added to the camera-ready version.
R2.2. Depth of ablation study Resp: Although limited, the paper includes comparisons with the 4D reconstruction. Further suggested ablation study will be addressed in future work.
R2.3. Prospective undersampling Resp: The reviewer is correct. Validating our method using various prospective undersampling strategies would further strengthen the findings, and we anticipate consistent results. This will be addressed in future work as noted in the Discussion.
R3.1. Quantitative values (R2* and QSM) Resp: We agree that the accuracy of ROI-based R2* and QSM measurements varies with acceleration factors. Our results indicate that R2* is more sensitive to undersampling artifacts than PDFF and QSM, with marginal improvements in two subjects. Nevertheless, visual assessments demonstrated that the proposed method consistently produced more reliable and consistent R2* and susceptibility maps, as suggested by lower standard deviations across all subjects and acceleration factors. Fully addressing the reviewer’s concern requires a systematic analysis of the entire post-processing pipeline—from water-fat separation and background field removal to dipole inversion—as each may introduce bias affecting accuracy. Additionally, the regularization parameter along the echo dimension should be tuned per subject and acceleration factor. This will remain as future work.
R3.2. Citation of Kang et al. (2025) MedIA. Resp: We have cited the paper in the Discussion with added wording.
Meta-Review
Meta-review #1
- Your recommendation
Invite for Rebuttal
- If your recommendation is “Provisional Reject”, then summarize the factors that went into this decision. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. You do not need to provide a justification for a recommendation of “Provisional Accept” or “Invite for Rebuttal”.
N/A
- 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. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’
N/A
Meta-review #2
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Reject
- Please justify your recommendation. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’
This manuscript presents a 5D multi-echo respiratory motion-resolved MRI compressed sensing reconstruction method. The method demonstrated improved image quality compared to a previous reconstruction approach. However, in response to the reviewers’ concerns about the lack of innovation, particularly the high similarity to a recently published article, the authors did not clarify how their method differs from that work or explain its novelty in comparison. While a direct comparison may not be strictly necessary, I share the reviewers’ concerns regarding the limited innovation.
Meta-review #3
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Reject
- Please justify your recommendation. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’
The authors did not adequately address the concern raised by Reviewer 3 regarding the similarity to the recent work by Kang et al. (“5D image reconstruction exploiting space-motion-echo sparsity for accelerated free-breathing quantitative liver MRI”). They only referenced the 2023 paper, but the problem formulation is very similar, and the number of subjects used for evaluation is the same. I do not believe this paper is ready for publication unless the authors clearly clarify the differences between their work and the recent study.