Application of a Randomized Algorithm for Extracting a Shallow Low-Rank Structure in Low-Frequency Reverberation
Round 1
Reviewer 1 Report
This article proposes an improved Go-SOR decomposition method based on the subspace-orbit randomized singular value decomposition (SOR-SVD). The authors provide a physical interpretation of the decomposed low-rank structure which is consistent with the reverberation interference striation (RIS). The advantage of the Go-SOR is the fast computation speed compared with the original Go algorithm and the SOTA algorithm.
The work is original, attractive, and meets the standard of Remote Sensing，but there are some confusions and suggestions as follows:
Major comments:
(1) The most attractive point is the physical interpretation of the low-rank structure. What is the difference between the low-rank structure and the RIS? How to use the low-rank structure for underwater acoustic? Would you at least consider this topic for future work?
(2) What is the limitation of the Go-SOR?
some minors：
(1) Line 22 Reverberation clutter, caused by the inhomogeneity of the water column
(2) Line 144 dr type
(3) Line 153 “the m-th mode”
(4) Line number loss between Line 154 and 155
(5) “We definie circle-similarity r(q) as” should be “define”
(6) Line 185 “develops”
(7) Fig. 3(c) and Fig. 6(b) should be revised because of the “outperformed” legends.
(8) Table 1 describes the data processing time of the algorithms. Thus, the computing environment and hardware facilities should be included in the article.
English writing is fluent.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
In this paper, author proposes a new algorithm for extracting shallow low-rank structure in low-frequency reverberation. This algorithm combines the SOR-SVD algorithm and the GO decomposition algorithm. Author uses this algorithm and other classic algorithm to process experimental data of shallow seabed reverberation in the South China Sea and demonstrate the algorithm is better in terms of definition index of the low-rank structure and computational efficiency. Then author present an idea that a bi-static low-frequency reverberation simulation model can be transformed into a mono-static distant seabed reverberation model, when the transition indicator circle-similarity close to 1. What is more, author examines the interference characteristics and proposes that the interference of the 5th and 7th modes mainly control the low-rank structure in the experimental environment of the South China Sea. This paper proposes many valuable achievements and it is a remarkable article, but there are some issues should be clarified.
1. Be attention to the layout and format. Many figures and tables are separated from their descriptions, such as line 163 ,165 ,167 ,227 and so on. Some figures have the same problem. For example, figure 4, table 1 and table2 are put in the head of section 4 without any explanation and the figure 6 in line 276 is in the back of its description in line 269. These mismatches result in hardness to understand.
2. Additionally, there are some very little mistakes, such as the coined words “unvectorizing” need explanation and the “G0-SOR” in line 268.
3. In line 232, it is mentioned that the spectrograms vary with different pings in Figure 4, but the reader cannot directly judge whether the changes are very different from the figure. It is better to give the measured indicators.
4. The conclusions in the Discussion only discover patterns from the results of the algorithm, but lack theoretical support and are not linked to the reverberation theory and the formulas given earlier.
5. Table 1 compares the computing time of Go-SOR, Original Go, and ALM-SOR-SVD RPCA methods. However, the calculation time is greatly affected by hardware, and it also has a significant impact on the same hardware at different times. It is hoped that the author can indicate whether to perform under the same conditions or adopt more reasonable performance indicators.
OK
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
