Deterministic Construction of Compressed Sensing Measurement Matrix with Arbitrary Sizes via QC-LDPC and Arithmetic Sequence Sets

Round 1

Reviewer 1 Report

In this paper the authors proposed a deterministic design for the measurement matrix in the compressed sensing problem. The paper is written well and the structure is okay however it needs some improvement in the text, e.g. correcting typos and improving the quality of the figures.

- My major concern is on the novelty and originality of the paper. While the authors claim that this is a novel method, there exist a number of relevant papers with relatively similar idea which have not been cited. Some of these papers are given here:

1. https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7073409

2. https://www.radioeng.cz/fulltexts/2013/13_03_0851_0860.pdf

3. https://arxiv.org/abs/1012.0602

4. https://www.hindawi.com/journals/mpe/2016/6340430/

The authors must also conduct a major background review to address the above papers and also some other papers that address the optimisation of the measurement matrix such as:

1. https://www.mdpi.com/1424-8220/21/4/1229

2. https://www.mdpi.com/2227-7390/9/4/329

3. https://www.sciencedirect.com/science/article/pii/S0165168411003665

And many more.....

my other comments are:

- section 2.2 starts with a couple of sentences which are Unclear and should be explained further. what are check and variable nodes?

- The quality of most figures are very poor.

- In the experiments, the authors should also run an experiment to show the reconstruction performance as the dimension of the measurement matrix changes.

 

 

 

Author Response

Thanks very much for taking your time to review this manuscript. we really appreciate all your comments and suggestions! Please find my itemized responses in below and my revisions in the resubmitted files.

We apologize for the poor language of our manuscript. We have now worked on both language and readability and have also involved native English speakers for language corrections. We really hope that the flow and language level have been substantially improved.

 

Point 1: While the authors claim that this is a novel method, there exist a number of relevant papers with relatively similar idea which have not been cited. Some of these papers are given here:

 

Response 1: Some references are not cited. Modified references according to the comment. Thank you for your suggested references. The second reference you suggested has been cited in the original manuscript. Thus, we added three references(References[21][22][23] in the revised manuscript).

 

Point 2: The authors must also conduct a major background review to address the above papers and also some other papers that address the optimization of the measurement matrix such as:

 

Response 2: Some references are not cited. Modified references according to the comment. Thank you for your suggested references. we added three references(References[35][36][37] in the revised manuscript), and modified content according to the comment. The precedent version of the content(Line 54 and 55, page2) has been replaced, becoming Line 55,56 and 57, page 2.

 

Point 3: section 2.2 starts with a couple of sentences which are Unclear and should be explained further. what are check and variable nodes?

 

Response 3: a couple of sentences which are unclear. Descriptions of check nodes and variable nodes have been added. Thank you for your advice. We added the descriptions of check nodes and variable nodes in section 2.2 (Line 135,136,and 137, page 3 in the revised manuscript ).

 

Point 4: The quality of most figures is very poor.

 

Response 4: The quality of most figures is very poor. The figures in the paper are a little blurry. We improved the quality of all the figures in the paper. Thank you for your advice.

 

Point 5: In the experiments, the authors should also run an experiment to show the reconstruction performance as the dimension of the measurement matrix changes.

 

Response 5: Thank you for your advice. It is very important. Thanks to your advice, we have found the inadequacies in our present work. We're missing an experiment. We added an experiment about the reconstruction performance as the dimension of the measurement matrix changes, as show in Figure 3 (page 9), and added descriptions of Figure 3 (Line 292-300, page 8 and 9 in the revised manuscript). Thank you for your advice.

the revised manuscript please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors propose a method to construct a deterministic measurement matrix with an arbitrary size, for CS applications, using QC-LDPC and arithmetic sequence sets.

The work is very presented very well, with an extensive and clear state of the art. The objectives of the paper are clearly reported and the paper itself is well written.

The only phrase that i would rewrite is the one between line 81 and 82 "The experimental results show that the..."

The experimental evaluation is exhaustive, and the advantages of the proposed deterministic matrix is clear, but if possible, i would suggest to compare the performance of the proposed deterministic matrix with other deterministic matrices, since the authors themself made clear that in the literature there are other efforts in the field, with the objective of finding or creating deterministic matrices for CS applications.

Author Response

Thanks very much for taking your time to review this manuscript. we really appreciate all your comments and suggestions! Please find my itemized responses in below and my revisions in the resubmitted files.

We apologize for the language error in our original manuscript. We have now worked on both language and readability and have also involved native English speakers for language corrections. We really hope that the flow and language level have been substantially improved.

 

Point 1: The only phrase that i would rewrite is the one between line 81 and 82 "The experimental results show that the..."

 

Response 1: We apologize for the language error. We have rewritten the sentence” The experimental results show that the..." in our original manuscript(Line 81 and 82, page 2), becoming Line 84,85 and 86, page 2.

 

Point 2: The experimental evaluation is exhaustive, and the advantages of the proposed deterministic matrix is clear, but if possible, i would suggest to compare the performance of the proposed deterministic matrix with other deterministic matrices, since the authors themself made clear that in the literature there are other efforts in the field, with the objective of finding or creating deterministic matrices for CS applications.

 

Response 2: Thank you for your advice. It is very important. We have found the deficiencies in our present work. On the one hand, the measurement matrix construction method proposed by us has better performance than several typical measurement matrices; on the other hand, it can be used in the follow-up single pixel imaging experiments to show the performance advantages of measurement matrices. Since the column of Hadamard matrix is fixed to the power of 2, the size of measurement matrix is limited, and large storage space is required. Based on these limitations of the Hadamard matrix, we proposed a deterministic measurement matrix of arbitrary size. However, it lacks of comparisons with the construction methods of deterministic measurement matrix proposed in some references, so we will increase the comparison of these methods in the subsequent research work to reflect the superiority of our method. Thank you again for your suggestions to help me.

Revised manuscript please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors made effort to address the comments. New experiment is added. The paper can be accepted.