An Inertial Relaxed CQ Algorithm with Two Adaptive Step Sizes and Its Application for Signal Recovery
, Tanadon Chaobankoh 1, Khwanchai Kunwai 1 and Thanasak Mouktonglang 1,*Round 1
Reviewer 1 Report (New Reviewer)
Comments and Suggestions for AuthorsComments for author File: 
Comments.pdf
Author Response
Please see the attachment.
Best regards
T. Mouktonglang
Author Response File: Author Response.pdf
Reviewer 2 Report (New Reviewer)
Comments and Suggestions for AuthorsPlease find my comment in attached file.
Comments for author File: Comments.pdf
It should be improved.
Author Response
Please see the attachment.
Best regards
T. Mouktonglang
Author Response File: Author Response.pdf
Reviewer 3 Report (New Reviewer)
Comments and Suggestions for AuthorsIn this paper, the authors proposed an inertial relaxed CQ algorithm with two adaptive step sizes to solve the SFP. Strong convergence of the proposed algorithm is proved. Numerical experiments demonstrate the efficiency and reliability of the proposed algorithm, and it outperforms existing algorithms in terms of accuracy and speed.
The paper is original and the proofs are correct.
1. Please highlight the main contribution;
2. Please track the latest references and delete several unnecessary references [13-16].
Author Response
I would like to thank the reviewers for their detailed comments and careful suggestions of the manuscript. I have taken the comments to improve and clarify the manuscript.
Firstly, I would like to inform that we decided to remove references (previously) 13,14,15 and 16 and include a new reference (now) [6]. The list of the algorithm's requirements has been reorganized, as shown on Page 5, line 88. For example, (R1) is now used instead of (1).
1. The main contribution has been highlighted by revising the final paragraph of the Introduction.
2. The reference has been updated.
Reviewer 4 Report (New Reviewer)
Comments and Suggestions for AuthorsThis manuscript proposed a novel inertial relaxed CQ algorithm with two adaptive step sizes for solving the SFP. The effectiveness of the proposed algorithm was verified by a signal recovery problem in compressed sensing and compared with existing algorithms. The following comments need to be addressed.
1. More explanations should be added to demonstrate the reason to conduct this research. One sentence “Motivated and inspired by the above-mentioned results” is not convincing.
2. More explanations should be added to demonstrate why to use the parameters in the comparative experiment with existing algorithms.
Author Response
I would like to thank the reviewers for their detailed comments and careful suggestions of the manuscript. I have taken the comments to improve and clarify the manuscript.
Firstly, I would like to inform that we decided to remove references (previously) 13,14,15 and 16 and include a new reference (now) [6]. The list of the algorithm's requirements has been reorganized, as shown on Page 5, line 88. For example, (R1) is now used instead of (1).
- The main contribution has been highlighted by revising the final paragraph of the Introduction. Also the discussion in the final section (Numerical Exemplications) has been expanded to include additional details and explanations.
- The explanation for the parameter selections can be found on page 11, line 138.
Round 2
Reviewer 3 Report (New Reviewer)
Comments and Suggestions for AuthorsThe revised version addresses all comments and it can be accepted for publication.
Reviewer 4 Report (New Reviewer)
Comments and Suggestions for AuthorsThis manuscript can be accepted now.
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
Comments and Suggestions for AuthorsPlease see the attached file for the comments and suggestions.
Comments for author File: Comments.pdf
The language should be modified appropriately.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe author investigated an inertial CQ relaxed algorithm with two self-adaptive stepsizes for solving the split feasibility problem. They established a strong convergence theorem under standard assumptions and demonstrated its application in signal processing. Although this work aims to extend the findings from references [17] and [12], it appears to be an artificial extension with minimal novelty. Several concerns from the cited works need to be addressed by the authors to justify this extension.
(1) Adding an additional gradient function to the established proximal gradient (in this case, CQ) method amy not enhance algorithm performance. For large-case scenarios, the computational time required to calculate the gradient (or Jacobian) of the matrix could be significant, negatively impacting the algorithm's computational efficiency. This modification seems to be an artifical extension that could degrade performance rather than improving it.
(2) While dual stepsize parameters might influence algorithm performance, their determination is generally complex. Algorithms with fewer parameters are often more efficient. To validate the necessity of two control parameters, the authors should provide computational comparisons betweenalgorithms with one parameter and those with multiple parameters demonstrating the practical benefits of their importance.
(3) The authors need to justify the use of the product of two real sequences for stepsize selection. In the proposed method, the authors used \phi_n*\tau_n where \phi \in [1,\infty), \tau_n>1, what is the difference of this with \alpha \in (0,\infty) which had been used in many literature. In fact the latter seems to be more general than the former which is too restrictive. The current choice seems like a superficial extension without substantial justification.
(4) The methodology and proofs provided by the authors are standard and lack novelty. They follow established lines of argument without introducing significant new insights or techniques.
Comments on the Quality of English LanguageThe author should improve the quality of the English usage in the paper.
