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Abstract
The analytical projector (system matrix) used in most PET reconstructions does not incorporate Compton scattering and other important physical effects that affect the process generating the PET data, which can lead to biases. In our work, we define the projector from the generative model of a Monte-Carlo simulator, which already encompasses many of these effects. Based on the simulator’s implicit distribution, we propose to learn a continuous analytic surrogate for the projector by using a neural density estimator. This avoids the discretization bottleneck associated with direct Monte-Carlo estimation of the PET system matrix, which leads to very high simulation cost. We compare our method with reconstructions using the classical projector, in which corrective terms are factored into a geometrically derived system matrix. Our experiments were carried out in the 2D setting, which enables smaller-scale testing
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2024/paper/3386_paper.pdf
SharedIt Link: pending
SpringerLink (DOI): pending
Supplementary Material: https://papers.miccai.org/miccai-2024/supp/3386_supp.pdf
Link to the Code Repository
N/A
Link to the Dataset(s)
N/A
BibTex
@InProceedings{Ber_Simulation_MICCAI2024,
author = { Bergere, Bastien and Dautremer, Thomas and Comtat, Claude},
title = { { Simulation Based Inference for PET iterative reconstruction } },
booktitle = {proceedings of Medical Image Computing and Computer Assisted Intervention -- MICCAI 2024},
year = {2024},
publisher = {Springer Nature Switzerland},
volume = {LNCS 15007},
month = {October},
page = {pending}
}
Reviews
Review #1
- Please describe the contribution of the paper
This paper seeks to use more accurate Monte Carlo simulation for the system model in PET image reconstruction. This is contrasted with the Radon transform in this paper. It would be clear that, in general, Monte Carlo simulation is able to model the imaging physics and detector characteristics for PET imaging more accurately than any other model, hence this paper proposes a way of achieving this accurate modelling by neural conditional density estimation.
- Please list the main strengths of the paper; you should write about 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 seeks to use a more accurate system model via Monte Carlo through use of neural networks, as it is otherwise not easy to use a Monte Carlo based system model within iterative PET reconstruction.
The results in figure 2 show that the EM reconstruction with just one noise realisation when using the SBI matrix matches more closely with the mean EM image from 10 noise realisations. This contrasts with the Radon matrix, where the single replica reconstruction is more affected by noise when compared to the mean of 10. Hence there do appear to be visual improvements in image quality.
Figure 3 bears this out with a bias standard deviation trade off, showing that the SBI method delivers lower noise for a given level of bias, whether for EM reconstruction or MAP reconstruction. Good results.
The results in figure 2 show that the EM reconstruction with just one noise realisation when using the SBI matrix matches more closely with the mean EM image from 10 noise realisations. This contrasts with the Radon matrix, where the single replica reconstruction is more affected by noise when compared to the mean of 10. Hence there do appear to be visual improvements in image quality.
Figure 3 bears this out with a bias standard deviation trade off, show that the SBI method delivers lower noise for a given level of bias, whether for EM reconstruction or MAP reconstruction. Good results.
- Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.
The paper wrongly assumes that “In statistical model-based reconstruction, ad hoc corrective terms …are estimated and factored into the PET system matrix … this step is subject to arbitrary choices and specification errors.” This is a gross misrepresentation of system modelling and data correction / modelling in PET image reconstruction, which is far from ad hoc and arbitrary.
The authors do not compare to normal system modelling in PET (which uses not just the factorised system matrix considered here, but also models the scatter and randoms components).
The authors contrast EM with MAP, which I take to mean ML with MAP, so naming should be clearer (rather than contrasting an algorithm name, EM, with an objective, MAP).
As these are small scale tests, why not compare to a gold standard of very high count Monte Carlo results stored in a system matrix, and then used with MLEM and MAPEM?
- 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.
- Do you have any additional comments regarding the paper’s reproducibility?
The paper lacks critical details on aspects of the training and network architecture to make this reproducible.
- Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review. Pay specific attention to the different assessment criteria for the different paper categories (MIC, CAI, Clinical Translation of Methodology, Health Equity): https://conferences.miccai.org/2024/en/REVIEWER-GUIDELINES.html
Better to compare to known system modelling methods in PET, with factorised system models and additive scatter and randoms components. The Radon transform is a low benchmark for comparison.
Could also compare with a high-count Monte Carlo results even for point sources, stored in a system matrix, then used with MLEM and MAPEM, to compare with the neural approximation used here.
The paper is limited on detail regarding network training, for instance, the number of examples used for training, validation and testing.
The authors have mentioned using the validation dataset to tune hyperparameters, but important information such as the network architecture and loss function are missing.
Error, section 2: “tnnihilation photons” should be “annihilation”
- 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
Reject — should be rejected, independent of rebuttal (2)
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
Limited improvement in results and comparison with state of the art PET system modelling and reconstruction.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed
Weak Accept — could be accepted, dependent on rebuttal (4)
- [Post rebuttal] Please justify your decision
• This paper if regarded as a proof-of-concept only, is a new and interesting approach to PET image reconstruction by defining a continuous projector, which incorporates realistic physical effects such as Compton scatter. However, the proposed pipeline requires significant computational resources, making it potentially of limited feasibility for clinical use under current setup, and the generalisation of the proposed method may be an issue. Nonetheless, replies to the reviews are reasonable. The method is novel and of interest and hence could potentially be accepted.
Review #2
- Please describe the contribution of the paper
This paper presents a novel approach to PET image reconstruction by defining a continuous projecter, which incorporates realistic physical effects such as compton scatter and positron physics
- Please list the main strengths of the paper; you should write about 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 use of a continuous Monte Carlo projecter allows for a more flexible and realistic representation of the PET imaging process, which is quiet interesting, as most of the reconstruction and simulation methods didn’t take this factor into account.
- Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.
The validation part is weak, making it difficult to see the potential of the proposed projector in actual clinical applications. The manuscript lacks experiments from clinical settings and more detailed analysis.
- 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.
- Do you have any additional comments regarding the paper’s reproducibility?
N/A
- Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review. Pay specific attention to the different assessment criteria for the different paper categories (MIC, CAI, Clinical Translation of Methodology, Health Equity): https://conferences.miccai.org/2024/en/REVIEWER-GUIDELINES.html
- Consider validating the proposed method using real PET data to enhance the practical relevance and appeal of the research to clinical practitioners.
- Explore the computational demands and feasibility of implementing the proposed method in real-time clinical settings to better understand its practical limitations and requirements.
- 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
Weak Reject — could be rejected, dependent on rebuttal (3)
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
This work considers the impact of scattering and electron physical properties in PET projections, which makes it an interesting study. However, my concerns are 1. the lack of clinical data validation, 2. limited impact as the improvements demonstrated in the experiments are not significantly pronounced, and 3. clinical significance that remains to be further proven.
- Reviewer confidence
Confident but not absolutely certain (3)
- [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed
N/A
- [Post rebuttal] Please justify your decision
N/A
Review #3
- Please describe the contribution of the paper
The paper proposed a methodology for PET reconstruction that incorporates the Compton scattering effect, which is not part of conventional PET based on the Radon transform.
- Please list the main strengths of the paper; you should write about 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 suggested a pipeline for more accurate PET reconstruction that can account for phenomena such as Compton scattering. The proposal introduces a novel method in the field and shows promising results. The novelty of the paper can be attributed to the use of a neural conditional density estimator as a surrogate for the projector. This allows for learning a continuous representation of the projector, avoiding the limitations associated with the discretization inherent in traditional methods.
- Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.
The pipeline is complex and requires significant computational resources, making it potentially infeasible for clinical use. It’s challenging to train neural networks to generalize well, and the pipeline may not ideally be universal. Additionally, the accuracy of the stochastic simulator is crucial and may introduce bias here. I believe more experiments are needed to evaluate this pipeline for clinical purposes.
- Please rate the clarity and organization of this paper
Very 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.
- Do you have any additional comments regarding the paper’s reproducibility?
I suggest the authors to release the source code and/or dataset for the reproducibility purpose.
- Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review. Pay specific attention to the different assessment criteria for the different paper categories (MIC, CAI, Clinical Translation of Methodology, Health Equity): https://conferences.miccai.org/2024/en/REVIEWER-GUIDELINES.html
The study suggested a novel approach for PET reconstruction, potentially improving image accuracy by considering Compton scattering. Bridging the gap between the physics behind PET signals and current reconstruction methods is valuable. The main notable contribution is the application of neural conditional density estimation to overcome the conventional Radon projection limitations. However, there is a lack of demonstrations regarding clinical feasibility. For such a complex pipeline, it’s important to discuss the complexity, training, generalizability, and how to address these limitations for clinical purposes.
- 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
Accept — should be accepted, independent of rebuttal (5)
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The proposed pipeline is notably innovative and could significantly advance current reconstruction methods. The concept of using a continuous surrogate model for the PET represents a substantial leap over conventional approaches. Nonetheless, the study lacks evidence of clinical feasibility.
- Reviewer confidence
Confident but not absolutely certain (3)
- [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed
Accept — should be accepted, independent of rebuttal (5)
- [Post rebuttal] Please justify your decision
For clinical use, the pipeline requires significant modifications. However, as a proof of concept, it demonstrates a substantial level of novelty and innovation. This foundational work provides a strong basis for further development and refinement, potentially leading to impactful clinical applications in the future.
Author Feedback
We thank the reviewers for their thoughtful comments. We are encouraged that they found our approach novel and innovative. We are pleased that all reviewers found our explanations clear and that (R4) identified that beyond just performance gains in our example, the proposed pipeline could advance current reconstruction methods.
We note, however, that one of the main concerns shared by reviewers (R1, R4) is the lack of discussion of clinical application: As stated in our introduction, our work is essentially a proof of concept. To this end, all our experiments were carried out in the 2D setting, which enables smaller-scale testing. Clinical feasibility ultimately depends on the scalability of our method to 3D, which seems achievable without major changes.Indeed, learning a continuous model remains a density estimation problem in low-dimensional spaces (only three coordinates are needed to define an emission source and four for a line of response). Conclusive experiments with this regression step have been carried out in 3D using our same model, but are not included in this work. In terms of computational resources, the main limitations are likely to be related to the discretization of the continuous model during reconstruction. Another important question concerns the management of the possible bias introduced by the simulator and the regression, as pointed by (R4).
We address other concerns that were formulated :
[@R3] The authors do not compare to normal system modeling in PET (which also models the scatter and randoms components) : The formulation was perhaps not very clear, but in end of section 4.4, it is stated exactly that we must take scatter into account for the reference factorized model. We then explicitly state how we have done this, by adding to the Poisson model the scatter component that is estimated via simulation from a first reconstructed image. This method is consistent with what is used in practice. As for random events, they are not considered in our simulator and therefore not included in the models.
[@R3] The paper is limited on detail regarding network training.Information such as the network architecture and loss function are missing: We do not agree. The description of neural networks, which are classic MLPs (fully connected), is not the main element to remember in our approach, and is therefore rather short. However, we mentioned that the neural nets used in MDN are MLPs with four hidden layers of size 256. We explicitly gave the formula for the loss function in equation (2): “Choosing the best density estimator then becomes an optimization problem on w, with the conditional likelihood (2) over the train set as the objective” (Section 2). We also specify the total number of simulated data (3 millions) used for training and validation.
[@R3] Why not compare to a gold standard of very high count Monte-Carlo results stored in a system matrix? Even though our 2D experiments are of smaller scale than 3D, the PET matrix still contains 2 billion terms and is not sparse since scatter is taken into account. Therefore it could take up to 10^11 simulations (unless symmetries are imposed) to estimate it directly using Monte Carlo, which is very expensive. In com- parison we used 3.10^6 simulations in our model to approximate the conditional distribution of observations for any point source (see Figure 1).
Recap : Our goal is to propose a new conceptual approach that allows to efficiently incorporate a realistic generative model of the PET process into an iterative model-based reconstruction. As Monte-Carlo estimation of the system model in PET is still considered to be the most accurate modeling technique, we believe that this relatively fast and flexible method, which does not impose sparsity or symmetry of the resulting PET matrix, is promising. We would like to end by reiterating that clinical application was not part of the scope of this article, but should possibly be addressed in in future research.
Meta-Review
Meta-review #1
- 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’
One of the reviewer is unconvinced. However the paper has clear novelty and introduces a new way of modeling realistic effects such as compton scatter in PET reconstruction. Hence accept recommendation.
- What is the rank of this paper among all your rebuttal papers? Use a number between 1/n (best paper in your stack) and n/n (worst paper in your stack of n papers). If this paper is among the bottom 30% of your stack, feel free to use NR (not ranked).
One of the reviewer is unconvinced. However the paper has clear novelty and introduces a new way of modeling realistic effects such as compton scatter in PET reconstruction. Hence accept recommendation.
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. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’
The paper presents a novel a proof-of-concept method for to PET image reconstruction. Despite having preliminary evaluation, it is sufficient for a conference paper. One of the reviewers changed his/her reject rating to weak accept, raising the threshold above acceptance. I thus recommend acceptance.
- What is the rank of this paper among all your rebuttal papers? Use a number between 1/n (best paper in your stack) and n/n (worst paper in your stack of n papers). If this paper is among the bottom 30% of your stack, feel free to use NR (not ranked).
The paper presents a novel a proof-of-concept method for to PET image reconstruction. Despite having preliminary evaluation, it is sufficient for a conference paper. One of the reviewers changed his/her reject rating to weak accept, raising the threshold above acceptance. I thus recommend acceptance.