A Backprojection-Based Autofocus Imaging Method for Circular Synthetic Aperture Radar

Round 1

Reviewer 1 Report

This manuscript presents a backprojection-based  autofocus imaging method based on prewitt operator and PSO for enhancing the image resolution of a CSAR. The effectiveness of the proposed method is validated by experiments.

The following comments are given for improving the quality of the manuscript.    1. Explain the derivations and physical meanings of (2) and (3). 2. Cite the references where (2) and (3) come from if there is any.  3. To enhance the quality of Fig. 5, it's suggested to insert (11)-(17) into corresponding blocks in Fig. 5.    

Author Response

Dear Reviewer1

  Thank you very much for taking the time to review our manuscript titled [A Backprojection-Based Autofocus Imaging Method for Circular Sythetic Aperture Radar] We appreciate your valuable comments and suggestions, and we would like to express our sincere gratitude for your expertise and thorough evaluation.

  Here are the specific modifications we made in response to each of your suggestions.

1.[ Explain the derivations and physical meanings of (2) and (3)]

  Assume the tran smit signal of the SAR system be a series of linear frequency modulation(LFM) pulses

(1)

  Where t is the full time , N is the total number of pulses contained in the transmit signal, T is the pulse repetition period, and the linear FM signal of a signal pulse is

(2)

  Where rect(·) denotes the rectangular window function,  is the fast time variable,  is the pulse width of the transmit signal, the  is the center frequency of the transmit signal, and K is the linear tuning frequency.

   After the transmitted signal is reflected by any point target P in the observation scene, the point target echo signal returned to the receiving antenna is

(3)

  The above equation  represents the backscattering coefficients of the target P;  is the antenna modulation factor; and c is the speed of light. After substituting equation 2 into equation 3, we get

(4)

  CSAR  is also based on the “go-stop-go” assumption, that is, because the speed of antenna movements is much smaller than the speed of electromagnetic waves, so the signal in a pulse time in the process of transmitting to be received, ignoring the change in antenna position, it will be considered to remain stationary.

  The slow timecan be used as the time quantity to describe the antenna motion, and the relationship between the fast and slow time is:

(5)

  In equation 4, , are influenced by the relative position between the target and the antenna . According to the above assumptions where the fast time variable can be neglected, that is , . Substituing equation(5) into (4), the echo signal can be represented by the two dependent variables of fast time  and slow time .

(5)

  After orthogonal demodulation, the point target echo recorded by the system becomes

(6)

  Equation 6 is the mathematical model of the point target echo signal under CSAR.

  The target in the actual scene can be regarded as composed of multiple point targets, so the echo signal received by the radar is composed of the accumulated of all point target echo signals in the irradiated scene, so the expression of the total echo signal is

(7)

2.[ Cite the references where (2) and (3) come from if there is any]

I have cited the relevant literature as you requested

3.[ To enhance the quality of Fig. 5, it's suggested to insert (11)-(17) into corresponding blocks in Fig. 5.]

  I have made the relevant changes as you requested

Author Response File: Author Response.pdf

Reviewer 2 Report

This manuscript analyses the azimuthal and range error for circular SAR and then uses this analysis to determine formulas for these errors in terms of the position and velocity of the radar.  

Feature extraction is performed with the Prewitt operator, but the details of the Prewitt operator are not included.  They should be so that the interested reader does not have to do research on this topic on their own.  

In the results from the real data, a good result is shown in Figure 13 which shows the proposed method substantially sharpens the image.  However, it would be better to quantify this by using some numerical error so that it is not necessary to only rely on visual quality as determined by the human eye.

Some of the figures were misnumbered - for example there are two Figure 3's, the latter of which should actually be Figure 4.  For the experiments with the synthetic data, the error model did not seem correct.  There were uniformly-distributed random errors introduced to each axis of the trajectory, but it appears no consideration as made for temporal correlation, since these errors should at least be partially be correlated in time for each axis.

Some more detailed description of the BP algorithm should be given in this paper. 

Finally, the TX frequency of the radar for CSAR is not given and it should be.

Some corrections are included in the attached PDF file.

Comments for author File: Comments.pdf

See the attached PDF file for some corrections.

Author Response

Thank you very much for taking the time to review our manuscript titled [A Backprojection-Based Autofocus Imaging Method for Circular Sythetic Aperture Radar] We appreciate your valuable comments and suggestions, and we would like to express our sincere gratitude for your expertise and thorough evaluation.

  Here are the specific modifications we made in response to each of your suggestions.

1.[ Feature extraction is performed with the Prewitt operator, but the details of the Prewitt operator are not included.  They should be so that the interested reader does not have to do research on this topic on their own. ]

  The Prewitt operator is a differential operator for image edge detection, which is based on the principle of edge detection using the difference generated by the gray value of pixels in a specific region. Since the Prewitt operator uses 3×3，it is suitable for recognizing images with more noise and gradual gray scale, and its calculation formula is shown as follows:

     

2.[In the results from the real data, a good result is shown in Figure 13 which shows the proposed method substantially sharpens the image.  However, it would be better to quantify this by using some numerical error so that it is not necessary to only rely on visual quality as determined by the human eye.]

Thanks to your comments, I added Table 4 to the original text to calculate the Azimuth resolution/cm Range resolution/cm PSLR/dB for the two images.

3.[ Some of the figures were misnumbered - for example there are two Figure 3's, the latter of which should actually be Figure 4.  For the experiments with the synthetic data, the error model did not seem correct.  There were uniformly-distributed random errors introduced to each axis of the trajectory, but it appears no consideration as made for temporal correlation, since these errors should at least be partially be correlated in time for each axis.]

  I have corrected the numbering of the figures, and for the motion error, I believe that the random error can effectively reflect the reliability of the method in this paper. If the added errors are correlated in time, it is difficult to determine exactly how the errors obey the distribution, which does not help the conclusions of this paper very much, so I still use random errors to verify the method of this paper

4.[ Finally, the TX frequency of the radar for CSAR is not given and it should be.]

  The TX frequency of the radar for CSAR is 9.6GHz and I had marked it in the original manuscript.

Author Response File: Author Response.pdf

Reviewer 3 Report

In this paper, the authors presented a new autofocus and sub-aperture fusion method for CSAR data. It is based on the prewitt operator that extracts sub-aperture image feature points as a new dataset, and on Particle Swarm Optimization (PSO) that estimates the radar slope error on the new dataset. CSAR imaging and error models as well as CSAR auto focusing method are explained in a clear and consistent manner. The effectiveness of this method was confirmed on data obtained by simulations as well as on real data obtained by measurements. The following comments are addressed to the authors in order to improve the paper:

-          It is necessary to explain what the abbreviation "ABP" represents. This abbreviation is used to name the algorithm against which the proposed method is compared.

-          It is necessary to provide information on which hardware platform was used to implement the proposed method, as well as information on the real-time performance of the method.

-          In the conclusion of the paper, the sentence "In this paper, we present a new autofocus and sub-aperture fusion method for CSAR data, based on the backpropagation algorithm" is stated. It is necessary to explain in what context the word "backpropagation" is used.

-          It is necessary to expand the conclusion to include more text that refers to concrete results and less text that is similar to the abstract of the paper.

Author Response

 Thank you very much for taking the time to review our manuscript titled [A Backprojection-Based Autofocus Imaging Method for Circular Sythetic Aperture Radar] We appreciate your valuable comments and suggestions, and we would like to express our sincere gratitude for your expertise and thorough evaluation.

  Here are the specific modifications we made in response to each of your suggestions.

1.[ It is necessary to explain what the abbreviation "ABP" represents. This abbreviation is used to name the algorithm against which the proposed method is compared.]

I have marked the first occurrence of ABP and cited the literature detailing the ABP method.

2.[It is necessary to provide information on which hardware platform was used to implement the proposed method, as well as information on the real-time performance of the method.]

  I have marked the hardware platform as well as the software model in the text. Regarding real-time, the time-domain algorithm has no significant advantage over the frequency-domain algorithm because I do not think it is necessary to demonstrate the real-time performance of the algorithm in this paper

3.[In the conclusion of the paper, the sentence "In this paper, we present a new autofocus and sub-aperture fusion method for CSAR data, based on the backpropagation algorithm" is stated. It is necessary to explain in what context the word "backpropagation" is used.]

  Thank you very much for your comments, but the backward projection algorithm is the basic algorithm of the time domain algorithm, and expanding the backward projection algorithm would make this paper lengthy, for which I have cited references to introduce the content of the backward projection algorithm.

4.[ It is necessary to expand the conclusion to include more text that refers to concrete results and less text that is similar to the abstract of the paper.]

  Thank you very much for your suggestion, I have revised the conclusion section

Author Response File: Author Response.pdf