Efficiency of Orthogonal Matching Pursuit for Group Sparse Recovery

Round 1

Reviewer 1 Report

1. In line 74 there is a link to formula (1.1), and it should be (1).
2. For clarity, it would be good to put the results of the BP method in Fig. 1. It would be nice to have a similar drawing, but in the presence of noise.
3. In Tables 1 and 2, it would be good to give the MSE values in the presence of noise.

Author Response

Your time and effort, as well as that of other reviewers, are greatly appreciated. Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

This study proposed the Group Orthogonal Matching Pursuit (GOMP) algorithm to recover group sparse signals from noisy measurements. The authors proved the instance optimality of GOMP algorithm for any decomposable approximation norm. It has been demonstrated the robustness of GOMP under the measurement error.. The simulation results showed that the GOMP is efficient for group sparse signal recovery and outperforms Basis Pursuit in both scalability and solution quality.

 Comments:

1)         Please present explicitly your principal contributions that in opinion of this reviewer could be in Algorithm: GOMPM (y), theorems 2, 3. Underlining your scientific contributions gives for potential reader better understanding the scientific value of this study.

2)         This reviewer thinks that authors should present much more details about their experimental set. It is very difficult for potential reader understanding what signals or dataset for them have been used in experiments. Also. it would be preferable presenting much more graphical material for different signals that can  justify the quality of the proposed method in comparison with existing ones.

3)         This reviewer thinks that your manuscript could be much more readable if the authors put the proofs for several theorems and other mathematical calculations as the appendix text.

Author Response

Your time and effort, as well as that of other reviewers, are greatly appreciated. Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

The manuscript formulates the Group Orthogonal Matching Pursuit for recovering group sparse signals from limited measurements subject to noise. The authors rigorously and clearly demonstrate the robustness of GOMP under the group restricted isometry property, providing numerical experiments comparing the accuracy and efficiency of GOMP relative to the standard basis pursuit

The paper is well organized, defining all appropriate terms and reviewing related literature. The theory presented appears novel and mathematically sound. There are several minor issues that I recommend be addressed before  publication:

-A more intuitive description of the GOMP algorithm would be helpful, prior to stating theorem 2.

-Are there any other reasonable competitive algorithms one should directly compare GOMP with aside from the basis pursuit?

Author Response

Your time and effort, as well as that of other reviewers, are greatly appreciated. Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The authors have attended all comments of this reviewer