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Abstract
Fluorescence Molecular Tomography (FMT) enables noninvasive quantification of early-stage tumors, but its clinical utility is hampered by the severe ill-posedness of its inverse reconstruction problem. Traditional iterative methods rely on proximal gradient descent and soft-thresholding for non-convex sparse optimization, yet suffer from poor stability under strong noise and tissue scattering—attributed to their sensitivity to hand-crafted parameters, gradient approximation errors, and rigid fixed global sparsity thresholds.To address these limitations, we propose the Multi-Scale Graph Deep Unfolding Network with Gradient-Threshold Learning (MS-GDUN), a physics-guided deep unfolding framework that synergizes iterative reconstruction logic with graph neural networks. MS-GDUN unfolds classical iterative pipelines into a layered learnable architecture, enabling end-to-end joint learning of iteration-specific gradient update directions and node-adaptive sparsity thresholds in place of manual parameter tuning. We construct physics-constrained graphs via finite-element mesh photon transport distances, use Graph Convolutional Blocks (GCB) to model multi-hop photon diffusion correlations, and introduce a Multi-Scale Graph Cross-Attention (MSGC) mechanism to fuse local-global features across four scales, mitigating single-scale limitations and enhancing reconstruction structural consistency.Extensive experiments on simulated and clinical datasets validate that MS-GDUN outperforms state-of-the-art conventional iterative and learning-based methods in tumor localization accuracy and morphological fidelity. This work establishes MS-GDUN as a robust, reliable FMT reconstruction paradigm with great potential for early tumor detection.Code is available at https://github.com/LeTeddy/MS-GDUN.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/1669_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
https://github.com/LeTeddy/MS-GDUN
Link to the Dataset(s)
N/A
BibTex
@InProceedings{HeXia_MSGDUN_MICCAI2026,
author = { He, Xiaowei AND Qiu, Chunyu AND Zhao, Xin AND Zhang, Liuyuan AND He, Xuelei AND Guo, Hongbo},
title = { { MS-GDUN: Multi-scale Graph Deep Unfolding Network with Gradient-Threshold Learning for FMT Reconstruction } },
booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026},
year = {2026},
publisher = {Springer Nature Switzerland},
volume = {LNCS ActiveX VT_ERROR: },
month = {September},
page = {pending}
}
Reviews
Review #1
- Please describe the contribution of the paper
The proposed MS-GDUN represents a significant advancement in Fluorescence Molecular Tomography (FMT) reconstruction. The framework integrates adaptive multi-scale graph convolution and a node-adaptive sparse update strategy, enhancing both performance and robustness. This novel approach not only preserves physical interpretability but also ensures scalability, while improving the model’s resilience to noise and sparsity, which are common challenges in FMT 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.
1.Clear and Well-Written: The paper is well-organized and clearly presents both the methodology and experimental results, making the technical aspects easy to understand for readers. 2.Innovative Methodology: The introduction of a physics-guided deep unfolding framework for FMT reconstruction is highly innovative. By incorporating multi-scale graph convolutional blocks and adaptive sparse updates, MS-GDUN improves the accuracy and robustness of FMT reconstruction, making it a notable contribution to the field. 3.Strong Experimental Evaluation: The authors provide extensive experimental validation on both simulated and clinical datasets. MS-GDUN significantly outperforms existing methods in key metrics, such as localization accuracy and shape fidelity, underscoring its potential for real-world applications, especially in early tumor detection. 4.Practical Clinical Relevance: The model exhibits strong potential for clinical translation. Its ability to handle high-resolution meshes and its improved localization accuracy are critical for real-world FMT applications, making it highly relevant for preclinical and clinical use in early tumor detection.
- 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.Model Complexity and Computational Cost: While the proposed method offers substantial improvements in reconstruction accuracy, the computational complexity of multi-scale graph convolutions and the node-adaptive sparse update strategy may limit its scalability for large-scale clinical datasets. Exploring optimizations or alternative approaches to reduce computational overhead would strengthen the practical applicability of the method. 2.Experimental Validation and Dataset Diversity: Although the experimental results are promising, further validation on a broader set of clinical datasets, particularly from different tumor types and imaging modalities, would better demonstrate the generalizability and robustness of the proposed method. Additionally, a more detailed comparison with clinical benchmarks would enhance the claims regarding its clinical applicability.
- 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
In Section 2, especially in the subsections related to the multi-scale graph feature extraction (2.1) and the adaptive sparse update strategy (2.3), a bit more explanation regarding the architecture and the relationships between different stages of the unfolding process would be valuable. Additionally, I would recommend including further details on the computational efficiency of the proposed method, particularly in terms of the required memory and time complexity when dealing with high-resolution meshes.
- 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?
This paper makes a substantial contribution to the field of FMT by combining deep learning with physics-based models, leading to significant improvements in reconstruction accuracy. The methodology is novel, well-executed, and the experimental validation is comprehensive. The technical innovations and the potential for clinical applications make this work highly impactful.
- 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 author has addressed all my questions, and I am inclined to accept this paper.
Review #2
- Please describe the contribution of the paper
A physics-guided deep unfolding framework is introduced for FMT reconstruction, with three main contributions. First, it incorporates physics-informed global context modeling. Second, it develops a node-adaptive sparsity mechanism with gradient threshold learning to alleviate gradient vanishing and maintain high resolution in multi-source scenarios. Third, it presents a multi-scale graph feature aggregation strategy with cross-attention to address the limitations of single-scale approaches, enabling robust representation of structural details.
- 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 problem is interesting. Formulation is rigorous. Experiments conducted for simulation and in-vivo.
- 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 performance of the method is evaluated through comparisons, the computational complexity is not discussed. Additionally, there are several instances where the readability could be improved for better clarity.
- Please rate the clarity and organization of this paper
Satisfactory
- 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
The study is interesting and addresses an important problem. However, I feel that the computational complexity of the proposed approach is not sufficiently discussed. It would be helpful to include details such as training time per epoch, inference time, and memory requirements to better assess the practical feasibility of the method. Additionally, the presentation of results could be improved for clarity. For instance, in Table 1, the title for MS-GDUN is highlighted in bold, and all corresponding values (except one) are also in bold. It is not clear whether bold formatting is intended to indicate the best-performing values, as this is not explicitly stated and does not appear to be consistent across all entries. Kindly clarify the rationale for this formatting. Minor Comments The abbreviation “MS-GDUN” is not defined in the abstract. It would be helpful to introduce it in the abstract. On Page 3, the full stop is placed before the references [22], [23] in the first sentence; it should be placed after the references. In Equation (10), the Softplus function is used but not defined. A brief definition would improve clarity for readers unfamiliar with it. Page 6: The sentence “To quantitatively evaluate the accuracy of MS-GDUN in source localization and shape reconstruction, we compared it with deep unfolding methods (ISTA-Net and FISTA-Net), a network based on GCN approach (ResGCN), and a based on deep learning reconstruction method (IPS).” is difficult to follow and appears to be missing a word (e.g., “network”). It may benefit from rephrasing for clarity. Page 6, Section 3.2: The sentence “Similarly, ResGCN performed unsatisfactorily when the source separation was small, which can be attributed to its lack of based on deep unfolding generalization capability in graph convolution, leading to training overfitting.” is unclear and would benefit from revision for readability. Page 6, Section 3.2: In the sentence “As indicated by the quantitative metrics in Table 1, MS-GDUN achieved superior performance in terms of Dice,” it would be helpful to include the corresponding Dice score for completeness.
- 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 the manuscript presents comparative performance evaluations, it does not address the computational complexity of the proposed method, which is important for assessing its practical applicability. Additionally, there are several instances where the clarity and readability of the text could be improved.
- Reviewer confidence
Somewhat confident (2)
- [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 clarifications are provided in the rebuttal.
Review #3
- Please describe the contribution of the paper
The paper addresses the ill-posedness of Fluorescence reconstruction by introducing MS-GDUN, which is a physics-guided deep unfolding network. The authors transition the traditional sparse graph manifold learning iterative solver into an end-to-end learnable architecture. The Multi-scale graph cross-attention module fuses local and global topological features from the finite-element mesh to dictate the gradient update direction. They also propose a node-adaptive gradient-threshold learning mechanism.
- 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.By mapping the SGML-IRSTA optimization steps directly into the network’s forward pass, the model retains the mathematical interpretability of classical inverse solvers while leveraging the representational power of GNNS.
2.Predict node-level adaptive shrinkage thresholds is a good insight for FMT since tissue scattering severity varies drastically with depth, a global threshold is inherently flawd, the learned spatial adaptivity addresses this physical reality.
- 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.For Deep Unrolling network, the number of unfolding stages is vital hyperparameter as it states the trade-off between reconstruction accuracy, memory footprint and gradient propagation stability. A sensitivity analysis evaluating N versus reconstruction performance and inference time is important for a method of this nature.
2.The study restrict attention to a local neighborhood to control costs, while the actual computational burden is ambiguous. Given the mesh scale (6674 nodes, 33357 elements) and the parallel execution of multi-scale laplacian graph convolutions the memory overhead could be substantial. A quantitaitve comparison of parameter counts, training time per epoch and single-sample inference time aginst the baseline could be helpful.
3.In table 1, the deep learning baseline performs poorly (Dice=39.9%), The authors didn’t clarify if this baseline was tuned to a comparable model capacity and trained to convergence. The comparison lacks of fairness.
4.A code link is provided while in the main text, the training details such as initial learning rate, optimizer choice, and specific numerical values of the neighborhood radii used to construct the multi-scale Laplacian matrices didn’t mentioned, it would be better if these details can be provided.
- 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 has provided an anonymized link to the source code, dataset, or any other dependencies.
- 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.
(4) Weak Accept — marginally above the acceptance threshold, but would not mind if rejected, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The method design of MS-GDUN is relevant to the MICCAI community, which bridges the gap between interpretable physics-based inverse solvers and topological graph representation learning. The proposed MSGC and adaptive thresholding mechanisms are well-motivated by the underlying physics of photon scattering. However, the omissions regarding model complexity and hyperparameters (the undefined number of unfolding stages and the hidden computational footprint of executing multi-scale graph cross-attention on dense 3D meshes) are concerns.
- 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 authors provided a clear rebuttal that addressed few concerns. The quantitative breakdown (linear complexity, 8-10 GB peak memory, and only 7,218 parameters) explained the model’s scalability on dense meshes. The authors also defined the missing hyperparameters such as the 6 unfolding stages and the specific neighborhood radii (0.5/1.0/1.5 mm) which improves the transparency of the methodology. The clarification that the IPS baseline was tuned to convergence on identical data splits, confirming that the comparison is unbiased. Since methodological and computational ambiguities have been resolved, I recommend accepting this manuscript.
Author Feedback
We thank the reviewers for their valuable comments. We have thoroughly addressed all concerns with detailed explanations and quantitative results to improve the work’s rigor and reproducibility. 1.Computational Complexity & Scalability (R1, R2, R4) (1) Complexity analysis: Multi-scale Laplacians (L0–L3) are precomputed, fixed, and shared across stages with no learnable parameters. They are sparse by design—each node connects to a small local neighborhood, yielding O(N) non-zeros. Sparse multiplication eliminates O(N2) dense costs, reducing graph operations to O(N). KNN cross-attention is local, and adaptive sparse updates run node-wise. Overall complexity is linear in N, ensuring scalability. On 6,674-node meshes, costs are lower than FISTA-Net/IPS and comparable to ResGCN. (2) Parameter efficiency: MS-GDUN has only 7,218 learnable parameters from 6 lightweight blocks (~1.2K each). No parameters scale with mesh nodes (N=6,674), and Laplacians are fixed. This N-independent design avoids memory explosion for large meshes. (3) Quantitative runtime/memory: Training: ~1.2 h/epoch (RTX A6000, batch=8). Inference: 80-150 ms/sample. Peak GPU memory: 8-10 GB. Sparse Laplacians and local attention limit overhead, confirming clinical scalability. 2.Methodology & Architectural Design (R1, R4) We clarify unfolding dynamics, hyperparameter sensitivity, and training details. (1) Unfolding stages: Ablation over L=4–10 confirms L=6 optimizes accuracy-efficiency. Stages run sequentially: each takes Xk−1, computes physics-consistent features, extracts multi-scale graph representations via GCB-L, predicts gradients via MSGC, and updates Xk via ASUS. Stages share Laplacians; gradients and thresholds evolve progressively, with early stages correcting global structure and later stages refining local details, forming clear inter-stage dependencies. (2) Training detail: PyTorch (3.11), 100 epochs, batch=8, RTX A6000, AdamW (1×10−3 LR). Laplacian radii: 0.5/1.0/1.5 mm. All hyperparameters are documented for reproducibility. (3) Module interactions: GCB-L extracts local (L0–L2)/global (L3) features. MSGC fuses multi-scale features via local KNN attention with sensitivity-weighted keys/values. ASUS applies Softplus-predicted node-adaptive thresholds to suppress noise. Modules form a unified pipeline enhancing structural consistency. 3.Experimental Comparison & Fairness (R1, R4) (1) Baseline fairness (R4.3): All methods are standard FMT benchmarks, strictly reimplemented and tuned to convergence with identical 8:2 splits and settings. IPS, the pioneering deep learning method, serves as quantitative/qualitative reference. It has competitive localization but inherent sparse-source artifacts (Dice=39.9%, EED=4mm). Including IPS enables comprehensive comparison, highlighting our artifact suppression and structural fidelity. IPS limitations are known; comparisons are unbiased. (2) Generalization (R1.2): Experiments use simulated dual-source (EED=4/6 mm) and in vivo mouse glioma models—standard FMT setups. Conference scope limits large multi-center experiments; public multi-center FMT data is scarce. Our deep unfolding algorithm is grounded in 3D reconstruction theory, not dataset-specific features, supporting generalization to diverse tumors/modalities. We analyze cross‑tumor and cross‑modality generalization, and benchmark against published results, verifying the method’s robustness and clinical applicability. 4.Manuscript Format Revision (R2) All formatting and presentation issues have been revised. (1) Standardized bold formatting for optimal/suboptimal values in Table 1.(2) Defined Softplus: Softplus(x)=ln(1+e^x). (3) Minor revisions include defining MS-GDUN in the abstract, standardizing reference punctuation, refining sentences, and supplementing exact Dice scores (81.1%/87.7%/54%). All reviewer concerns are fully resolved with rigorous explanations, quantitative evidence, and clear mechanism interpretations.
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.
The paper proposes MS-GDUN, a physics-guided deep unfolding network combining graph convolutional blocks, multi-scale graph cross-attention, and node-adaptive sparsity thresholding for FMT reconstruction, validated on simulated and in-vivo data. Several substantive concerns are raised across the reviews. The practical applicability of the framework is difficult to assess given the absence of any characterization of computational cost relative to baselines, which is particularly relevant for a method built on multi-scale graph operations over dense 3D meshes. The role of the number of unfolding stages, a defining hyperparameter for deep unrolling networks, is also not addressed. The fairness of the baseline comparison requires clarification, particularly whether the deep learning baseline was set up under comparable conditions given its notably low Dice. Several training and architectural details, including learning rate, optimizer, and the neighborhood radii used to construct the multi-scale Laplacian matrices, are missing from the main text. Readability also requires improvement, with several unclear or grammatically broken passages and ambiguous formatting in Table 1.The rebuttal should address the major reviewers’ concerns including these points.
- 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 MS-GDUN, a physics-guided deep unfolding network for fluorescence molecular tomography reconstruction that combines graph convolutional blocks, multi-scale graph cross-attention, and a node-adaptive sparsity thresholding mechanism, validated on simulated and in-vivo data. The reviewers agree that the method is well motivated by the physics of photon scattering, that mapping the iterative solver into a learnable architecture preserves interpretability, and that the comparative results show clear gains in localization accuracy and shape fidelity. The principal concerns across the reviews and the meta-review were the absence of any characterization of computational cost, the unspecified number of unfolding stages, the fairness of the baseline comparison, and missing training details, together with several readability issues. The rebuttal addressed these concretely, specifying the complexity and memory footprint, parameter count, unfolding stages and neighborhood radii, and the conditions under which the baseline was tuned, and the two reviewers who had placed the paper at or below the threshold confirmed these resolved their concerns. The authors are encouraged to fold the complexity analysis, hyperparameter specification, and the noted formatting and language corrections into the camera-ready version, as committed.
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.
Following Reviewer #2 upgrading to accept after the rebuttal, all three submitted opinions favor acceptance. Strengths include the principled deep unfolding framework, multi-scale graph modelling, the gradient-threshold mechanism for adaptive sparse recovery, and competitive performance against comparison baselines. The primary weaknesses raised by R1 (implementation details) and R4 (comparison depth) were partially addressed in the rebuttal.
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.
All the reviewers are satisfied with the rebuttal.