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Abstract
Computed tomography (CT) is a widely used medical imaging technique to scan internal structures of a body, typically involving collimation and mechanical rotation. Compton scatter tomography (CST) presents an interesting alternative to conventional CT by leveraging Compton physics instead of collimation to gather information from multiple directions. While CST introduces new imaging opportunities with several advantages such as high sensitivity, compactness, and entirely fixed systems, image reconstruction remains an open problem due to the mathematical challenges of CST modeling. In contrast, deep unrolling networks have demonstrated potential in CT image reconstruction, despite their computationally intensive nature. In this study, we investigate the efficiency of unrolling networks for CST image reconstruction. To address the important computational cost required for training, we propose UnWave-Net, a novel unrolled wavelet-based reconstruction network. This architecture includes a non-local regularization term based on wavelets, which captures long-range dependencies within images and emphasizes the multi-scale components of the wavelet transform. We evaluate our approach using a CST of circular geometry which stays completely static during data acquisition, where UnWave-Net facilitates image reconstruction in the absence of a specific reconstruction formula. Our method outperforms existing approaches and achieves state-of-the-art performance in terms of SSIM and PSNR, and offers an improved computational efficiency compared to traditional unrolling networks.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2024/paper/2336_paper.pdf
SharedIt Link: pending
SpringerLink (DOI): pending
Supplementary Material: N/A
Link to the Code Repository
https://github.com/Ishak96/UnWave-Net
Link to the Dataset(s)
www.kaggle.com/datasets/ishak21/aapm-cst
BibTex
@InProceedings{Aya_UnWaveNet_MICCAI2024,
author = { Ayad, Ishak and Tarpau, Cécilia and Cebeiro, Javier and Nguyen, Maï K.},
title = { { UnWave-Net: Unrolled Wavelet Network for Compton Tomography Image 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
Authors present a deep unrolled network for Compton scatter tomography (CST) image reconstruction incorporating a wavelet-based regularization term. The method uses a discrete wavelet transform on the input features, decomposing them into low-frequency and high-frequency components across four sub-bands. The regularization term is applied to the low-frequency features. Quantitative and qualitative experiments are presented comparing the proposed technique and state-of-the-art methods (TV, U-Net, U-Net, DuDoTrans, LEARN, RegFormer). The results show an excellent performance (PSNR, SSIM).
- 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.
- Novelty: Authors propose a unrolled network for Compton scatter tomography (CST) image reconstruction. The technique includes a non-local regularization term based on wavelets.
- Convincing experiments. The results show a good performance (PSNR, SSIM) when compared to some state-of-the-art methods (TV, U-Net, U-Net, DuDoTrans, LEARN, RegFormer). -The paper is well-written and easy to follow. The method is described in detail and straightforward to reproduce.
- 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.
- Software framework and version used are not specified.
- Although, the proposed method presents lower time costs than some deep unrolling networks (RegFormer, LEARN), the time is still high compared to post-processing methods.
- 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?
- The code is not available at the moment, but enough details to reproduce it are given.
- The dataset used by authors (AAPM dataset) is publicly available. The used dataset is described and cited.
- A description of the computing infrastructure (hardware) used is presented but a clear declaration of what software framework and version authors used is not specified.
- 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
Authors should include a description of what software framework and version used to develop the network.
- 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 topic of the paper is relevant and interesting to the MICCAI community.
- The results show a good performance (PSNR, SSIM) when compared to some state-of-the-art methods (TV, U-Net, U-Net, DuDoTrans, LEARN, RegFormer).
- The code is not available, but enough details to reproduce it are given.
- 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
N/A
- [Post rebuttal] Please justify your decision
N/A
Review #2
- Please describe the contribution of the paper
The paper proposes an unrolled reconstruction approach for Compton Scatter Tomography, a really challenging problem.
- 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 approach is a novel composition of ideas in CT reconstruction. -The paper does compare to the relevant state-of-the-art. -The paper is evaluated well.
- 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.
- Only minor points detailed below.
- 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?
The paper may not be entirely reproducible, but the concepts are described in a way that will allow reimplementation. Paper uses open data.
- 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 paper presents the problem at hand and theory very well. Methods are compared to all relevant state-of-the-art approaches they should compare to. As their setup is different from typical CT geometries, they use their own implementations of such which means a lot of time and effort that I want to appreciate at this point. Results and effectiveness are demonstrated convincingly.
I noticed that they missed the first MICCAI paper on deep learning CT from 2016 and a paper by Ye et al. from 2017 that is the first to use wavelets in a DL CT setting (Medical physics, 44(10), e360-e375.). This is only a minor point, but might be interesting for the authors.
Of course, it would be nice to see real scanner data, but this is well beyond the scope of the present data and therefore simulations are appropriate at this point.
- 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?
Method and results are convincing. The topic that is addressed is also clinically relevant and may lead to the development of entirely new CT systems that may safe orders of magnitude of dose. Until we get there is still a long way, but this paper is surely one step into this direction.
- 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
This paper presents a reconstruction algorithm for a specific compton scatter tomography setup for which no analytic inversion formula exists. The authors apply an unrolled network architecture to this problem based on the forward and pseudo inverse mapping of the imaging operator and a term representing the gradient of a regularizer which is fitted in a data-driven way. In addition, they propose a strategy to reduce the computational complexity of the regularizer term by applying a deep model only to the LL part of the wavelet transformed signal.
- 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.
This study applies the concept of unrolled networks, which has been well explored for conventional CT, to the task of compton scatter tomography reconstruction. This seems to be an interesting and well-suited idea since there exists no exact analytical inversion formula for the specific scanner design that the authors consider. Further, the authors propose to apply the network predicting the gradient of the regularization term only for the low frequency part after wavelet transformation. This is a novel idea which can in principle also benefit other types of unrolled architectures. Using this technique, the authors report faster inference times for 2 out of 3 of the unrolled comparison methods. The paper is well-written and evaluated.
- 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 study uses simulated data for training and evaluation which is based on some assumptions (e.g. monoenergetic source). The authors add Gaussian and Poissonian noise to the simulated measurements to model a more realisitc setup. From my understanding, Compton scatter tomography is an immature imaging technique such that working on simulations is necessary. However, given that this is a data-driven algorithm I would expect some discussion of the limitation of the current simulation approach.
Further, the paper investigates a 2D reconstruction problem. Given that Compton scattering is a 3D process, most photons would not stay in the imaging plane after the scattering event. I wonder whether the presented approach could be extended to 3D volumes. The wavelet-based reduction of computation could have an even larger effect in the 3D case. - 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?
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
This is a well-organized paper and the evaluation of the proposed method shows its benefits, but it lacks a discussion of potential limitations, especially concerning the simulation of the measurement data as well as the restriction to 2D.
- 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?
Overall, this paper is an interesting contribution in a field where the image reconstruction problem is less understood than in conventional CT. The motivation to use unrolled networks for compton scatter tomography is clear and the method is evaluated in comparison to multiple other unrolled as well as postprocessing algorithms showing that it works effectively. The wavelet-based technique to reduce computational complexity could potentially be applied to other unrolled approaches.
- 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
Author Feedback
We appreciate the thoughtful feedback provided by the reviewers and value their recognition of the paper’s well-written quality. We are pleased that they acknowledge the novelty of our method, particularly highlighting the efficiency of our wavelet non-local regularization term. The reviewers also found the topic clinically relevant, noting its potential to contribute to the development of new CT systems that could significantly reduce radiation doses. They appreciated that our method is well-described and easy to reproduce. We are encouraged by their recognition of our method’s strong performance, which effectively enhances PSNR and SSIM across diverse simulated scenarios compared to relevant state-of-the-art methods. Additionally, we want to express our gratitude for acknowledging the time and effort invested in setting up our own CST geometry implementation, which deviates from classical CT setups. We will ensure that the source code, along with the dataset and physics systems, will be made available soon. We are grateful for all the valuable suggestions and will incorporate them to further improve our work.
Q #1 - Time costs compared to post-processing methods: Reducing time costs for unrolling networks remains a challenge due to their iterative nature. While post-processing methods are data-intensive, unrolling networks leverage physics constraints to outperform them. To improve efficiency, we can consider reducing the number of iterations required for convergence by using second-order quasi-Newton methods like L-BFGS.
Q #2 - Missing references of wavelets-based methods: Thank you for pointing out those references. We appreciate the insight and will consider them in our future revisions.
Q #3 - Limitation of the current simulation approach: As the reviewer pointed out, CST is still an emerging imaging technique with only a few prototypes under development. A practical CST system should include a monoenergetic source and energy-resolved sensors to capture scattered photons by their energy, and a 2D system would also use plane collimators to restrict photons to a plane. However, it cannot be guaranteed that each photon is scattered only once before reaching a sensor. Therefore, the forward model of a CST system must consider multiple-order scattering. Our proposed model accounts only for first-order scattering as significant for reconstruction, treating multiple-order scattering as noise. Although Compton kinematics ensures that first-order scattering represents most scattered photons, the impact of multiple-order scattering on data degradation remains an open question. An alternative approach would be to model multiple-order scattering in the forward model, as suggested in [1], where the author includes second-order scattering. Additionally, the forward model must consider matter attenuation, incorporating two exponential terms in the Radon transform, as explained in [2]. Currently, this problem is addressed with iterative algorithms for reconstruction correction [3]. Finally, finite-sized sources and sensors, along with their imperfections, should also be included in the model. While the exact impact of this on data requires further quantification, blur is anticipated.
Q #4 - Extension of this modality in three dimensions: We acknowledge the concern about the 2D reconstruction problem given that Compton scattering is inherently a 3D process. Extending our approach to 3D volumes is indeed possible and potentially beneficial. A 3D setup, with a fixed source and a detector moving on a sphere, would eliminate the need for collimators and lead to a new toric Radon transform. Although the inversion of this transform presents theoretical challenges, ongoing work aims to address these issues.
References: [1] G. Rigaud et al., Inverse Problems, Vol. 34, 2019 [2] C. Tarpau et al., IEEE TRPMS, Vol. 4, 2020. [3] C. Tarpau et al., NDT in Aerospace, Vol. 25, 2020.
Meta-Review
Meta-review not available, early accepted paper.