A Nonlinear Volterra Filtering Hybrid Image-Denoising Method Based on the Improved Bat Algorithm for Optimizing Kernel Parameters

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript couples a nonlinear Volterra filtering framework with an improved Bat-algorithm (VWDBA) to denoise images corrupted by mixed Gaussian and salt-and-pepper noise. The engineering motivation is clear and the route—optimizing Volterra kernel parameters via a population-based search—is reasonable. Reported experiments show competitive PSNR/SSIM and visually better edge retention at higher noise levels, with apparent convergence under moderate population sizes and iterations.

1. The paper’s main contribution appears to be the velocity-weighted disturbance within a Bat-algorithm for Volterra kernel identification. Please clarify the specific novelty versus standard BA and other meta-heuristics, and explicitly state the methodological gap your approach fills in mixed-noise denoising.
2. In Related Work/Methodological Context and Discussion, add a recent Communications Earth & Environment study that uses region--scale intelligent optimization with an end-to-end correction framework to improve data consistency under complex/extreme conditions, emphasizing real-time correction and uncertainty handling. This perspective aligns closely with the manuscript’s goals of robust parameter search and detail preservation under mixed noise and spatially non-uniform degradations.
3. Complement PSNR/SSIM with edge-aware and perceptual metrics (e.g., GMSD, LPIPS). Provide statistical significance tests (e.g., paired t-test) and effect sizes. For visuals, use zoomed crops and error maps to substantiate “detail preservation.”
4. Unify symbols and equation formatting; add a variable table and a small heatmap example of third-order kernels for intuition. Improve figure captions with input/output dimensions and key hyperparameters.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

For the publication, authors need to carefully solve the following comments:

1. The manuscript introduces the VWDBA-Volterra method, but the novelty over previous Bat algorithm–based optimization is not emphasized strongly enough. The introduction should clearly distinguish this work from earlier Volterra–Bat approaches, specifying what the velocity weight perturbation adds in terms of convergence speed, global search ability, or denoising quality.
2. The experiments focus mainly on the Lena image and a few classical noise conditions. To enhance reliability, the authors should compare runtime and computational complexity with baseline methods (e.g., KSVD, WNNM, LRTV) to justify practical applicability, if possible.
3. The paper presents ΔPSNR and ΔSSIM values, but need to discuss trade-offs between PSNR and structural preservation (SSIM), especially where baseline methods outperform in certain aspects.
4. Several figures (e.g., Figures 3–7, 9–11) are too small or unclear, making it difficult to visually evaluate denoising quality. Please enlarge key visual comparisons. In addition, ensuring all figure labels and legends are clear and consistent (for example, Figure 2 mislabels "(a)" twice).
5. From an optimization perspective, the study (“A hybrid SMOTE and Trans-CWGAN for data imbalance in real operational AHU AFDD: A case study of an auditorium building”) used grid search for hyperparameter tuning Please cite and discuss how your optimization approach differs from grid search (e.g., search-space coverage, computational cost, convergence behavior, and susceptibility to local optima) and justify why your method is more appropriate for this problem.
6. While the methodology is mathematically detailed, practical reproducibility is limited. The authors should provide pseudocode or a concise algorithm summary for VWDBA-Volterra.
7. Discuss potential applications (e.g., medical imaging, remote sensing, surveillance), showing why this method is more suitable than alternatives in real-world settings.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This paper presents a nonlinear Volterra filter for image denoising, with the filter’s kernel parameters optimized using an improved Bat Algorithm (VWDBA). The improvement comes from introducing a velocity weight perturbation mechanism to help avoid local optima and speed up convergence. The method is tested on grayscale images corrupted with Gaussian noise, salt-and-pepper noise, and their mixture. The authors compare their approach with several established denoising algorithms and report higher PSNR and MSSSIM scores, along with better visual preservation of edges and details.

• The choice of comparison methods is somewhat dated. The paper compares against KSVD, WNNM, LRTV, WESNR, and LSM-NLR, but leaves out more recent deep learning approaches that currently set the benchmark in image denoising. Including at least one modern learning-based baseline would provide a fairer context for evaluating the contribution.
• The experiments rely only on PSNR and MSSSIM. While these are standard, they do not always reflect perceived image quality. Additional evaluation with metrics that capture perceptual quality, or tests on a more diverse set of images beyond Lena, would make the results more convincing. It would also be useful to report variance over multiple runs since the optimization algorithm is stochastic.
• Volterra filters can be computationally heavy, especially at third order with memory lengths of 6/4/3. The paper claims “less computation” compared with other methods, but no runtime or complexity analysis is provided. Without this, the claim of real-time potential is not well supported.
• The algorithm does not involve “training” in the machine learning sense — it’s an optimization of filter parameters using VWDBA. But the testing is limited: only one test image (“Lena”) is used consistently throughout the experiments.
• The discussion of results is also mostly descriptive, and the paper would be stronger if the authors provided more insight into why their algorithm performs better, as well as comments on computational cost and possible limitations.

Comments on the Quality of English Language

The manuscript would benefit from careful language editing.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Firstly, I want to thank the authors for their detailed response to the first review and think the manuscript is substantially improved. I think this paper can be accepted with minor revision and one important caveat that needs addressing.

The minor revision concerns the evidence for perceptual/ statistical robustness. Please (i) report LPIPS alongside PSNR/SSIM/GMSD as mean ± SD over a benchmark image set (state N), and (ii) add a brief Methods note describing this procedure plus one visual panel (error maps + zoomed crops) to substantiate the “better detail preservation” claim.

Author Response

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Reviewer 2 Report

Comments and Suggestions for Authors

There is no further comment. I recommend that this paper is published.

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

I thank the authors for their revisions and the effort to improve the manuscript. However, all experiments are still conducted using only the 8-bit grayscale Lena image, which is no longer recommended for research due to copyright and ethical concerns. Using a single test image also limits the validity of the findings and does not demonstrate generalization. Please replace or supplement Lena with standard benchmark images or datasets (e.g., BSD68, Set12, Kodak24) and report averaged results across multiple samples to provide stronger and more broadly applicable conclusions.

Author Response

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Author Response File: Author Response.pdf

Round 3

Reviewer 3 Report

Comments and Suggestions for Authors

The revisions have clearly addressed my previous concerns. The manuscript is now much stronger and more convincing in demonstrating the effectiveness and robustness of the proposed VWDBA-Volterra method.