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Abstract
Positron emission tomography (PET) reconstruction is a challenging inverse problem, where projection data often contain low statistics. While current supervised learning methods offer strong noise suppression abilities, they may suffer from generalization issues and are in many cases not accurate quantitatively. To overcome these challenges, we propose a novel self-supervised Time-of-Flight PET (TOF-PET) reconstruction framework that utilizes Implicit Neural Representations (INR) to model PET images. Specifically, we introduce a differentiable forward projection model based on the imaging mechanism for TOF-PET and reformulate TOF-PET reconstruction problem using INR. To enhance image smoothness, we develop a ray-based total variation (TV) regularization term, distinct from the traditional TV. For the internal structure of our INR, we integrate a multi-resolution hash encoder with our designed prior-image encoder, where the latter provides sufficient image prior and always delivers reliable initial reconstructions for arbitrary network depth. Experiments on brain and chest datasets show that our method outperforms traditional iterative algorithms and self-supervised approaches in noise suppression and contrast recovery. Compared to conventional NeRF-based architectures, our model is more compact and converges faster, providing an efficient solution for TOF-PET reconstruction. The source code repository is hosted on GitHub: https://github.com/zyl123300/PD-INR.git
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2025/paper/3778_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
https://github.com/zyl123300/PD-INR.git
Link to the Dataset(s)
N/A
BibTex
@InProceedings{LonYux_PDINR_MICCAI2025,
author = { Long, Yuxuan AND Zhang, Yulin AND Wang, Hong AND Kuang, Xiaodong AND Huang, Hailiang AND Rao, Fan AND Liu, Huafeng AND Zheng, Yefeng AND Zhu, Wentao},
title = { { PD-INR: Prior-Driven Implicit Neural Representations for TOF-PET Reconstruction } },
booktitle = {proceedings of Medical Image Computing and Computer Assisted Intervention -- MICCAI 2025},
year = {2025},
publisher = {Springer Nature Switzerland},
volume = {LNCS 15962},
month = {September},
page = {459 -- 469}
}
Reviews
Review #1
- Please describe the contribution of the paper
The paper proposes a novel self-supervised Time-of-Flight PET (TOF-PET) reconstruction framework that leverages Implicit Neural Representations (INR) to model PET images. It introduces a new framework, termed prior-driven INR (PD-INR), which integrates image priors into conventional INR-based modeling. To further enhance image smoothness, a novel ray-wise total variation (TV) regularization term is introduced in the feature domain, specifically tailored for PD-INR. Experimental results on brain and chest datasets demonstrate that the proposed method outperforms traditional iterative algorithms and existing self-supervised approaches in terms of noise suppression and contrast recovery.
- 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.
Novel Formulation: The paper presents a novel self-supervised TOF-PET reconstruction framework based on Implicit Neural Representations (INR), offering a fresh perspective distinct from existing TOF-PET reconstruction methods. The mathematical formulation enhances the interpretability of the approach and provides a solid theoretical foundation.
Clinical Data: The model is rigorously evaluated on real-world datasets, including chest PET images acquired in clinical settings for diagnostic purposes, demonstrating the method’s relevance to practical medical applications.
Originality: The proposed framework introduces a novel ray-wise total variation (TV) regularization term in the feature domain, specifically designed for the INR framework. The flowchart clearly illustrates the reconstruction pipeline, emphasizing the method’s innovation and clarity.
Strong Evaluation: Experimental results validate the effectiveness of the proposed method in accurately reconstructing anatomical structures and reducing image artifacts. These findings suggest strong potential for clinical application and significant improvement in the quality of TOF-PET reconstructions.
- 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.
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The ablation study does not specify whether the reported PSNR metric corresponds to a single image or an average over multiple images. Additionally, the data representation in Figure 5 is ambiguous and requires clarification.
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The manuscript lacks quantitative evaluation results on clinical datasets (i.e., chest data). It is recommended to include corresponding metrics to support the method’s effectiveness in real-world clinical scenarios.
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The manuscript does not provide comparisons in terms of model parameters or inference time. Given that runtime efficiency is a critical concern for neural representation-based methods, such comparisons are essential for assessing the practicality of the proposed approach.
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- 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.
- 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.
(4) Weak Accept — could be accepted, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The comparison methods are outdated, and the INR has been established for several years. Adding more recent and vaned methods would better demonstrate the advantages and relevance of the proposed approach.
- Reviewer confidence
Confident but not absolutely certain (3)
- [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 to use prior-driven Implicit Neural Representation (PD-INR) as a novel self-supervised method for TOF-PET reconstruction, with a ray-based total variation (TV) regularization term to enhance image smoothness. On brain and chest datasets, the proposed method outperforms traditional iterative algorithms and self-supervised approaches in noise suppression and contrast recovery.
- 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 prior-based implict neural representation is a novel application in TOF-PET reconstruction, following the physical and physiological formulation.
The ray-based total variation (TV) regularization term is more efficient compared with discrete image space traditional TV, enhancing smoothness.
The evaluation and comparison with other baselines are comprehensive, with tumor recovery analysis.
- 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 significance test results are missing in quantitative analysis.
A comprarison of time and memory consumption is missing.
- 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
The font doesn’t look like the same as in MICCAI template, please fix this.
- 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 — could be accepted, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The novel methodology and application regarding INF TOF-PET reconstruction with some discussions missing
- Reviewer confidence
Confident but not absolutely certain (3)
- [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
The authors propose a novel framework for TOF PET reconstruction based on Implicit Neural Representations. To ensure convergence, the method incorporates a prior derived from the intensities of neighboring pixels obtained through an initial reconstruction, along with Total Variation (TV) regularization applied along the rays.
- 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 paper is very well-written and easy to follow. It offers extensive comparisons across a broad range of reconstruction approaches, including iterative, self-supervised, and supervised methods. The results are promising and demonstrate the potential of the approach. The authors also provide an insightful ablation study to analyze the contribution of various components, such as regularization strength and the inclusion of each prior. The clarity of the presentation is excellent. Figures are well-designed and supported by comprehensive explanations. In particular, Figure 1 does an outstanding job of clearly summarizing the methodology and we congratulate the authors for that.
- 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.
One limitation of the study lies in its evaluation, which is restricted to simulated data. For future work, we strongly encourage the authors to validate the method on real TOF-PET datasets to demonstrate its applicability in clinical settings. The paper has a strong experimental focus, but would benefit from a more detailed analysis of how the results are influenced by different factors. For instance, it would be helpful to clarify (1) the motivation for introducing a prior, given that the neural network is already trained to minimize a similar objective function, and (2) why the addition of TV regularization appears to produce blurrier images, despite its typical role in promoting piecewise constant reconstructions.
- 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
I have some minor comments:
- The number of images in each dataset is not mentioned (or was easy to miss). Even if this number is small, explicitly stating it would be better for completeness.
- Is there a necessity for using the Poisson log-likelihood instead of the L2 norm as loss function? Would the results significantly change?
- The authors note that convergence becomes difficult when removing the prior based on neighboring pixel intensities. These instabilities probably stem from the use of the Poisson log-likelihood objective. I wonder whether a simple clipping strategy—applied either to the input values or directly to the gradient—might mitigate this issue. Could the authors provide some insight or preliminary observations on this?
- The manuscript does not clearly specify how the prior was constructed, beyond stating that it was obtained from projection data. It would be helpful if the final version explicitly clarified this.
- 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 is very complete and well-written. The results are encouraging, and the authors not only apply INR to the TOF-PET problem, but also investigate priors to help the reconstruction in this specific case.
- 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
Author Feedback
We thank Reviewer 1 (R1), Reviewer 2 (R2) and Reviewer 4 (R4) for their valuable comments. Regarding the reproducibility, we will release a GitHub link of our codes in the camera-ready submission. Here, we will first reply to the major concerns from the reviewers.
R1 suggested to clarify the motivation for introducing the prior. In fact, the introduction of prior image helps our INR to be well warmed up, that the INR starts from a prior image during iterative optimization. This not only helps convergence, but also enhances the reconstruction efficiency that it allows us to use 1-layer MLP. Removing the prior would naturally increase the difficulty in convergence, as R1 also noticed in the experimental results. Additionally, R1 mentioned that the TV regularization appears to produce blurrier images. This is expected because while TV effectively suppresses noise, it also tends to smooth fine details - a well-known trade-off in regularized reconstruction.
R1 and R2 mentioned that the number of images used in the results requires clarification. In our experiments, we evaluated the method using one brain case and one chest case. Since our approach follows a self-supervised paradigm, it is likely to generalize effectively to other data. Furthermore, all quantitative results were obtained by averaging across 20 independent realizations (including random noise simulation and reconstruction) to ensure statistical reliability. Regarding another comment from R2, we confirm that Figure 5 was plotted using the results from chest data, and we will explicitly state this in the revised manuscript to avoid any ambiguity.
R1 and R2 suggested to conduct clinical experiments. We have conducted preliminary clinical experiments using retrospective data acquired with the DigitMI 930 PET/CT system (RAYSOLUTION Healthcare). Patients received intravenous injections of 18F-FDG at doses ranging from 0.05 to 0.12 mCi/kg. The full-count EM reconstruction was used as the ground truth, while low-dose data were simulated via downsampling. Our method achieved a PSNR/SSIM of 36.5/0.948, significantly outperforming EM (34.9/0.881) and MAP (35.7/0.895). Further studies are currently underway.
R2 and R4 also emphasized the importance of comparing model parameters (or memory consumption) and inference time. We will add those results in the camera-ready submission.
R4 mentioned the need to add statistical significance testing. In our study, PSNR and SSIM are included as standard image-level metrics, although they may not fully capture the diagnostic quality of PET images. Therefore, we also report clinically relevant metrics such as contrast recovery (CR) and background noise (STD), which were computed over 20 independent realizations to ensure statistical robustness. We have begun significance testing and observed consistent trends, suggesting our method is stable. The below will show our response to the minor concerns from reviewers.
R1 raised a question why our method uses Poisson likelihood loss instead of L2 loss. Poisson likelihood loss is supported by the imaging physics of PET. Specifically, the projection counts acquired by PET scanners inherently follow Poisson statistics. In our preliminary experiments, we found that the Poisson loss leads to superior reconstruction results as compared with L2 loss.
R1 also suggested the authors to clarify how the prior was constructed. In our method, the prior image is obtained by performing an initial OSEM [11] reconstruction on the raw projection data. We will provide more detailed descriptions in the final version.
R2 suggested including more recent methods for comparison. We will compare with more advanced methods in the future. As R4 mentioned the font issue in our manuscript, we will check and adjust our font formatting in the final submission to ensure full compliance with the MICCAI template requirements.
Meta-Review
Meta-review #1
- Your recommendation
Provisional Accept
- 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”.
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