Sub-Aperture Partitioning Method for Three-Dimensional Wide-Angle Synthetic Aperture Radar Imaging with Non-Uniform Sampling
Round 1
Reviewer 1 Report
The work addresses an important scientific issue. The state of literature in the subject of the work is comprehensively described. There is a lack of literature references to mathematical expressions in the work, which makes it difficult for the reviewer to assess which expressions are original and which are not. It is worth noting the experiment carried out to confirm the described method, which increases the value of the work. The editing of the work, eg line 162, requires a slight correction.
Author Response
Point 1: There is a lack of literature references to mathematical expressions in the work, which makes it difficult for the reviewer to assess which expressions are original and which are not.
Response 1: Thanks for your recommendation. In our revised manuscript, the literature references to mathematical expressions which are not original are added.
Point 2:The editing of the work, eg line 162, requires a slight correction.
Response 2:Thanks for your careful checks. Based on your comment, we have corrected the “where represents the imaging resultof the sub-aperture, and represents the final imaging result.” into “where represents the imaging resultcorespoonding to the sub-aperture and represents the final imaging result.” in the revised manuscript.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This paper presents an advancement in signal processing techniques for SAR imaging. It addresses the important problem of how best to process data taken from vehicles moving in curvilinear paths. The adaptive non-uniform sub-aperture approach is an interesting and possibly important contribution.
Some items for the authors to consider:
In Figure 3. Are the new and improved sub-apertures unique? Can the shapes, in addition to size be chosen to optimize the output.
In Figure 9 and 10, the 3-D results show ellipsoid shapes, when the underlying shape is a trihedron. Is there an explanation? Also Figure 12 shows some more trihedral shapes in the image.
The conclusions state that the proposed method is verified by experiments. Were these numerical or physical experiments?
The method for sub-aperture optimization used the Fisher Information as the driving criterion. Why was this criterion chosen? Are there other competing criteria that may be worth considering (perhaps maximum entropy)?
How fast does the algorithm work? Is is possible to do a rapid analysis so that the flight path can be altered in an adaptive manner to get better resolution?
Note that 'data' is the plural of 'datum.' It is better to say 'data are' rather than 'data is.'
Author Response
Point 1: In Figure 3. Are the new and improved sub-apertures unique? Can the shapes, in addition to size be chosen to optimize the output.
Response 1: We feel great thanks for your professional comments on our work. As you are concerned, the new and improved sub-apertures is not unique. The equal-interval sub-aperture partitioning method, as most commonly used method, divides the aperture with constant sub-aperture size. In order to compare with the equal-interval method, the proposed method only changes the azimuth size of sub-aperture to ensure that the 3-D resolution of each sub-aperture is consistent, keeping the shape of sub-aperture in the proposed method the same as in the equal-interval method. Indeed, the idea of changing the shape of sub-aperture is really interesting, and it may have a great performance. After the aperture is divided by the proposed method, the 3-D resolution of each sub-aperture is consistent. However, it is possible that the elevation resolution of one sub-aperture is higher than that of another sub-aperture, while the azimuth resolution is lower, since the sampling is non-uniform in both elevation and azimuth. This inconsistency may also have an influence on the resolution of the final imaging result. Therefore, in order to ensure that the resolution of each sub-aperture in each direction is the same, changing the shape of sub-aperture is a great way. Thank you for your suggestion. This interesting problem will be further studied in future.
Point 2:In Figure 9 and 10, the 3-D results show ellipsoid shapes, when the underlying shape is a trihedron. Is there an explanation? Also Figure 12 shows some more trihedral shapes in the image.
Response 2:Thanks for your comments. Trihedral, as a canonical reflector, usually can be approximated as an ideal point scatter, and its imaging result is a bright spot. When the resolution is high and the resolution of each direction is the same, the 3-D imaging result of trihedral is expected to be a sphere. However, when the resolution of each direction is different, the 3-D imaging result is an ellipsoid, as shown in figure 9, 10 and 12. In fact, because the extent of elevation is 24 degrees while the extent of azimuth is only about 10 degrees, the elevation resolution is finer than the azimuth resolution, which makes the imaging result in figure 9, 10 and 12 ellipsoid. We have added the statement of “Because the extent of elevation is 24 degrees while the extent of azimuth is only about 10 degrees, the elevation resolution is finer than the azimuth resolution, which makes the imaging result in Figure 9 ellipsoid.” in line 300-302.
Point 3:The conclusions state that the proposed method is verified by experiments. Were these numerical or physical experiments?
Response 3:Thanks for your comments. The statement of “the proposed method is verified by experiments” is inaccurate. In the section of the Experiments and Results, we use electromagnetic simulation data to carry out our experiments. Therefore, the statement of “the proposed method is verified by experiments” was corrected as “the proposed method is verified by using electromagnetic simulation data” in our revised manuscript.
Point 4:The method for sub-aperture optimization used the Fisher Information as the driving criterion. Why was this criterion chosen? Are there other competing criteria that may be worth considering (perhaps maximum entropy)?
Response 4:Thanks for your suggestion. We chose the Fisher Information as the driving criterion for two reasons. Firstly, the Fisher Information is widely used in the field of radar signal processing. Most importantly, the Fisher Information provides the lower bound of parameter estimation accuracy, and the accuracy of position estimation depicts the 3-D resolution. Therefore, the Fisher Information is chosen. As far as we are concerned, the maximum entropy implies the amount of information contained in the data, and it could also be used to evaluate the quality of the image. However, the maximum entropy may be not connected directly to the performance of parameter estimation. Maybe there are other competing criteria, and we could study this problem further in future.
Point 5:How fast does the algorithm work? Is it possible to do a rapid analysis so that the flight path can be altered in an adaptive manner to get better resolution?
Response 5:We think it is possible to do a rapid analysis so that the flight path can be altered in an adaptive manner since the proposed algorithm is fast. Specially, in the case of our experiment, it takes an average of 0.73 seconds to determine the size of each sub-aperture, and 6.57 seconds to divide the aperture into nine sub-apertures. Simulation results presented above were performed in MATLAB 2016b on a system with Intel i5-6500 @3.20 GHz CPU and 12 GB of memory.Although the algorithm needs several iterations to search for the appropriate size of sub-aperture, the speed of the proposed algorithm is fast due to the low computational complexity of calculating. Therefore，it is possible to adjust the flight path rapidly according to the current value of .It is mentioned in our paper that agreat diversity of samples result in a higher resolution of imaging results. Accordingly, the flight path needs to be more dispersed when the value of is large. In summary, an optimization algorithm is needed to determine the flight path. Thank you for your suggestion. This interesting problem will be further studied in future.
Point 6:Note that 'data' is the plural of 'datum.' It is better to say 'data are' rather than 'data is.'
Response 6:Thanks for your correction, and it has been corrected in our revisedmanuscript.
Author Response File: Author Response.pdf
Reviewer 3 Report
In the present manuscript, the Authors present a partitioning method for non-uniformly sampled SAR imaging systems, which allows to obtain sub-apertures with high and consistent resolution. The topic is interesting and suitable for the journal. Although the manuscript is generally well structured, I have some concerns the Authors should address before it can be published.
First of all, it is not clear if the trajectories used for the UAV are somewhat standard and or optimized. Some more discussions about this point should be added. Moreover, what happens if different trajectories and number of UAVs are used? Please better discuss this point, with particular reference to the impact on the developed partitioning procedure and on its effectiveness.
Moreover, although in the signal model assumed by the Authors in (1), a noise is correctly then into account, all the numerical results seems to be performed in a noiseless case (or at least the noise level is not specified). A discussion concerning the effect (if any) of the noise and of the other eventually present source of errors on the reconstruction capabilities of the developed optimized sub-aperture SAR imaging procedure should be provided.
Author Response
Point 1: First of all, it is not clear if the trajectories used for the UAV are somewhat standard and or optimized. Some more discussions about this point should be added. Moreover, what happens if different trajectories and number of UAVs are used? Please better discuss this point, with particular reference to the impact on the developed partitioning procedure and on its effectiveness.
Response 1: Thanks for your professional comments on our work. The trajectories used for UAVs in our manuscript are not optimized by ourselves. In fact, these trajectories are derived from Reference [9]. Accordingly, the curve trajectory in Reference [9] is used as the trajectories for UAVs in our article. To explain this, we have added the statement of “The curve trajectory in Reference [9] is used as the trajectories for UAVs.” in line 45.
9. Austin, C.D.; Ertin, E.; Moses, R.L. Sparse signal methods for 3-D radar imaging. IEEE J. Sel. Top. Signal Process.2011,5, 408–423.
The proposed sub-aperture partitioning method can be applied to any trajectories, although only the trajectory in Figure 1 is used in the experiments of our manuscript. When using different trajectories and number of UAVs, the proposed method is expected to perform better than the equal-interval partitioning method. This is because, regardless of the shape of the trajectories and the number of UAVs, as long as the trajectories are non-uniform, the resolution of each sub-aperture will be different when the aperture is divided with equal intervals. However, the non-uniform portioning method ensures that the resolution of each sub-aperture is high and consistent, thus always performs better than the equal-interval partitioning method.
Figure 1.The flight trajectory of TomoSARand five UAVs with SAR system in cooperative flight.
The experimental results using different trajectories and number of UAVs are given below.
(a) (b)
Figure 2.The flight trajectory. (a) trajectory 1; (b) trajectory 2.
(a) (b)
Figure 3.Result of sub-aperture partitioning. (a) trajectory 1; (b) trajectory 2.
(a) (b)
Figure 4.Resolution comparison of imaging results using different sub-aperture partitioning methods. (a) trajectory 1; (b) trajectory 2.
Figure 2 gives two different trajectories. The non-uniform sub-aperture partitioning results of the two different trajectories are shown in Figure 3. Figure 4 gives the resolution comparison of imaging results using different sub-aperture partitioning methods. It can be seen from Figure 4 that our proposed method has a higher resolution imaging result for both trajectory 1 and trajectory 2,when comparing with the equal-interval partitioning method. In addition, it is noteworthy that the resolution improvement brought by our proposed method is different for different trajectories. Specifically, when the sampling of trajectory is closer to the regular and uniform sampling, the resolution improvement may be not obvious, as shown in Figure 4b.
Point 2:Moreover, although in the signal model assumed by the Authors in (1), a noise is correctly then into account, all the numerical results seems to be performed in a noiseless case (or at least the noise level is not specified). A discussion concerning the effect (if any) of the noise and of the other eventually present source of errors on the reconstruction capabilities of the developed optimized sub-aperture SAR imaging procedure should be provided.
Response 2:Thanks for your great suggestion. Here, we give the non-uniform sub-aperture partitioning results when the SNR is -20 dB, 0dB and 20dB respectively.
(a) (b) (c)
Figure 5.Result of sub-aperture partitioning. (a) SNR=-20dB; (b) SNR=0dB; (b) SNR=20dB.
It can be seen from Figure 5 that the noise has no effect on the sub-aperture partitioning, since the partitioning results are determined by the sampling position. Specially, Equation (9) implies that the term of noise and matrix are sepatated in the CRLB of position estimation. The procedures of our proposed sub-aperture partitioining mehod are based on the matrix , hence the partitioning results of different SNRs are same in Figure 5.
Figure 6.Resolution comparison of different SNRs
Figure 6 gives the resolution of imaging result obtained by the equal-interval and the proposed method when the SNR changes from -30dB to 30dB. It can be seen from Figure 6 that the quality of the imaging result is worse for lower SNR. However, the noise does not have obvious effect on the resolution improvement brought by the proposed method.
Author Response File: Author Response.pdf
