From Iterative Methods to Neural Networks: Complex-Valued Approaches in Medical Image Reconstruction

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

There are a few minor revisions to be addressed, along with several questions for clarification.

Regarding the minor revisions:

The paragraph structure throughout the manuscript lacks clear separation, which negatively impacts readability. It is recommended to revise the paragraph organization to improve the overall flow and comprehension.

In addition, a period is used after the word "Figure"; however, a period should only be used when the term is abbreviated. Therefore, it should either be written as "Figure No." or abbreviated correctly as "Fig. No."

In lines 393 and 394, Figure 9 is described as showing the results of the CVNN. However, Figure 9 actually presents the results of the RVNN. Given the overall context of the results, the reference to Figure 9 in line 393 should be corrected to Figure 8.

Regarding my questions:

In line 89, the χ is expressed as 

χ=(ε(r)-ε_b)/ε_b - jσ(r)/(ωε_b).

However, according to references such as:

W.-K. Park, “Direct sampling method for retrieving small perfectly conducting cracks,” Journal of Computational Physics, vol. 373, pp. 648–661, Nov. 2018,
and
M. Haynes, J. Stang, and M. Moghaddam, “Real-time Microwave Imaging of Differential Temperature for Thermal Therapy Monitoring,” IEEE Transactions on Biomedical Engineering, vol. 61, no. 6, pp. 1787–1797, June 2014,

the χ is often expressed as

χ=(ε(r)-ε_b)/ε_b - j(σ(r)-σ_b)/(ωε_b).

Of course, the sign of the imaginary part may differ depending on whether the time-harmonic dependencs is assumed to be exp(jωt) or exp(-jωt), but this distinction should be made clear in the manuscript.

Regarding my comments:

Although this may be partly due to the lack of clear paragraph separation, the description of the contributions of this paper appears to be insufficient.
Complex-valued neural networks (CVNNs) have already been introduced in previous literature. Therefore, if the novelty of this paper lies in the application of CVNNs to microwave imaging, the description of the novelty and contributions needs to be more clearly articulated.

It would be helpful for readers' understanding if the experimental setup described in lines 332 and 333 is illustrated in a figure.

Author Response

Dear Reviewer 1,

Thank you very much for your constructive and detailed feedback on our manuscript. We have carefully addressed all your comments, including the correction of the figure reference, improvements to paragraph structure and formatting, and clarification of the expression for χ. Additionally, we have revised the introduction to better highlight the novelty and contributions of our work, and we have included a new figure illustrating the experimental setup to improve clarity.

A detailed point-by-point response is provided in the attached document. We sincerely appreciate your insights, which have helped us improve the quality and clarity of the manuscript.

Sincerely,

Authors.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript addresses an important and timely topic by proposing a deep learning-based method for surface defect detection in industrial applications. The idea of combining CBAM attention mechanisms with U-Net and integrating multi-scale feature fusion through PAN is well-motivated. The experimental results demonstrate promising improvements over baseline models on multiple datasets, including NEU-DET and DAGM2007.

1. While the integration of CBAM and PAN is practical, it could be argued that the innovation is incremental. The manuscript should more clearly highlight what is new in this particular combination and whether it has been attempted previously in similar works.
2. There is no mention of whether the code or model weights will be released. Consider adding a link to a public repository or clarifying future plans for reproducibility.
3. The manuscript reports improved results, but lacks statistical analysis (e.g., standard deviations, significance tests). Consider including such metrics to strengthen the claims.
4. It would be useful to elaborate on the class distribution and whether the model performance varies across defect types.
5. Could the authors explain why they chose CBAM over other attention mechanisms like SE or BAM? Was there a comparative experiment done before finalizing CBAM?
6. In what ways does PAN specifically contribute to improved detection in small defect regions? Can this be quantified or visualized?
7. How does the model perform in real-time scenarios? Have the authors evaluated inference speed or hardware requirements?
8. Is there any consideration for model generalization to unseen datasets or different surface materials?
9. Would the authors consider extending this work toward a lightweight version of the model for embedded systems?

Comments on the Quality of English Language

There are minor grammatical errors and awkward phrasing throughout the manuscript.

A thorough proofreading or editing for language quality would improve the readability.

Author Response

Dear Reviewer 2,

We sincerely thank you for your thoughtful and constructive review of our manuscript. Your comments have been very valuable in helping us improve the clarity, completeness, and scientific rigor of the work.

In response to your feedback, we have added a public GitHub repository link to support reproducibility, and incorporated statistical metrics such as standard deviation over multiple runs. Additionally, we expanded our analysis to cover class distribution, inference speed, generalization to unseen datasets, and the potential development of a lightweight version for embedded systems.

We would like to clarify that the terms CBAM, PAN, NEU-DET, and DAGM2007 do not appear in our manuscript. As such, we could not provide detailed responses to those points but have clarified this in the response document.

A detailed, point-by-point reply to all comments is included in the attached response. We greatly appreciate your feedback, which has contributed meaningfully to strengthening the manuscript.

Sincerely,
Authors

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The work brings significant substantive value, presenting an innovative approach to the problem of medical image reconstruction by using complex neural networks (CVNN). By combining classical iterative methods with modern machine learning, the authors show that it is possible to obtain higher quality reconstruction while simplifying the modeling process. In particular, they prove that CVNN networks are more effective than their real counterparts (RVNN) in complex data processing tasks, which is of direct importance for the development of precise diagnostic methods in microwave imaging.
- Integration of iterative methods (Born Iterative Method + QP) with CVNN is an original approach.
- The proposal of three variants of architectures (CV-MLP, CV-CNN, CV-UNET) and their comparison is a valuable contribution.

However, in places the text of the publication has an "encyclopedic" tone instead of a scientific one - it is worth taking a slightly more critical approach when describing earlier works in the first part of the work. The sections describing CVNN layers (especially CV-UNET) contain very detailed information, their understanding would be much easier with more diagrams or explanations of existing ones.

Needs to be improved:

• Although quantitative results (MSE, Re) are presented, basic statistical analysis (e.g. confidence intervals, statistical significance) is missing. Please add discussion of statistical significance or variability across multiple runs.
• A more detailed explanation of hyperparameter tuning and possible regularization techniques would strengthen the robustness of the design.
• The insignificant "0" should be removed from the table.
• In Figure 8 and 9 there are letter designations a), b), c) that are not explained in the legend.
• In the text, when citing figures, an unnecessary dot is placed.
• It would be worth deepening the analysis of limitations and indicating possible directions for further research - optional.
• Some small mistakes - marked on attached pdf file.

Out of curiosity, how long did the calculations take?

Comments for author File: Comments.pdf

Author Response

Dear Reviewer 3,

Thank you for your valuable and encouraging feedback. We appreciate your recognition of the originality and relevance of our approach, as well as your suggestions for improving the manuscript.

In response, we have revised the introduction to adopt a more scientific tone, clarified the CV-UNET architecture with an improved figure, added statistical analysis across multiple runs, and discussed hyperparameter tuning and regularization. We have also addressed the minor issues you noted, including figure formatting, legend clarification, and training time reporting. A detailed point-by-point response is included in the attached document.

Thank you again for helping us strengthen our work.

Sincerely,

Authors

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

This manuscript presents a comprehensive study on the application of Complex-Valued Neural Networks (CVNNs) for medical microwave image reconstruction. The authors propose a two-stage methodology: first using the Born Iterative Method (BIM) with quadratic programming for initial estimation, followed by applying different CVNN architectures (CV-MLP, CV-CNN, and CV-UNET) for refinement. The paper methodically compares these complex-valued networks against their real-valued counterparts to demonstrate the advantages of processing complex data directly in the complex domain. Experimental results using breast phantom models show that CV-UNET outperforms other architectures in terms of reconstruction accuracy and computational efficiency.

The paper presents valuable contributions to the field of complex-valued neural networks for medical imaging reconstruction and should be published after addressing the following specific major comments.

Major Comments

1. The authors should acknowledge the limitations of using only breast phantom models from UWCEM and discuss how this might affect the generalizability of their approach to other anatomical structures or imaging scenarios.
2. While Figures 6-9 provide good visual comparisons, a more detailed quantitative analysis of specific regions of interest (e.g., tumor detection accuracy) would strengthen the paper's clinical relevance.
3. Include ablation studies to better understand the contribution of each component of the proposed methodology (e.g., the impact of different activation functions, initialization strategies, or network depths).
4. Add detailed comparisons of computational requirements (training time, memory usage, inference speed) between CVNN and RVNN architectures, as efficiency is mentioned as an advantage but not thoroughly quantified.
5. Expand the discussion section to better articulate how the improved reconstruction quality might translate to clinical benefits such as improved diagnosis or reduced false positives/negatives.

Minor Comments

1. Figure 1 could be improved with more detailed labeling to help readers understand the electromagnetic configuration scheme more clearly.
2. Some mathematical notations are introduced without sufficient explanation, particularly in equations (10)-(14).
3. The description of the CReLU activation function should include a brief explanation of why it satisfies the Cauchy-Riemann equations only in certain intervals.
4. The authors mention using the Adam optimizer with a learning rate of 0.001, but a discussion on how this parameter was selected or if other values were tested would be beneficial.
5. The paper could benefit from a clearer discussion of limitations and potential future work in the conclusion section.

Questions for Authors

1. Have the authors explored other complex-valued activation functions beyond CReLU, and if so, what was their impact on performance?
2. How sensitive are the results to the initial estimation quality from the BIM approach? Would a poorer initial estimate significantly degrade the final reconstruction?
3. Have the authors considered the application of their method to other medical imaging modalities that involve complex data, such as MRI?
4. What is the rationale behind using 40 epochs for training? Was this determined empirically, or were early stopping criteria implemented?
5. How does the proposed method perform with noisy measurements, which are common in real-world clinical settings?

Suggestions for Authors

1. Consider expanding the dataset to include more diverse anatomical structures or imaging scenarios to demonstrate the generalizability of your approach.
2. Provide more discussion on the clinical implications of improved reconstruction quality.
3. Include more detailed analysis of computational efficiency and training requirements.
4. Address the minor grammatical and clarity issues throughout the text.
5. Consider exploring other complex-valued activation functions and network architectures in future work.

Author Response

Dear Reviewer 4,

Thank you for your thorough and constructive review. We greatly appreciate your positive evaluation of our contributions and your detailed suggestions for improvement.

In response, we have expanded the discussion of limitations and future work, including the need for validation on other anatomical structures beyond breast phantoms. We also added quantitative analysis for regions of interest, ablation studies, and detailed comparisons of computational efficiency between CVNN and RVNN architectures. Minor issues such as figure clarity and mathematical notation have also been addressed. Additionally, we have clarified training choices and model robustness under noisy conditions.

A full point-by-point response to all major and minor comments is included in the attached document. Your feedback has been invaluable in improving the manuscript.

Sincerely,

Authors

Author Response File: Author Response.pdf