Reviewer 1:

I. Abstract:

1. The updated abstract reflects this paper’s image reconstruction method steps. Firstly, an automatic color equalization algorithm(ACE) is used to improve the contrast of the low-light image containing noise. Secondly, the maximum betweencluster variance method(OTSU) was used for threshold segmentation. Then, according to the segmentation threshold, the image was enhanced by gradient using the enhancement function. Finally, the P-M model was used to denoise and enhance the gradient image.

2. The method proposed in this paper is mainly elaborated at the beginning of the third sentence of the abstract.

3. The title is updated to:Low illumination fog noise image denoising method based on ACE-GPM.

4. The comparison results between the proposed method and other methods are reflected in the abstract. Compared with other denoising methods, the ACE-GPM method proposed in this paper improves image contrast and removes noise while effectively retaining image details and texture information. The information entropy value is increased by 0.42 on average. In addition, the proposed method requires fewer computational resources while maintaining image quality.

II. Introduction:

In the introduction of the revised version, this paper first expounds on the common types of noise in digital images and the reasons for their generation. Subsequently, we explain the denoising methods proposed in the literature and their advantages and disadvantages. Finally, we show the proposed method’s working block diagram and method steps so readers can better understand our method.

III. Method:

1. In the ninth paragraph of the introduction, this paper elaborates on the anisotropic P-M diffusion equation model and its advantages and disadvantages in image denoising and enhancement. This model has a wide range of application values in image processing, but due to its limitations, some areas also need improvement.

2. In the research method section of this paper, part D elaborates in-depth, and how to apply the OTSU method for gradient enhancement is introduced in detail. At the same time, we also clarify how the method ADAPTS to the P-M model and its embodiment of the performance improvement of the P-M model.

3. At the end of the introduction, this paper shows a simple working block diagram of the proposed method and elaborates each step in detail.

IV. Experiment:

1. In the revised manuscript’s experimental part, this paper adds two sets of visual contrast and FOM merit evaluation to verify the effectiveness and reliability of the proposed method comprehensively. These additional experimental groups are intended to provide more exhaustive empirical support for our approach.

2. The revised manuscript details the hardware and software specifications in Section A of the experiment. The introduction section clearly describes the working steps of the proposed method. Each part of the research method constitutes the processing flow of the method in turn.

3. This paper studies the noise reduction problem of low-light fog images. We propose an effective denoising method for fog noise in low-light fog images.

4. This paper selects low-light fog noise images taken under natural conditions, and the comparison results between visual benchmark images and images processed by the method are provided in Section D of the experiment.

5. In Table 2 of the original paper, we detail the objective index evaluation of the images processed by various methods, including indicators such as average brightness, standard deviation, information entropy, peak signal-to-noise ratio (PSNR), and similarity index (SSIM). Because these evaluation metrics are not explained in detail in the original paper, it may have brought you questions. Therefore, in Section B of the experimental section of the revised manuscript, we present the FOM merit evaluation index and its calculation formula in this paper. In Tables 3, 4, and 5 in Section D, we detail the FOM merit evaluation index data of the processed images by each denoising algorithm.

6. According to the data in Table 2 of the original paper, the running time of vari- ous methods for processing waterfall images may need to be more intuitive to show their effects. Therefore, after expert advice, this paper shows the line chart of running time for images with different resolutions in FIG. 7, part E of the experiment of the revised manuscript. This gives the reader a clearer picture of how different processing methods differ in running time and helps the reader evaluate the performance of each method more accurately.

7. The revised version of experiment section E shows the evaluation data of each part of the proposed method and the total time complexity.

8. In the previous version, the introduction of OTSU’s algorithm may have some things that could be improved. Based on the expert feedback, this paper gives a more comprehensive description of the OTSU threshold method. It explains in detail how it is applied to the P-M model in Section B of the revised version of research methods.

9. With revisions and updates, the references and conclusions in this paper have been refined. In the references, we included some crucial articles published recently to ensure the timeliness and relevance of this paper. At the same time, in the conclusion section, we point out some limitations of the proposed method. We still need to adaptively select the P-M model’s critical parameters for different pixel and definition images.

Reviewer 2:

A: In the revised version of Experiment Section D, we show the contrast effect clearly in the form of a table. See Table 2 for details.

B: In the experiment D section of the revised draft, we conduct multiple comparison experiments of eight existing denoising algorithms. We use the visual effect and FOM figure of merit as evaluation indicators to compare and evaluate the performance of various methods.

C: The format of the references has been corrected, and references have been made to recent journal articles to ensure the timeliness and relevance of this article.

D: For readers’ convenience, this paper’s work block diagram is provided in the revised draft, and the specific operation steps of each part are described in detail. Such an arrangement provides a more transparent and intuitive understanding, which helps readers better grasp the main content and ideas of this paper.

E: The proposed method is currently suitable for low-light fog images, so images with different sharpness (low contrast, high contrast, brightness) have yet to be applied to the algorithm for performance evaluation.

Reviewer 3:

1. Abstract: We have revised and updated the paper’s abstract according to the expert advice. Firstly, this paper leads to the proposed method for the problems of the existing P-M model. Secondly, the implementation of the method proposed in this paper is briefly described. Finally, the experimental results comparing the proposed method with other denoising methods in the literature are described to prove the effectiveness of the proposed method.

2. Introduction: In the revised manuscript’s introduction section, we describe this paper’s workflow in detail and clearly explain the tasks of each stage. In this way, we can more accurately communicate our work’s content, goals, and importance so that readers can better understand our work.

3. References Cited: After revision, all references cited in this paper have been updated to ensure timeliness and relevance.

4. Format and formula: After carefully reviewing and revising the first draft and referring to the reference articles provided by experts, we have revised the format and formula to ensure that the final revised draft meets the rigorous, stable, rational, and official requirements in form and content.

5. Flowchart of the paper framework: At the end of the introduction section of the revised manuscript, we attach a flowchart of the work of this paper, which details the tasks and objectives of each stage.

6. Image clarity: In the revised version, to more fully demonstrate the effectiveness of the proposed method, we conduct more comparative experiments and improve the image’s contrast.

7. Ablation Experiment: In the revised version, the ablation experiment is added to Part F of an experiment to evaluate the influence of each part of the method and the combination of each part on the P-M model to reflect the effectiveness of the improved strategy in this paper.

Attachments

Attachment

Submitted filename: Response to Reviewers.pdf

Thank you for taking time out of your busy schedule to read my manuscript and for your reply letter. For the questions and opinions of the experts, I will reply one by one.

Given the problem that Expert 1 and Expert 3 pointed out that they did not receive relevant responses in the last round of review, we at this moment make the following remarks: In the previous submission, the PDF called "Response to Reviewers" had pages 1 and 2 in response to Expert 1's review, and page 4 in response to expert 3's review. Since the experts could not see the corresponding reply, I will attach the related reply content from the last time for your reference in this reply. First, the response to the previous round of expert 1's opinion is as follows:

First, the response to the previous round of expert 1's opinion is as follows:

一、Abstract：

1. The updated abstract reflects this paper's image reconstruction method steps. Firstly, an

automatic color equalization algorithm(ACE) is used to improve the contrast of the low-light

image containing noise. Secondly, the maximum between-cluster variance method(OTSU) was

used for threshold segmentation. Then, according to the segmentation threshold, the image was

enhanced by gradient using the enhancement function. Finally, the P-M model was used to denoise

and enhance the gradient image.

2. The method proposed in this paper is mainly elaborated at the beginning of the third sentence

of the abstract.

3. The title is updated to ： Low illumination fog noise image denoising method based on

ACE-GPM

4. The comparison results between the proposed method and other methods are reflected in the

abstract. Compared with other denoising methods, the ACE-GPM method proposed in this paper

improves image contrast and removes noise while effectively retaining image details and texture

information. The information entropy value is increased by 0.42 on average. In addition, the

proposed method requires fewer computational resources while maintaining image quality.

二、Introduction：

In the introduction of the revised version, this paper first expounds on the common types of noise

in digital images and the reasons for their generation. Subsequently, we explain the denoising

methods proposed in the literature and their advantages and disadvantages. Finally, we show the

proposed method's working block diagram and method steps so readers can better understand our

method.

三、Method：

1. In the ninth paragraph of the introduction, this paper elaborates on the anisotropic P-M

diffusion equation model and its advantages and disadvantages in image denoising and

enhancement. This model has a wide range of application values in image processing, but due to

its limitations, some areas also need improvement.

2. In the research method section of this paper, part D elaborates in-depth, and how to apply the

OTSU method for gradient enhancement is introduced in detail. At the same time, we also clarify

how the method ADAPTS to the P-M model and its embodiment of the performance improvement

of the P-M model.

3. At the end of the introduction, this paper shows a simple working block diagram of the

proposed method and elaborates each step in detail.

四、Experiment：

1. In the revised manuscript's experimental part, this paper adds two sets of visual contrast and

FOM merit evaluation to verify the effectiveness and reliability of the proposed method

comprehensively. These additional experimental groups are intended to provide more exhaustive

empirical support for our approach.

2. The revised manuscript details the hardware and software specifications in Section A of the

experiment. The introduction section clearly describes the working steps of the proposed method.Each part of the research method constitutes the processing flow of the method in turn.

3. This paper studies the noise reduction problem of low-light fog images. We propose an

effective denoising method for fog noise in low-light fog images.

4. This paper selects low-light fog noise images taken under natural conditions, and the

comparison results between visual benchmark images and images processed by the method are

provided in Section D of the experiment.

5. In Table 2 of the original paper, we detail the objective index evaluation of the images

processed by various methods, including indicators such as average brightness, standard deviation,

information entropy, peak signal-to-noise ratio (PSNR), and similarity index (SSIM). Because

these evaluation metrics are not explained in detail in the original paper, it may have brought you

questions. Therefore, in Section B of the experimental section of the revised manuscript, we

present the FOM merit evaluation index and its calculation formula in this paper. In Tables 3, 4,

and 5 in Section D, we detail the FOM merit evaluation index data of the processed images by

each denoising algorithm.

6. According to the data in Table 2 of the original paper, the running time of various methods for

processing waterfall images may need to be more intuitive to show their effects. Therefore, after

expert advice, this paper shows the line chart of running time for images with different resolutions

in FIG. 7, part E of the experiment of the revised manuscript. This gives the reader a clearer

picture of how different processing methods differ in running time and helps the reader evaluate

the performance of each method more accurately.

7. The revised version of experiment section E shows the evaluation data of each part of the

proposed method and the total time complexity.

8. In the previous version, the introduction of OTSU's algorithm may have some things that could

be improved. Based on the expert feedback, this paper gives a more comprehensive description of

the OTSU threshold method. It explains in detail how it is applied to the P-M model in Section B

of the revised version of research methods.

9. With revisions and updates, the references and conclusions in this paper have been refined. In

the references, we included some crucial articles published recently to ensure the timeliness and

relevance of this paper. At the same time, in the conclusion section, we point out some limitations

of the proposed method. We still need to adaptively select the P-M model's critical parameters for

different pixel and definition images.

Secondly, the response to Expert 3's last round of comments is as follows:

1. Abstract：We have revised and updated the paper's abstract according to the expert advice. Firstly, this paper leads to the proposed method for the problems of the existing P-M model. Secondly, the implementation of the method proposed in this paper is briefly described. Finally, the experimental results comparing the proposed method with other denoising methods in the literature are described to prove the effectiveness of the proposed method.

2. Introduction：In the revised manuscript's introduction section, we describe this paper's workflow in detail and clearly explain the tasks of each stage. In this way, we can more accurately communicate our work's content, goals, and importance so that readers can better understand our work.

3. References Cited: After revision, all references cited in this paper have been updated to ensure timeliness and relevance.

4. Format and formula: After carefully reviewing and revising the first draft and referring to the reference articles provided by experts, we have revised the format and formula to ensure that the final revised draft meets the rigorous, stable, rational, and official requirements in form and content.

5. Flowchart of the paper framework: At the end of the introduction section of the revised manuscript, we attach a flowchart of the work of this paper, which details the tasks and objectives of each stage.

6. Image clarity: In the revised version, to more fully demonstrate the effectiveness of the proposed method, we conduct more comparative experiments and improve the image's contrast.

7. Ablation Experiment: In the revised version, the ablation experiment is added to Part F of an experiment to evaluate the influence of each part of the method and the combination of each part on the P-M model to reflect the effectiveness of the improved strategy in this paper.

Finally, a reply to the opinions of the experts in this round:

Review 1：

一、Comments on the Introduction:

1. According to your professional suggestions, we have carefully revised the middle part of the third page of the revised manuscript to focus on the core contributions of this paper. In addition, we have redrawn the system block diagram and refer to the paper "Underwater Image Enhancement by Attenuated Color Channel Correction and Detail Preserved Contrast. The overview diagram of the method in Enhancement "draws a block diagram of the working of the proposed method. The work block diagram shows the graphical information of each step in detail to help readers understand the research content of this paper more intuitively.

2. In the introduction section, we discuss five representative noise-denoising algorithms in-depth. The following is the literature corresponding to these denoising algorithms:

1. Paper 1：Natural digital image mixed noise removal using regularization Perona–Malik model and pulse coupled neural networks.Soft Computing. 2023: 1-10.

2. Paper 2：Underwater image enhancement by attenuated color channel correction and detail preserved contrast enhancement. IEEE Journal of Oceanic Engineering 2022, 47(3): 718-735.

3. Paper 3：Natural image noise removal using nonlocal means and hidden Markov models in transform domain. The Visual Computer. 2018, 34: 1661-1675.

4. Paper 4：Underwater image enhancement via piecewise color correction and dual prior optimized contrast enhancement. IEEE Signal Processing Letters. 2023, 30: 229-233.

5. Paper 5：Additive Gaussian noise removal based on generative adversarial network model and semi-soft thresholding approach. Multimedia Tools and Applications.2023, 82(5): 7757-7777.

二、Comments on the experiment:

1. According to your advice from experts, to objectively evaluate the quality of test images, we have added evaluation indicators such as peak mean square Error (RMSE), Square Absolute Error (AME), and mean square error of Structural Similarity (SDME). These metrics help to measure image quality more comprehensively, and their specific mathematical formulas have been detailed in Experiment Section B. With these improvements, we can evaluate the performance of various methods in terms of image quality more accurately.

2. To verify the effectiveness of the proposed enhancement method, this paper compares the latest representative image enhancement methods and briefly describes their algorithm process, advantages, and disadvantages. The following is a list of literature corresponding to enhancement methods:

（1）Low-Light Image Enhancement Method Based on Retinex Theory by Improving Illumination Map. Applied Sciences. 2022, 12(10): 5257.

（2）Low-illumination image enhancement algorithm based on improved multi-scale Retinex and ABC algorithm optimization.Frontiers in Bioengineering and Biotechnology. 2022, 10: 865820.

（3）An adaptive low-illumination image enhancement algorithm based on weighted least squares optimization. Journal of Physics: Conference Series. IOP Publishing. 2022, 2181(1): 012011.

（4）Non-Uniform-Illumination Image Enhancement Algorithm Based on Retinex Theory. Applied Sciences. 2023, 13(17): 9535.

Review 2：

Based on your professional advice, I have reviewed the manuscript again and corrected some spelling and grammar errors. I have fixed abbreviations that need to be defined in appropriate places in the text. Given the system block diagram in the introduction section, I have referred to the paper Underwater Image Enhancement by Attenuated Color Channel Correction and Detail Preserved Contrast Enhancement, "which redraws the block diagram of the work and elaborates the working steps and the main contributions of this paper in the following. In addition, I have updated the comparative experiment method in the revised manuscript to address the problem that the comparative experiment method is not novel enough. I chose methods from recently published papers for comparative experiments, and the specific forms are as follows:

（1）Low-Light Image Enhancement Method Based on Retinex Theory by Improving Illumination Map. Applied Sciences. 2022, 12(10): 5257.

（2）Low-illumination image enhancement algorithm based on improved multi-scale Retinex and ABC algorithm optimization.Frontiers in Bioengineering and Biotechnology. 2022, 10: 865820.

（3）An adaptive low-illumination image enhancement algorithm based on weighted least squares optimization. Journal of Physics: Conference Series. IOP Publishing. 2022, 2181(1): 012011.

（4）Non-Uniform-Illumination Image Enhancement Algorithm Based on Retinex Theory. Applied Sciences. 2023, 13(17): 9535.

Review 3：

1. Aiming at the problem that the methods in related fields introduced in the introduction part need to be more novel, we have improved them in the revised draft by quoting the latest research methods and elaborating them in detail. These methods are as follows:

（1）Natural digital image mixed noise removal using regularization Perona–Malik model and pulse coupled neural networks.Soft Computing. 2023: 1-10.

（2）Underwater image enhancement by attenuated color channel correction and detail preserved contrast enhancement. IEEE Journal of Oceanic Engineering 2022, 47(3): 718-735.

（3）Natural image noise removal using nonlocal means and hidden Markov models in transform domain. The Visual Computer. 2018, 34: 1661-1675.

（4）Underwater image enhancement via piecewise color correction and dual prior optimized contrast enhancement. IEEE Signal Processing Letters. 2023, 30: 229-233.

（5）Additive Gaussian noise removal based on generative adversarial network model and semi-soft thresholding approach. Multimedia Tools and Applications.2023, 82(5): 7757-7777.

2. We take the problem of experts pointing out the working block diagram seriously. We draw on the paper "Underwater Image Enhancement by Attenuated Color Channel Correction and Detail Preserved Contrast " in the revised version. In the method overview diagram in "Enhancement," the working block diagram is redrawn, and the corresponding visual effects and enhanced result diagram are added. Under the working block diagram in the introduction section, we describe the specific operation steps in three detailed parts to provide a clear understanding and reference.

3. As for the parameters in Formula (6), we explain the necessary meaning of the parameters in the revised manuscript to ensure readers' correct understanding of the parameters.

4. In addition, in view of the lack of comparison experiments with the latest method enhancement methods in the investigation, we introduce the four latest techniques in the revised manuscript for comparison experiments. Specific citations are as follows:

（1）Low-Light Image Enhancement Method Based on Retinex Theory by Improving Illumination Map. Applied Sciences. 2022, 12(10): 5257.

（2）Low-illumination image enhancement algorithm based on improved multi-scale Retinex and ABC algorithm optimization.Frontiers in Bioengineering and Biotechnology. 2022, 10: 865820.

（3）An adaptive low-illumination image enhancement algorithm based on weighted least squares optimization. Journal of Physics: Conference Series. IOP Publishing. 2022, 2181(1): 012011.

（4）Non-Uniform-Illumination Image Enhancement Algorithm Based on Retinex Theory. Applied Sciences. 2023, 13(17): 9535.

5. Given the problem of formula subscripts proposed by experts, we conducted a comprehensive investigation and correction in the revised draft to ensure that the subscripts of all formulas have been corrected from italics to positive.

6. At the same time, given the clarity problem of the drawing pointed out by experts, we optimized the relevant pictures in the revised draft to improve the overall clarity and readability.

Thank you for taking time out of your busy schedule to read my manuscript and for your reply letter. For the questions and opinions of the experts, I will reply one by one.

Comments to the editors:

1.This paper re-cited the papers published in 2023-2024, and the updated literatures are as follows:

Reference 8：Plutino A, Tarini M. Fast ACE (FACE): an error-bounded approximation of Automatic Color Equalization[J]. IEEE Transactions on Image Processing, 2023.

Reference 9: Wang D, Liu Z, Gu X, et al. Feature extraction and segmentation of pavement distress using an improved hybrid task cascade network[J]. International Journal of Pavement Engineering, 2023, 24(1): 2266098.

Reference 10: Ning G. Two-dimensional Otsu multi-threshold image segmentation based on hybrid whale optimization algorithm[J]. Multimedia Tools and Applications, 2023, 82(10): 15007-15026

Reference 11：Du Y, Yuan H, Jia K, et al. Research on Threshold Segmentation Method of Two-Dimensional Otsu Image Based on Improved Sparrow Search Algorithm[J]. IEEE Access, 2023

Literature 14: Raonic B, Molinaro R, De Ryck T, et al. Convolutional neural operators for robust and accurate learning of PDEs[J]. Advances in Neural Information Processing Systems, 2024, 36

Reference 15: Zhang Q, Song X, Song S, et al. Finite-Time sliding mode control for singularly perturbed PDE systems[J]. Journal of the Franklin Institute, 2023, 360(2): 841-861

Among them, references 8 and 9 are the latest research on Automatic Color Equalization algorithm (ACE), references 10 and 11 are the latest research on the maximum between-cluster variance method, and references 14 and 15 are the latest research and application on partial differential equations.

2.In view of the problems in the organization of the article, this article has been updated as follows:

(1)The experimental part has been adjusted, the dataset used in this article has been summarized, and the GitHub access address has been provided: https://github.com/WuyiLi1999/Low_illumination_fog_noise_images.git.

(2)The original chapter of experimental environment, benchmark model experiment, model evaluation index and model parameter setting is integrated to form the chapter of "experimental setup".

(3)In the chapter of experimental results and analysis, the introduction of the comparison model, the comparison of advantages and disadvantages are organized. At the same time, the position of the comparison result chart and the evaluation index data table are updated, which makes the article more intuitive.

Regarding the comments of the three reviewers:

1.Whether to respond to the previous round of comments: Reviewer 2 did not receive any response to his comments, so we will keep the previous response below for review by reviewer 2

2.Answer the question "Is the manuscript technically sound, and does the data support the conclusions?" Question: In the experimental analysis stage, this paper analyzes multiple groups of visual effects and FOM merit evaluation indexes, and draws corresponding conclusions according to the data in the table. Time complexity analysis and ablation experiments are carried out to verify the proposed model.

3.Is the statistical analysis performed appropriately and rigorously? Problem: This paper uses 7 evaluation metrics to perform multiple group analysis and carries out time complexity analysis and visual analysis of processing time.

4.In response to the question "Did the authors make all data in their manuscript fully available?" Question: The experimental result data in this paper is based on the content in Section 3.2 Experimental setup. Please refer to the GitHub address for the calculation code of the data set and evaluation index data.

5.In response to the question "Is the manuscript presented in an understandable way and written in standard English? Problem: The author once again checked the spelling and grammar of the words in this article and corrected any problems found.

6.For the question of "reviewing comments to authors" : the comments to reviewer 1 have been submitted before. If reviewer 1 has not received the comments, the reviewer should reply again in this submission response; In response to the comments of reviewer 2, this paper re-cited the recently published literature. Please refer to the updated literature as follows:

Reference 8：Plutino A, Tarini M. Fast ACE (FACE): an error-bounded approximation of Automatic Color Equalization[J]. IEEE Transactions on Image Processing, 2023.

Reference 9: Wang D, Liu Z, Gu X, et al. Feature extraction and segmentation of pavement distress using an improved hybrid task cascade network[J]. International Journal of Pavement Engineering, 2023, 24(1): 2266098.

Reference 10: Ning G. Two-dimensional Otsu multi-threshold image segmentation based on hybrid whale optimization algorithm[J]. Multimedia Tools and Applications, 2023, 82(10): 15007-15026

Reference 11：Du Y, Yuan H, Jia K, et al. Research on Threshold Segmentation Method of Two-Dimensional Otsu Image Based on Improved Sparrow Search Algorithm[J]. IEEE Access, 2023

Literature 14: Raonic B, Molinaro R, De Ryck T, et al. Convolutional neural operators for robust and accurate learning of PDEs[J]. Advances in Neural Information Processing Systems, 2024, 36

Reference 15: Zhang Q, Song X, Song S, et al. Finite-Time sliding mode control for singularly perturbed PDE systems[J]. Journal of the Franklin Institute, 2023, 360(2): 841-861

Given the problem that Expert 1 and Expert 2 pointed out that they did not receive relevant responses in the last round of review, we at this moment make the following remarks: In the previous submission, the PDF called "Response to Reviewers" had pages 3 and 4 in response to Expert 1's review, page5 in response to expert 2's review, and page 6 in response to expert 3's review.Since the experts could not see the corresponding reply, I will attach the related reply content from the last time for your reference in this reply. First, the response to the previous round of expert 1's opinion is as follows:

First, the response to the previous round of expert 1's opinion is as follows:

一、Abstract：

1. The updated abstract reflects this paper's image reconstruction method steps. Firstly, an

automatic color equalization algorithm(ACE) is used to improve the contrast of the low-light

image containing noise. Secondly, the maximum between-cluster variance method(OTSU) was

used for threshold segmentation. Then, according to the segmentation threshold, the image was

enhanced by gradient using the enhancement function. Finally, the P-M model was used to denoise

and enhance the gradient image.

2. The method proposed in this paper is mainly elaborated at the beginning of the third sentence

of the abstract.

3. The title is updated to ： Low illumination fog noise image denoising method based on

ACE-GPM

4. The comparison results between the proposed method and other methods are reflected in the

abstract. Compared with other denoising methods, the ACE-GPM method proposed in this paper

improves image contrast and removes noise while effectively retaining image details and texture

information. The information entropy value is increased by 0.42 on average. In addition, the

proposed method requires fewer computational resources while maintaining image quality.

二、Introduction：

In the introduction of the revised version, this paper first expounds on the common types of noise

in digital images and the reasons for their generation. Subsequently, we explain the denoising

methods proposed in the literature and their advantages and disadvantages. Finally, we show the

proposed method's working block diagram and method steps so readers can better understand our

method.

三、Method：

1. In the ninth paragraph of the introduction, this paper elaborates on the anisotropic P-M

diffusion equation model and its advantages and disadvantages in image denoising and

enhancement. This model has a wide range of application values in image processing, but due to

its limitations, some areas also need improvement.

2. In the research method section of this paper, part D elaborates in-depth, and how to apply the

OTSU method for gradient enhancement is introduced in detail. At the same time, we also clarify

how the method ADAPTS to the P-M model and its embodiment of the performance improvement

of the P-M model.

3. At the end of the introduction, this paper shows a simple working block diagram of the

proposed method and elaborates each step in detail.

四、Experiment：

1. In the revised manuscript's experimental part, this paper adds two sets of visual contrast and

FOM merit evaluation to verify the effectiveness and reliability of the proposed method

comprehensively. These additional experimental groups are intended to provide more exhaustive

empirical support for our approach.

2. The revised manuscript details the hardware and software specifications in Section A of the

experiment. The introduction section clearly describes the working steps of the proposed method.Each part of the research method constitutes the processing flow of the method in turn.

3. This paper studies the noise reduction problem of low-light fog images. We propose an

effective denoising method for fog noise in low-light fog images.

4. This paper selects low-light fog noise images taken under natural conditions, and the

comparison results between visual benchmark images and images processed by the method are

provided in Section D of the experiment.

5. In Table 2 of the original paper, we detail the objective index evaluation of the images

processed by various methods, including indicators such as average brightness, standard deviation,

information entropy, peak signal-to-noise ratio (PSNR), and similarity index (SSIM). Because

these evaluation metrics are not explained in detail in the original paper, it may have brought you

questions. Therefore, in Section B of the experimental section of the revised manuscript, we

present the FOM merit evaluation index and its calculation formula in this paper. In Tables 3, 4,

and 5 in Section D, we detail the FOM merit evaluation index data of the processed images by

each denoising algorithm.

6. According to the data in Table 2 of the original paper, the running time of various methods for

processing waterfall images may need to be more intuitive to show their effects. Therefore, after

expert advice, this paper shows the line chart of running time for images with different resolutions

in FIG. 7, part E of the experiment of the revised manuscript. This gives the reader a clearer

picture of how different processing methods differ in running time and helps the reader evaluate

the performance of each method more accurately.

7. The revised version of experiment section E shows the evaluation data of each part of the

proposed method and the total time complexity.

8. In the previous version, the introduction of OTSU's algorithm may have some things that could

be improved. Based on the expert feedback, this paper gives a more comprehensive description of

the OTSU threshold method. It explains in detail how it is applied to the P-M model in Section B

of the revised version of research methods.

9. With revisions and updates, the references and conclusions in this paper have been refined. In

the references, we included some crucial articles published recently to ensure the timeliness and

relevance of this paper. At the same time, in the conclusion section, we point out some limitations

of the proposed method. We still need to adaptively select the P-M model's critical parameters for

different pixel and definition images.

Secondly, the response to Expert 3's last round of comments is as follows:

1.Abstract：We have revised and updated the paper's abstract according to the expert advice. Firstly, this paper leads to the proposed method for the problems of the existing P-M model. Secondly, the implementation of the method proposed in this paper is briefly described. Finally, the experimental results comparing the proposed method with other denoising methods in the literature are described to prove the effectiveness of the proposed method.

2.Introduction：In the revised manuscript's introduction section, we describe this paper's workflow in detail and clearly explain the tasks of each stage. In this way, we can more accurately communicate our work's content, goals, and importance so that readers can better understand our work.

3.References Cited: After revision, all references cited in this paper have been updated to ensure timeliness and relevance.

4.Format and formula: After carefully reviewing and revising the first draft and referring to the reference articles provided by experts, we have revised the format and formula to ensure that the final revised draft meets the rigorous, stable, rational, and official requirements in form and content.

5.Flowchart of the paper framework: At the end of the introduction section of the revised manuscript, we attach a flowchart of the work of this paper, which details the tasks and objectives of each stage.

6.Image clarity: In the revised version, to more fully demonstrate the effectiveness of the proposed method, we conduct more comparative experiments and improve the image's contrast.

7.Ablation Experiment: In the revised version, the ablation experiment is added to Part F of an experiment to evaluate the influence of each part of the method and the combination of each part on the P-M model to reflect the effectiveness of the improved strategy in this paper.

Finally, a reply to the opinions of the experts in this round:

Review 1：

一、Comments on the Introduction:

1. According to your professional suggestions, we have carefully revised the middle part of the third page of the revised manuscript to focus on the core contributions of this paper. In addition, we have redrawn the system block diagram and refer to the paper "Underwater Image Enhancement by Attenuated Color Channel Correction and Detail Preserved Contrast. The overview diagram of the method in Enhancement "draws a block diagram of the working of the proposed method. The work block diagram shows the graphical information of each step in detail to help readers understand the research content of this paper more intuitively.

2. In the introduction section, we discuss five representative noise-denoising algorithms in-depth. The following is the literature corresponding to these denoising algorithms:

1.Paper 1：Natural digital image mixed noise removal using regularization Perona–Malik model and pulse coupled neural networks.Soft Computing. 2023: 1-10.

2. Paper 2：Underwater image enhancement by attenuated color channel correction and detail preserved contrast enhancement. IEEE Journal of Oceanic Engineering 2022, 47(3): 718-735.

3. Paper 3：Natural image noise removal using nonlocal means and hidden Markov models in transform domain. The Visual Computer. 2018, 34: 1661-1675.

4. Paper 4：Underwater image enhancement via piecewise color correction and dual prior optimized contrast enhancement. IEEE Signal Processing Letters. 2023, 30: 229-233.

5. Paper 5：Additive Gaussian noise removal based on generative adversarial network model and semi-soft thresholding approach. Multimedia Tools and Applications.2023, 82(5): 7757-7777.

二、Comments on the experiment:

1.According to your advice from experts, to objectively evaluate the quality of test images, we have added evaluation indicators such as peak mean square Error (RMSE), Square Absolute Error (AME), and mean square error of Structural Similarity (SDME). These metrics help to measure image quality more comprehensively, and their specific mathematical formulas have been detailed in Experiment Section B. With these improvements, we can evaluate the performance of various methods in terms of image quality more accurately.

2.To verify the effectiveness of the proposed enhancement method, this paper compares the latest representative image enhancement methods and briefly describes their algorithm process, advantages, and disadvantages. The following is a list of literature corresponding to enhancement methods:

Thank you for taking time out of your busy schedule to read my manuscript and for your reply letter. For the questions and opinions of the experts, I will reply one by one.

1.Title : This manuscript has been carefully revised, and the title has been precisely adjusted in response to the problem raised by the reviewers. The revised title is "Low illumination fog noise image denoising method based on ACE-GPM" to more accurately reflect this paper's research content and focus.

2.Abstract： Based on the reviewers' valuable comments, the “abstract ” part has been carefully optimized. In the abstract, we first point out the existing problems, clarify the main research methods adopted, and give a brief overview of the experimental results as the concluding part of the abstract. Such modifications help readers quickly understand this paper's core content and research results.

3.Introduction： After careful consideration of the reviewers' valuable comments on the introduction section, this manuscript has revised the introduction section accordingly. The revised content highlights the innovation of this paper even more and clarifies the overall architecture of the research methodology. We adopted the reviewers' suggestions to make this paper more rigorous, sedate, rational, and in line with the requirements of the official language style.

4.Formula：After careful consideration of the valuable suggestions of the reviewers on the formula, this revised version of the manuscript comprehensively reviewed and revised the formula involved and elaborated and explained the various parameters in the formula to ensure the logic and rigor of the paper.

5.Framework flow chart: After the reviewer pointed out the lack of a paper framework flow chart in the original manuscript, the revised version of this manuscript actively adopted the reviewer's suggestions. It referred to the literature resources recommended by the reviewer. After careful modification and improvement, we draw a detailed framework flow chart of the research method in this paper and give a comprehensive and in-depth explanation of the various components within the framework. Through these improvements, we expect to significantly improve the readability and intelligibility of the paper and provide readers with a more transparent and intuitive display of research ideas and methodologies. Refer to the last section of the introduction in the paper for a detailed framework flowchart and illustration.

6.Low resolution: After careful consideration and review, the revised version of this manuscript has been thoroughly checked and addressed, given the low resolution of the images raised by the reviewers. We have made the necessary optimizations and upgrades to the pictures to ensure their clarity and resolution reach a higher standard, thus more accurately conveying the research content and results. These improvements will contribute to the overall quality and readability of the manuscript.

7.Ablation experiments: After careful consideration of the valuable comments of the reviewers, we have supplemented the revised manuscript with ablation experiments. Specifically, we conduct relevant Settings in Section 3.5 of the paper and verify the effectiveness of the proposed improved scheme through an exhaustive analysis. This addition is intended to fully demonstrate the depth and breadth of the research while also providing readers with clearer and more robust evidence support.

8.Spelling and grammatical: In response to the reviewers' comments on spelling and grammatical errors in this manuscript, we will review the paragraphs one by one and accurately revise the sentences with grammatical errors to ensure the accuracy and fluency of the text.

9.Conclusions: After carefully considering the reviewers' comments on this paper's conclusions, we have decided to revise and improve the findings in the manuscript. The revised conclusion not only elaborates on the workflow and performance of the proposed method but also deeply analyzes the limitations of the proposed method and important directions for future research. Such revisions aim to improve the scientific and rigorous nature of the study and provide more accurate and comprehensive references for researchers in related fields.

10.charts and graphs: After careful study of the reviewers' feedback on the charts and graphs of the manuscript, we have decided to focus on the presentation of charts and tables in this revision and to improve their readability and accuracy through appropriate magnification and optimization measures.

11.Reference: Given the problem of inconsistent reference format raised by the reviewers, we have carried out a comprehensive revision of the reference section in the original manuscript. This revision aims to ensure that all cited documents follow a uniform formatting standard, thus improving the academic normativity and readability of the paper. We thank the reviewers for their valuable comments. We will continue to work hard to improve the quality of the paper.

12.Introduction: Based on the suggestions the reviewers put forward, this revised manuscript's introduction first summarizes the common noise types and their corresponding denoising algorithms. It makes it clear that the main research object of this paper is the low-light fog noise image. Through carefully designed experiments, we verify that the proposed method can effectively preserve the detailed texture information of the image while removing the fog noise in the picture, ensuring that the image quality is comprehensively improved.

13.Time complexity: Given the problem raised by the reviewers that the time complexity of the method needed to be evaluated in the manuscript, this revised manuscript has added a detailed analysis of the time complexity in Section 3.4.

14.OTSU's threshold: In response to the reviewer's feedback on the need for in-depth elaboration of OTSU's threshold, this revised manuscript elaborates on the specific steps of OTSU's algorithm in Section 2.2. It explores in depth the performance improvement that can be achieved by the algorithm in this study. We are committed to providing precise and detailed instructions to ensure readers fully understand the specific application and impact of OTSU's threshold in this study.

15.FOM merit evaluation index: In response to the reviewer's request for a more comprehensive evaluation of the method's performance in this paper, the revised manuscript has added multiple reliable performance evaluation indicators based on the original experimental setup. It includes peak mean square error (RMSE), Mean absolute error (AME), and mean square error of structural similarity (SDME). These new evaluation indexes will form a more complete evaluation system to reflect the method's performance in practical applications accurately.

Attachments

Attachment

Submitted filename: Response to Reviewers.pdf