An Efficient Spectrum Reconstruction Algorithm for Non-Uniformly Sampled Signals and Its Application in Terahertz SAR

Round 1

Reviewer 1 Report (Previous Reviewer 3)

The authors provide much clearer explanations about their work's motivations and innovations. These motivations and innovations make their work valuable for the THz SAR imaging area. I have no more concerns or issues about the current manuscript.

Reviewer 2 Report (Previous Reviewer 1)

The authors have addressed all my comments carefully, i think it is suitable for publication.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Manuscript entitled “An Efficient Spectrum Reconstruction Algorithm for Nonuniformly Sampled Signals and Its Application in Terahertz SAR" shows that The authors reconstructed the spectrum of non-uniformly sampled signal based on regularization algorithm. This algorithm can reconstruct non-uniformly sampled signal more accurately, and has better imaging quality than BPA algorithm. Finally, the above conclusions are proved by simulation and experimental results. In general, the analysis of this paper is promising. It may be suitable for publication in Remote Sensing after some detailed revisions. The comments are as follows:

 1.      Equations in general seems to come from nowhere. Are there other works that use these formulae? If yes, please cite them. If no, please explain better the formulae.

2.      In the introduction, the author mentions that the BPA algorithm will consume a lot of computing resources. In order to make the article more clear, it is suggested to add a comparison between the proposed method and the BPA method.

3.      The flowchart in Figure 7 wastes some space in the article. It is recommended to redraw the diagram to make full use of the editable space in the article.

4.      When verifying the method, it is not enough to use only two examples (the letter A and the crosswalk), which have a large chance and cannot effectively reflect the advantages of the method proposed in the paper. Therefore, it is suggested to add some experiments in this part.

5.      In section 5, when comparing the proposed method with other algorithms, other traditional azimuth adopting methods should be added for comparison.

6.      Details: To the naked eye alone, there is no obvious difference between Figures 13b and 13c.

7.      With the same example as above, there is no significant difference in the images generated by the three methods(Figure 15). What is the significance of placing such pictures in the text?

Minor editing of English language required.

Author Response

Dear Reviewer

We greatly appreciate your valuable comments and recognition of the value of our article. The purpose of this letter is to address some areas where we have encountered some confusion regarding your comments. We would like to clarify these points in order to make better revisions to our manuscript. Specifically, we would like to discuss the following:

Comment: In section 5, when comparing the proposed method with other algorithms, other traditional azimuth adopting methods should be added for comparison.

Response: Regarding your comment, we would like to inquire if you meant to suggest adding a comparison with traditional SAR imaging algorithms such as the RDA algorithm. If that is the case, we will incorporate this aspect in our subsequent revisions. If not, please kindly let us know what specific content you would like us to include. We will diligently address your feedback and make the necessary modifications.

Comment: To the naked eye alone, there is no obvious difference between Figures 13b and 13c.With the same example as above, there is no significant difference in the images generated by the three methods(Figure 15). What is the significance of placing such pictures in the text?

Response: We are sorry for the lack of clarity in our manuscript that led to your confusion. In Figures 13b and 13c, indeed all three algorithms demonstrate good imaging results. The purpose of conducting this set of experiments was to illustrate that under low levels of non-uniform sampling, all three algorithms can achieve satisfactory imaging results. However, in the second set of experiments involving pedestrian crosswalks (Figure 15), there are certain differences in the imaging results among the three algorithms. Specifically, AR-RDA does not yield satisfactory results, as evidenced by noticeable blurring in certain locations. Additionally, due to the non-uniformity of sampling positions, the imaging results of BPA exhibit certain geometry distortions.

Modification plan: We should note that it is indeed difficult to discern the subtle differences in the imaging results among the three algorithms in Figure 15. To address this, we plan to highlight the areas where the differences between the three algorithms are more pronounced using red boxes in Figure 15. This will make it easier to visualize the disparities. Additionally, following your suggestion, we will include an additional set of experiments in Section 5 to further demonstrate the effectiveness of our proposed algorithm.

The above are the issues we wanted to discuss with you. We sincerely appreciate your valuable comments on our manuscript, despite your busy schedule. Your feedback has been immensely helpful in improving our manuscript. We extend our heartfelt wishes to you.

 

Yours Sincerely,

Guohua Zhang

Reviewer 2 Report

Overall, the paper is well-written. However, there are few instances where reference should be added as well as a few minor modifications will be good to incorporate.

Line 52, restructure the sentence.

Before Line 68, briefly introduce Tikhonov regularization.

After Line 130, add a sentence on significance of δM.

Why the constants in selected simulation signals are different? s1(t) = sin(2000πt) and s2(t) = cos[20000π(t − 0.05) 2 ]

Line 141-142, add reference.

Line 149, why FFT is used here? add one sentence before.

Line 150, add reference. Additionally, what is Nyquist sampling rate? What is the relevance of it?

Mention why obtained results are compared with cubic spline interpolation, but not other interpolation?

Line 275, add reference.

Line 400 and 408, are the value of N_m and 'a' randomly selected? Why particular those two values?

Reviewer 3 Report

This article presents an efficient spectrum reconstruction algorithm for nonuniformly sampled signals targeted at Terahertz SAR imaging. However, the specific gaps this work aims to address in spectrum reconstruction for nonuniformly sampled signals, as stated in the introduction, are unclear. The authors mention in lines 64 to 66 that the method in reference [16] lacks general applicability, especially for imaging scenarios involving close-range distances. However, it is not evident how the proposed method addresses these issues, making it difficult to understand the novelty of their approach.

Furthermore, the comparison of methods in the experiments is confusing. It would be more appropriate to compare the proposed spectrum reconstruction method with state-of-the-art spectrum reconstruction methods, rather than SAR imaging methods. Additionally, the visual comparisons in Fig. 13 and Fig. 15 do not clearly show the differences between the results before spectrum reconstruction and after reconstruction.

In terms of technical comments, the structure of the description of the proposed method seems unbalanced. Section 2 contains an excessive amount of content explaining basic knowledge, while section 3 lacks sufficient content regarding the derivation of the proposed method, especially for formulas 16 to 20, which are presented without proper derivations. A more comprehensive and balanced explanation of the proposed method and its derivations would improve the clarity and understanding of the manuscript.

Author Response

Dear Reviewer

Thank you for taking the time out of your busy schedule to review our manuscript with the ID remotesensing-2551818. Your comments have highlighted several areas that require modification, and your feedback has been invaluable in improving our paper. We are sorry for any confusion caused by our lack of clarity in certain sections of the manuscript. With this letter, we aim to address any lingering doubts and provide a comprehensive response to each of your comments, along with outlining our plans for future revisions.

Comment: The authors mention in lines 64 to 66 that the method in reference [16] lacks general applicability, especially for imaging scenarios involving close-range distances. However, it is not evident how the proposed method addresses these issues, making it difficult to understand the novelty of their approach.

Response: As you rightly pointed out, we did not mention in the manuscript how the proposed algorithm addresses close-range imaging issues, and we apologize for overlooking this aspect. The method mentioned in reference [16] addresses the azimuth non-uniform sampling problem in SAR through phase compensation. It has been successfully applied in the field of airborne SAR motion compensation and offers high computational efficiency. Our proposed method, on the other hand, is based on the principle of reconstructing the azimuth uniformly sampled spectrum to address the azimuth non-uniform sampling problem in THz SAR. Regardless of the distance, as long as the azimuth signal is band-limited, our method can reconstruct the azimutl uniformly sampled spectrum and, therefore, can address close-range imaging issues. Furthermore, our experiments and simulations were specifically conducted under close-range conditions, and the results demonstrate the effectiveness of the proposed algorithm in addressing close-range imaging challenges.

Revision strategy: In order to address this point, we will incorporate a more detailed explanation in the manuscript to provide a comprehensive understanding of this aspect. We would like to express our deep gratitude for your comment, as it has played a significant role in guiding our revisions.

Comment: However, the specific gaps this work aims to address in spectrum reconstruction for nonuniformly sampled signals, as stated in the introduction, are unclear.

Response: We understand your comment as suggesting that our proposed spectrum reconstruction algorithm did not effectively demonstrate the achieved results. In this aspect, there is indeed some room for improvement in our work. Although we showcased the effectiveness of our proposed algorithm by illustrating the error between the reconstructed signal using the algorithm and the original signal (Figure 4(f)), further clarification may be necessary. To address this, we propose the following modification plan: in the manuscript, we will present the error magnitude between the reconstructed signal spectrum using the proposed algorithm and the original signal spectrum, thus highlighting the specific gaps in spectrum reconstruction for nonuniformly sampled signals.

Comment: the comparison of methods in the experiments is confusing. It would be more appropriate to compare the proposed spectrum reconstruction method with state-of-the-art spectrum reconstruction methods, rather than SAR imaging methods.

Response: We deeply understand the intention behind your suggestion to validate the effectiveness of the proposed spectrum reconstruction algorithm. However, adopting this modification approach may deviate from the original problem that this article aims to solve. Allow us to provide the following explanation: the objective of our article is to address the azimuthal non-uniform sampling problem in THz SAR, rather than proposing a superior spectrum reconstruction method. Therefore, without comparing it to SAR imaging methods, we cannot effectively achieve this objective. While our proposed spectrum reconstruction method may not be the most accurate compared to state-of-the-art methods, experimental and simulation results demonstrate that it outperforms previous SAR azimuthal non-uniform sampling image reconstruction methods for THz SAR. Currently, there is no literature indicating that other spectrum reconstruction algorithms are more suitable for addressing the azimuth non-uniform sampling problem in THz SAR.

Comment: the visual comparisons in Fig. 13 and Fig. 15 do not clearly show the differences between the results before spectrum reconstruction and after reconstruction.

Response: We understand your comment as pointing out that Figures 13 and 15 do not show the results of the traditional SAR imaging algorithm before processing. The purpose of Figures 13 and 15 is to demonstrate that our proposed algorithm achieves better reconstruction results for THz SAR azimuthal non-uniformly sampled images compared to previous SAR non-uniform sampling image reconstruction algorithms. However, we did overlook the comparison with traditional SAR imaging algorithms. In the subsequent revisions, we will add the relevant content. We appreciate your valuable comment.

Comment: In terms of technical comments, the structure of the description of the proposed method seems unbalanced. Section 2 contains an excessive amount of content explaining basic knowledge, while section 3 lacks sufficient content regarding the derivation of the proposed method, especially for formulas 16 to 20, which are presented without proper derivations. A more comprehensive and balanced explanation of the proposed method and its derivations would improve the clarity and understanding of the manuscript.

Response: We sincerely appreciate your guidance in this aspect, as it will greatly assist us in improving the organization and structure of our article. In light of this, we propose the following modification plan: we will streamline the article’s description by removing some of the simpler formulas in Section 2. Additionally, in Section 3, because formulas are derived based on the works of others, we will ensure to include relevant citations before certain formulas. We deeply apologize for any oversight in this regard.

Regarding our responses above, if you have any additional inquiries or if you find any shortcomings in our proposed modification plan, please do not hesitate to reach out to us. We are more than happy to engage in further discussions and address any concerns you may have.

Once again, we sincerely appreciate your comments on our manuscript.

 

Yours Sincerely,

Guohua Zhang

Reviewer 4 Report

Dear Authors,

   I really enjoyed reading your paper. I found it very clear and effective mixing theoretical and practical approaches in an well-organized and efficient way.

Specifically, the article titled "An Efficient Spectrum Reconstruction Algorithm for Nonuniformly Sampled Signals and Its Application in Terahertz SAR" presents a remarkable contribution to the field of remote sensing and radar technology. The article promises an efficient and superior imaging solution to the challenges posed by nonuniform sampling in THz SAR, and upon examining the content, it undeniably delivers on these claims.

The authors of this article have adeptly addressed the critical issue of higher azimuth sampling rates causing severe non-uniform sampling problems in THz SAR. Their approach stands out as a viable alternative to traditional methods based on hardware adjustments and interpolation, which often struggle to meet the demands of higher imaging quality. The proposal of a new algorithm to reconstruct the wavenumber spectrum of SAR azimuth non-uniformly sampled signals using Tikhonov regularization is truly groundbreaking.

One of the most appealing aspects of the proposed algorithm is its computational efficiency, outperforming the widely used back projection algorithm (BPA) that demands significant computational resources. By transforming the spectrum reconstruction problem into a linear equation system and leveraging Tikhonov regularization, the algorithm showcases its ability to process data with superior speed and accuracy. This efficiency not only streamlines processing times but also opens up new possibilities for real-time applications in both military and civilian remote sensing fields.

The strength of this article lies in its foundation on precise theoretical formulations, ensuring the accuracy and reliability of the proposed algorithm. The inclusion of a regularization parameter to control solution errors adds an extra layer of robustness and leads to superior imaging quality compared to conventional azimuth resampling techniques. This level of attention to theoretical detail demonstrates the researchers' commitment to producing impactful results with practical applications.

The article is well-structured, providing readers with a comprehensive overview of the proposed algorithm's capabilities. From deriving an accurate spectrum reconstruction formula for nonuniform sampling signals with finite length to analyzing the influence of noise error on the solution, the authors leave no stone unturned in presenting a thorough analysis of their work.

Finally, the simulation and experimental results showcased in the article convincingly verify the effectiveness of the proposed algorithm. The successful implementation of the algorithm on THz SAR azimuth nonuniform sampling signals processed from the wavenumber domain reaffirms the practicality and reliability of this novel approach.

In conclusion, my only suggestion is a minor revision including and taking into consideration the following articles as well:

1. https://www.mdpi.com/2072-4292/10/12/2066

2. https://www.mdpi.com/2072-4292/15/6/1561?type=check_update&version=1