Paper: Implicit Neural Representations for Joint Sparse-View CT Reconstruction (ICLR-2024)

Reviewer comment (Evaluation):
For Figure 4b, there is a discussion that MAML might struggle to capture the shared features when many nodes are participating. Could you give bit detailed explanation? Also, which dataset are used for Figure 4? Was it 4DCT?

Author response:
In Figure 4b, we utilized an intra-person configuration on LungCT dataset from Decathlon. We have clarified this in the revision by clarifying it in the caption of Figure 4 “on intra-patient LungCT”. This additional detail should help readers better contextualize our findings.

Furthermore, we conducted new experiments that applied priors learned from different numbers of nodes to unseen data using an inter-person configuration on LungCT dataset. The results (E8 and Figure 19) exhibit a consistent trend with MAML's performance.

MAML is designed to identify an initial model that can be quickly fine-tuned to specific objects using a minimal number of gradient updates. Our hypothesis is that when the objects involved in joint training are excessively diverse, this initial model may not effectively generalize. Furthermore, while the original work [1] has successfully applied MAML to multiple objects in an image regression context, our empirical findings suggest that MAML struggles to develop a robust meta-model from many nodes when the reconstruction depends on projection measurements and the sampling is sparse.

We appreciate the opportunity to delve deeper into these aspects of our research, as understanding the nuances of these methods is crucial for advancing the field. We believe these additional experiments and discussions will offer valuable insights to the readers and contribute to a more comprehensive understanding of the potential and limitations of various methodologies in the realm of CT reconstruction.

Reviewer comment (Evaluation):
Why would MAML fail to learn meaningful prior in Supplementary Figure 10?

Author response:
In the visualization presented in Figure 10, it's observed that the learned prior of MAML does not depict a pattern that is immediately recognizable as a face, unlike those produced by FedAvg and INR-Bayes. 

It's important to clarify that this observation shouldn't necessarily be seen as an indication of MAML's inability to learn a meaningful prior. Firstly, the 'color lump' pattern associated with MAML is also discernible in the priors learned by our method, suggesting its potential relevance to the reconstruction process. 

Secondly, although FedAvg captures face-like prior, MAML's reconstruction results are quantitatively superior to those of FedAvg, as evidenced by the metrics presented alongside each image. This indicates that while the priors learned by MAML may not offer clear semantic interpretation visually, they contribute effectively to the task of reconstruction, which is the primary goal of these methods.

We appreciate this opportunity to delve deeper into the nuances of how different methods approach and learn priors. Our goal is not just to compare these methods quantitatively but also to offer insights into their qualitative aspects.

Reviewer comment (Evaluation):
How does the proposed framework compare to other state-of-the-art methods in terms of computational efficiency?

Author response:
Recognizing the relevance of this aspect, we have dedicated a new section in the appendix (E.6 and Table 5) to specifically address computation costs. This addition has also been made in response to similar queries from other reviewers. For your convenience, we have included Table 5 below, summarizing the computational costs of our method compared to other state-of-the-art approaches.

|                    | SingleINR | FedAvg | MAML  | INR-Bayes |
|--------------------|-----------|--------|-------|-----------|
| GPU Memory (MiB)   | 6338      | 6408   | 6344  | 6452      |
| Time (hrs:mins)    | 09:03     | 09:07  | 09:07 | 09:53     |

As indicated in the table, the additional computational overhead of our INR-Bayes method, when compared to SingleINR and other methods, is relatively modest. The primary additional computational time in our method involves the calculation of the latent variable and one-time Monte Carlo sampling per iteration. Our approach is deliberately devised to keep the computational overhead minimal while still harnessing the benefits of our Bayesian framework.

We hope this information adequately addresses your query regarding computational efficiency.

Reviewer comment (Presentation):
Missing bold text in 5th row of Table 3.

Author response:
Thank you for highlighting this oversight. We have now corrected Table 1 in our manuscript to ensure consistency and accuracy. Your attention to detail is greatly appreciated.

Reviewer comment (Novelty):
Small improvement. While the proposed method is conceptually appealing, the performance improvement appears to be minimal. As illustrated in Table 1, the gains, though in the positive direction, are relatively slight. Such incremental progress might raise questions about the practical implications and advantages of adopting this new approach over existing methods.

Author response:
We appreciate your perspective and would like to offer some additional context to highlight the significance of our results.

Firstly, it's important to note that PSNR is a logarithmic metric, meaning that even seemingly small numerical improvements can reflect substantial enhancements in image quality. Specifically, our method shows an average improvement of around 1.5 dB over single INR and approximately 0.5 dB over MAML. In the context of PSNR measurements over 30 dB, these improvements are indeed noteworthy.

Furthermore, in the “Applying to Unseen Data using Learned Prior” experiment, our method achieved an even more pronounced improvement – an increase of 0.9 dB over MAML and 1.4 dB over SingleINR. This further underscores the efficacy of our approach.

Another crucial aspect of our method is its robustness against overfitting, a prevalent issue in INR-based approaches. Typically, these methods experience a decline in reconstruction quality after reaching a peak performance, making it challenging to set an appropriate early stopping criterion in practical scenarios. In contrast, our method not only consistently achieves superior reconstruction quality but also maintains this level once reached. This stability is a significant practical advantage over existing methods, offering more reliable and consistent results.

We believe that these aspects collectively demonstrate the practical utility and advancements of our proposed method in the field of CT reconstruction.

Reviewer comment (Evaluation):
Increasing the number of nodes doesn't help much for almost all methods. Do the authors have any insights into this?

Author response:
The experiment depicted in Figure 4b was conducted using an intra-patient setup. Our hypothesis is that the statistics of a single patient's data can be effectively captured with just a few slices, and that adding extra nodes does not significantly improve the estimation. This phenomenon is likely to be consistent across different methods that extract statistical information from the INR network.

We have included a new experiment in the Appendix (E8 and Figure 19), conducted in an inter-patient setup. In this scenario, extracting statistics from a larger number of nodes should more accurately converge to the population statistics. Consequently, we observed a slight improvement in our method's performance as the number of nodes increased.

Reviewer comment (Theory):
What is the physical meaning of the learned priors? This prior is learned from 10 slices (which mimics 10 different patients). From this setting, I guess the prior may be some “average” CT image across these 10 images including mostly low-frequency signals. This guess is also supported by the illustration of learned prior in Figure 13 and 15, which is somewhat the general structure of the sliced anatomic structure. But why should this prior be helpful to reconstruct higher quality of CT for new patients? In the sparse-view CT reconstruction, due to the sparse sampling, what is always missing is the high-frequency signal in the detailed structure. Why does such an “average” image should be helpful to improve the final reconstruction image quality to get sharper and fine structures?

Author response:
The learned prior in our Bayesian method is modeled as a Gaussian distribution in the weight space of the INR. We use its mean to illustrate that the prior captures significant anatomical information in Figure 13 and 15. However, we emphasize that this is only one aspect of its role. The full potential of the prior encompasses the representation of uncertainty, distinguishing between universally observed patterns and those unique to fewer or individual subjects. This uncertainty allows for adaptive regularization during individual training, as each network autonomously determines which information to extract from the prior based on its own uncertainty and that of the prior. This process is facilitated by minimizing the KL divergence between the prior and the posterior distribution of the individual network. Such adaptability distinguishes the Bayesian framework from other methods and underpins its superior performance.

In sparse-view CT, the challenge predominantly arises from scanning at fewer angles compared to traditional CT. This often leads to the Nyquist-Shannon sampling theorem not being fully met, which can result in compromised reconstruction quality. Specifically, there's a perceived loss of high-frequency information in the reconstructed images. However, it's crucial to note that the high-frequency information isn't inherently lost during scanning; rather, it's the insufficiency of scans (or sampling) that impedes the accurate reconstruction of these high-frequency signals.
To demonstrate that sparse sampling doesn’t cancel out high frequency information, and with help of knowledge about low-frequency information we can reconstruct the high-frequency information, we design the following toy example. Consider a signal in the form y = sin(px) + cos(qx), where the coefficients p and q satisfy p, q \in [0, 1] and p < q. This inequality indicates that the signal comprises both high-frequency and low-frequency components. With sparse sampling, we obtain limited data, for instance, we know that when x = \pi, y = -0.5. From this single measurement, we cannot independently reconstruct the values of p or q. However, if the value of p (representing the low-frequency component) is known, we can deduce the value of q (representing the high-frequency component) from the sparse sample. Assuming p = 1/6, the equation becomes:
sin(\pi) +cos(q\pi) = -0.5.
Since sin(\pi/6) = 0.5, this equation simplifies to:
cos(q\pi) = -1,
which leads to the solution q = 1. 

This example illustrates how knowledge about low-frequency components can guide the reconstruction of high-frequency details, even with sparse sampling. Our method leverages this principle, utilizing the prior to fill in the missing information and thus enhance the overall reconstruction quality.

Reviewer comment (Experiments):
How to choose these 10 patients to get the prior? If we consider a setting to use the learned prior for new patients’ reconstruction, how shall we choose the 10 different patients to get the prior? Such as healthy patients or abnormal patients? For example, if there are some patients with tumors, does the learned prior also include such prior in the latent variables and indicate that in the new patients’ reconstruction? Shall there be any relationship between the new patients and prior patients? How can we know if the new patient is normal or abnormal before we get the CT image reconstructed?

Author response:
In our experiments, we don’t make specific requirements on the prior patients. For 4DCT, it’s natural to use all 10 phases to jointly reconstruct as they have the common changing trend. For intra-patient, we randomly select slices along the longitude, they also share the common changing trend as they are sampled from the same patient. For inter-patient experiments on Medical Segmentation Decathlon and Brain CT Hemorrhage Challenge, we randomly choose those prior slices. As they are representing the same area, lung or brain, they shall share some similarities which can be captured by the prior of our method. Specifically, the lungCT dataset of  Medical Segmentation Decathlon contains both images with tumor and without tumor, but we don’t make use of that information and randomly select 10 patients from the dataset, so the learned prior shall work for both normal and abnormal cases. Results show that our method is robust to the variation of these factors, suggesting that our method can improve the reconstruction quality without making additional requirements in normal CT applications. 

We added sentences “The dataset comprises scans both with and without tumors. For our experiments, we randomly selected patients and images without distinguishing between those containing tumors and those without, aiming for a diverse representation of lung CT images.” in the Dataset details section (D) to better clarify this point.

Reviewer comment (Experiments):
In the previous works, the paper mentioned “Lastly, while alternative joint CT reconstructions like (Shen et al., 2022) [2] use priors from pre-reconstructed images, and (Reed et al., 2021) [3] relies on finding a template image from 4DCT; their practical limitations led to their exclusion from our comparative analysis.” First, to my understanding, these two works are not doing the joint CT reconstruction as claimed in this paper. [2] is doing the CT and MRi reconstruction through INR by using a full-sampled prior image of the same patient as prior embedding, which is a very common setting for patients’ longitudinal study in clinics. [3] is doing dynamic CT reconstruction where different frames share some similarity while maintaining deformable motion, which is also very common in 4DCT setting with motion. Second, I do not see what is the “practical limitations led to their exclusion from our comparative analysis”, since these two papers’ setting may be more reasonable from practical applications. And their goal is to achieve better reconstruction results instead of fast convergence as [1], so I think these two papers may even be more important to be compared with to demonstrate the superiority of the proposed method.

Author response:
The works [2][3] also leverage information from (an)other object(s) to assist in the reconstruction of a single object. Classifying them as joint reconstruction methods may lead to some confusion, so we have updated the revision by changing the statement to “Lastly, while other INR-based CT reconstruction methods exist…”

Regarding [2], you are right in noting its practical approach where a fully-sampled reconstructed image of the same patient is used as a prior. This method is indeed intuitive and aligns well with common clinical practice for longitudinal studies. However, the challenge arises when the prior image does not closely match the target image. To illustrate this, we conducted an additional experiment, the results of which are presented in Figure 17. This experiment demonstrates that when there is a mismatch between the prior and target images, the performance of [2] can be inferior even to SingleINR with random initialization. The table below compares [2] with our method in different scenarios, including matched and unmatched priors. [2] achieves better PSNR with matched prior, but its SSIM is still lower than our method. In addition, all experiments in our paper only access a set of sparse measurements. Providing a fully-sampled prior image to Nerp can therefore be considered an unfair comparison.

|                | SingleINR             | Nerp match             | Nerp unmatch          | INR-Bayes              |
|----------------|-----------------------|------------------------|-----------------------|------------------------|
| PSNR           | 33.69 ± 0.06          | **35.33**  ± 0.10      | 32.83 ± 0.07          | 34.31 ± 0.07           |
| SSIM           | 0.883 ± 0.002         | 0.889 ± 0.001          | 0.849 ± 0.02          | **0.901** ± 0.001      |


As for [3], its focus on dynamic CT and the use of deformable motion are indeed relevant to our 4DCT experiment. However, this specific approach may not be directly applicable to other experimental settings presented in our paper. Moreover, their codebase is prohibited from release by their sponsor [https://github.com/awreed/DynamicCTReconstruction]. Despite reaching out to the authors, we have not yet received any response that would enable us to conduct comparison experiments with their approach. We appreciate your comments which have helped us refine our paper and re-evaluate our comparison methods. We believe our additional experiments and the ensuing discussion better contextualize our method’s advantages and limitations.

Reviewer comment (Experiments):
In the setting of “Applying to Unseen Data using Learned Prior”, how are the patients chosen to learn the prior? Would different prior patients influence the reconstruction for the same new patient? Would different number of prior patients influence the reconstruction for the same new patient? When adapt the new patients, will the latent variable also adapt to the new patient?

Author response:
Thank you for your insightful questions regarding the selection of patients for learning the prior and its influence on reconstructing new patients. We appreciate the opportunity to clarify these aspects and extend our analysis.

For the experiment mentioned in the main paper, we selected patients randomly, ensuring a consistent slice position across different patients by proportionally selecting slices relative to the total volume. This method accommodates the variation in the number of slices and volume sizes across patients, which can range from (112,512,512) to (636,512,512). In this particular experiment, the prior is not updated with data from the new patient. However, we acknowledge the potential for further enhancing the prior by including the new patient's data.

Addressing your query on the influence of different prior patients on the reconstruction of the same new patient, we extended our experiments (Appendix F.8). In this new experiment, we trained the prior using 10 different groups of patients, each group consisting of 10 randomly selected patients. We then used these 10 different priors to guide the reconstruction of the same new patient. As illustrated in Figure 19, our method effectively utilized these diverse priors to reconstruct the new patient, demonstrating robustness against variability in the selected prior patients.

Regarding your question about the impact of the number of prior patients, we conducted another experiment to investigate this. We trained our prior using varying numbers of patients, ranging from 5 to 40, and then applied these priors to the reconstruction of the same 5 new patients. The results, presented in Figure 18, indicate a gradual improvement in PSNR when employing priors learned from a larger pool of patients. This finding suggests that having priors from more patients can be beneficial for our method, enhancing the reconstruction quality.

We hope these additional experiments and their results comprehensively address your queries and provide further insights into the robustness and adaptability of our proposed method.

Reviewer comment (Evaluation):
Computational efficiency. Based on Algorithm 1, it seems that multiple networks are maintained and trained simultaneously for different patients. Also it needs to iterate through all patient, all time steps, with three loops interleaved. This algorithm looks very costly for memory and time efficiency. Can the paper report the memory and time used in training and testing with comparison of baseline methods?

Author response:
We understand that the algorithm's complexity and its implications on memory and time efficiency are crucial considerations.

While our methods iterate over multiple patients, SingleINR also needs to run on each of the patients in order to obtain their reconstructions. Figure 5 shows that all methods converge at a similar speed. In all experiments, we run all methods for 30000 iterations and compare their performance. While our method does incur additional computational complexity due to the optimization of the latent variables, we derive an efficient algorithm to achieve that (Line 6, 7 in Algorithm 1). The increase of the computational time of our method is therefore less than 10% compared to SingleINR. However, considering the enhanced reconstruction quality and robustness to overfitting achieved, this additional time investment can be justified.

To clarify the computational efficiency, we have expanded our appendix to include a detailed analysis of the computational cost. We've also included a comparative table (Table 5) in this discussion for easy reference. You can find this detailed comparison [here](https://openreview.net/forum?id=vyGp9Mty2t&noteId=CI64s0jmxF). 

We hope this additional information adequately addresses your query and provides clarity on the computational aspects of our method.

Reviewer comment (Presentation):
Using some framework figure may be better to illustrate the whole framework.

Author response:
Thank you for your feedback, we agree that a visual representation could enhance the clarity and understanding of our methodology.

While we believe that Figure 1 in our paper already offers a direct insight into the technical aspects of our method, we understand the importance of a more comprehensive visual overview. To address this, we have added a more detailed version of the method overview as Figure 7 in the appendix.

We hope that this additional figure will provide readers with a clearer understanding of our framework, especially before they delve into the more technical details of our approach. We are also open to further modifying the overview figure to make it even more comprehensive, should you have specific suggestions or comments in this regard.

Reviewer comment (Theory):
The statement in the introduction, "While dense measurements typically yield accurate reconstructions, measurements are often intentionally limited to reduce ionizing radiation or cost, resulting in sparse data," also implies that sparse-view CT is common in clinical practice, which the reviewer believes is not the case. Additionally, clarification is needed on how reducing the number of angles may reduce cost.

Author response:
Thank you for highlighting this aspect. We have revised our introduction to better articulate the context and potential advantages of sparse-view CT. Our new wording in the introduction is: “In specific situations, limiting the number of CT measurements can offer benefits such as reduced radiation exposure and cost management, which may lead to the use of sparse data.” This refined statement more accurately reflects the targeted use of sparse-view CT, emphasizing its potential benefits without suggesting widespread current clinical adoption.
In the realm of medical CT imaging, reducing the number of scanning angles can decrease patient exposure to ionizing radiation, a crucial consideration in frequent or high-risk scanning scenarios. This approach can also expedite the scanning process, potentially reducing wait times and increasing patient throughput in busy clinical settings. It can also potentially reduce the cost by lowering operational costs associated with extended scanner usage.
In industrial applications, where CT scanners often operate continuously in production environments, reducing scanning angles can significantly enhance efficiency. Shorter scan times increase throughput and reduce operational delays, directly impacting productivity. Additionally, decreased scanner usage results in lower energy requirements, contributing to cost savings and reduced environmental impact.
We believe that emphasizing these specific contexts provides a clearer understanding of where sparse-view CT can offer substantial advantages in both medical and industrial settings. We appreciate your feedback and hope this revised explanation addresses your concerns.

Reviewer comment (Experiments):
The statement in the introduction, "While many approaches learn the mapping from sparse-view to dense-view images using supervised learning [...] they often necessitate extensive, domain-specific datasets which are difficult to obtain in practice," is questionable because full-view acquisitions are the de-facto standard in clinical CT and sparse-view datasets can be easily simulated from these; such datasets are abundant (e.g., the LDCT Image and Projection data contains over 300 full-view, full-dose acquisitions).

Author response:
While it is true that full-view acquisitions are standard in clinical CT and sparse-view datasets can be easily simulated from these data, the challenge lies not merely in dataset availability. The primary difficulty is in obtaining domain-specific datasets that are sufficiently diverse and representative to train models effectively for a wide range of real-world applications. While simulated sparse-view datasets derived from full-view acquisitions provide a valuable resource, they may not fully capture the complexity and variability found in actual sparse-view scenarios. Secondly, in industrial contexts, new products frequently lack comprehensive full-view acquisitions. Our research focuses on methods that can generalize well from limited or sparse data. By using methods that do not solely rely on large, domain-specific datasets, we aim to improve the robustness and applicability of our models in diverse real-world scenarios, where obtaining such datasets might be impractical.

Reviewer comment (Experiments):
The authors do not compare their method against standard CNN-based methods, including approaches that implicitly or explicitly incorporate prior knowledge, or against other previously proposed INR reconstructing techniques for sparse-view CT.

Author response:
Our study focuses on approaches that excel in sparse-data environments. We selected comparison methods aligned with this focus, aiming to demonstrate the effectiveness of our approach in scenarios where data is inherently limited or sparse. This includes avoiding comparisons with methods that rely heavily on full-view acquisitions, as these do not align with the primary objective of our research, which is to excel in limited data scenarios. We have added sentences to the introduction section for clearer elaboration: “There are also works that adopt heuristic image priors, e.g., Total Variation (TV) [4,5,6], or use dense view images as priors [2, 7] to assist in reconstruction. However, these methods often lack domain-specific enhancements or require information from dense-view images.”

We acknowledge that our study did not include comparisons with standard CNN-based methods or approaches that implicitly or explicitly incorporate prior knowledge, such as the ones mentioned in [2]. The primary focus of our research was to explore the potential of Implicit Neural Representations (INRs) in utilizing the statistical regularities shared among different objects with similar representations to enhance CT reconstruction quality through joint reconstruction. Therefore, we primarily concentrated on comparing our method with other prior-embedding INR-based methods that align closely with our research question as stated in the introduction. We have revised the last sentence of the introduction to better reflect the scope of our work and the research question posed: “Our results establish that our method either outperforms or is competitive with existing INR-based baselines.” This aligns with our initial inquiry: “Can INRs utilize the statistical regularities shared among different objects with similar representations to enhance reconstruction quality through joint reconstruction?”

Regarding [2], it proposes an intriguing method of incorporating prior information from a previous image within a compressed sensing framework for 4DCT. While this approach is practically feasible for 4DCT, where scanning angles of different phases can be interleaved to form a dense-view reconstruction, it does not necessarily translate to our intra-patient and inter-patient settings. In these scenarios, even if the scans are conducted with interleaved angles, the substantial differences between the images can make it challenging to construct a cohesive and informative dense-view prior. This difference in the nature of the data and the specificities of our research focus led us to prioritize comparisons within the scope of INR-based methods.

Our study compares our method with a diverse range of techniques, including classical methods like FBP and SIRT, as well as advanced INR-based approaches like Single INR [8][9], FedAvg[11], MAML[10], and INRWild[12]. We also add a new baseline Nerp in Appendix F.7 in the revision. Our selection of comparison methods was driven by the desire to demonstrate the effectiveness of our approach across a spectrum of techniques, from classical to the latest INR-based methods. We thank the reviewer for also acknowledging our exhaustive literature review, as we believe this diverse comparison set provides a comprehensive assessment of our method's capabilities in handling sparse-view CT reconstruction challenges. If the reviewer thinks there is any relevant INR for sparse-view CT that we have missed, we would be very happy to receive this feedback for incorporation during the discussion period or later. Comparing our method against a broader range of techniques, including other prior incorporation methods, are interesting for us as future work.

Reviewer comment (Evaluation):
Figures 4, 5, and 6 lack error bars, and in Table 1 it is unclear over what the mean ± standard deviation is computed. The reviewer asks whether the improvements are statistically significant.

Author response:
The mean and standard error reported in our study are computed over all reconstructed images of our experiments, taking into account both random initializations and variations in image selections.

For instance, in the case of the 4DCT dataset, which has dimensions of 10x136x512x512, we perform joint reconstructions using groups of 10 images, each being 512x512 in size. To ensure a diverse set of data, we randomly select these images from indices ranging between 20 and 120 within the dataset. This approach yields a substantial sample size for each experiment, specifically, we calculate the mean and standard error across 1,000 images (10 images per group across 100 groups).

We appreciate your feedback as it highlighted the need for clearer explanation in our manuscript. To address this, we added the sentence “We calulate mean and standard error over all reconstructioned images in each experiment.” in the metrics subsection of section 5 (Experiments), offering a more detailed account of how these statistical measures were derived.

To rigorously evaluate the statistical significance of our method's improvements, we conducted a Wilcoxon signed-rank test comparing our results with those of the second-best method. The obtained p-values, being less than 0.05 in most cases, strongly suggest that these improvements are indeed statistically significant. For clarity and transparency, we present the detailed Wilcoxon signed-rank test results below:

| Experiment | Sample Size | Second Best Method | W-statistic (PSNR) | P-value (PSNR) | W-statistic (SSIM) | P-value (SSIM) |
|------------|-------------|--------------------|--------------------|----------------|--------------------|----------------|
| Intra-patient | 950 | MAML | 13252 | 2.16e-139  | 1617 | 7.72e-155 |
| Inter-patient Lung | 100 | MAML | 348 | 7.14e-14 | 67 | 2.88e-17 |
| Inter-patient Brain| 50 | MAML | 614 | 0.83 | 597 | 0.70 |
| 4DCT | 1000 | FedAvg | 186785 | 3.73e-12 | 4689 | 3.79e-159 |
| Adapt to new patient | 50 | MAML | 21 | 7.94e-13 | 0 | 1.78e-15 |

We have now highlighted in bold the results of both MAML and our method in Table 1 row 5 (Inter-patient Brain)  to demonstrate their statistically significant improvement over other methods. We appreciate your valuable feedback and hope that this additional analysis provides the necessary clarification.

Reviewer comment (Evaluation):
Metrics such as SSIM and PSNR are often not aligned with quality assessments by clinicians. The reviewer notes that a thorough evaluation such as a reader study is beyond the scope of the work, but believes the results in Table 1 do not justify the claim in the abstract that the method "sets a new standard in CT reconstruction performance." Upon visual inspection of Figures 2 and 3, the reviewer finds that the proposed method removes many anatomical details and doubts that a clinician would find it significantly better than, for example, SingleINR.

Author response:
We concur that PSNR and SSIM metrics may not always align with practical clinical assessments and acknowledge that incorporating human evaluation falls outside the scope of this paper and the ICLR conference. In evaluating our framework, it was necessary to select certain metrics for numerical comparison with other methods. Therefore, we chose PSNR and SSIM, which remain widely accepted and standard in both the machine learning and medical imaging fields, as evidenced by references [13], [14], [15], [16]. While we recognize that these metrics are not flawless, we believe that their limitations should not be viewed as a fundamental weakness of our paper.

To address your concerns, we have introduced a new section on limitations in our conclusion, highlighting the potential discrepancies between numerical metrics and clinical evaluations. The new limitation section now is: "We recognize that the metrics employed in our study may not always correlate with clinical evaluations [3][4]. If applied in a medical application, clinical verification of our method remains essential to understand its practical implications and efficacy in a given clinical setting." This addition aims to clarify the context and application of our findings. 

Additionally, we have carefully revised the abstract to more accurately represent our study's results and scope. The updated abstract now is: "Our results indicate marked advancements over baseline methods in standard numerical metrics, marking a progressive stride in CT reconstruction techniques." This revision aligns our claims with the evidence presented, while acknowledging the nuances of clinical applicability.

Reviewer comment (Reproducibility):
The computational complexity of the method is not provided. It is unclear whether all reconstructions in the main paper are performed on single 512×512 slices; the CBCT reconstructions in the appendix use a much smaller (clinically unusable) image matrix. The reviewer asks what the computational cost for one full patient reconstruction would be compared to other methods and a CNN baseline.

Author response:
We understand the importance of this aspect and have added a new section in the appendix that details the computation costs. For your convenience, we have replicated the information in Table 5 [here](https://openreview.net/forum?id=vyGp9Mty2t&noteId=CI64s0jmxF), which presents a comparative analysis of the computational requirements.

Due to the increased model capacity and therefore higher optimization complexity, our method exhibits slightly higher computational costs compared to other methods, but the increase is relatively small (less than 10%). 

Regarding the scope of our experiments, the main paper focuses primarily on slice-based analyses. For the 3D Cone-Beam Computed Tomography (CBCT) experiments presented in the appendix, we utilize volumes of size 128^3. This 3D experiment was designed as a proof-of-concept to demonstrate our method's applicability and effectiveness in a 3D context.

We acknowledge that the 128^3 volume size used in the 3D CBCT experiment is smaller than what is typically used in clinical settings. The choice of this size was primarily driven by computational constraints. For a comprehensive comparison, our experiments iterate over the whole dataset, which involves running hundreds of reconstructions across various methods. The total computational load is substantial. Thus, to manage these constraints effectively while still providing meaningful insights, we opted for smaller volume sizes for the 3D experiments. 

To provide a clearer perspective on the computational aspects, we included a new section in the Appendix (E6) that compares the computational costs across various INR-based methods, including our own. We also copied the comparison table [here](https://openreview.net/forum?id=vyGp9Mty2t&noteId=CI64s0jmxF) for your easier reference. While this comparison uses slice-based experiments, it offers a framework to extrapolate potential computational costs for larger, clinically relevant volumes.  

We hope this information clarifies your queries regarding the computational complexity and the scope of our experiments. We are continually working towards optimizing the method to handle larger volumes more efficiently.

Reviewer comment (Experiments):
The experiment configurations intra-patient and 4DCT violate the conditional independence assumption, and the reviewer asks whether this influences reconstruction quality.

Author response:
The conditional independence assumption allows us to decompose the variational inference problem related to the joint posterior distribution across objects. This assumption significantly simplifies the model and is instrumental in deriving an efficient algorithm for our Bayesian framework. Our experiments have shown that the INR-Bayes framework performs robustly in 4DCT and intra-patient configurations, producing high-quality reconstructions. This indicates that the framework’s capability to learn complex representations effectively compensates for any limitations introduced by the conditional independence assumption.