An Efficient MUSIC Algorithm Enhanced by Iteratively Estimating Signal Subspace and Its Applications in Spatial Colored Noise

Round 1

Reviewer 1 Report

The paper proposes a novel noise subspace removal method by the pre-projection technique. The line of research is highly relevant and the proposal is very promising, nevertheless, I recommend the paper to be majorly revised considering the following comments that are mainly related to the technical contribution and the strength of the simulations.

(1)      The technical contribution of the paper is weak and lacks of the theoretical guarantee. Thus, it is necessary to verify that the pre-projection technique can reasonably solve the two limitations as presented in abstract.

(2)      The abstract uses more content to discuss the limitation of existing works, while introduce the proposed method by short sections, which obviously is not reasonable. I suggest to simply introduce the limitations and put the details into the section introduction, and provide the in-depth discussions in term of the contributions.

(3)      The manuscript of the journal should be at least 15 pages, thus the authors should add some sections to meet the requirement of the journal, such as adding some experiment results.

(4)      I suggest to fuse the section “Discussion” into the section “Results”.

(5)      The core idea of the paper is to use the low-dimensional subspace to separate the noise from the noisy measurement, the thought has also been applied to the other fields, such as the hyperspectral image noise removal [1-2], thus the authors should discuss the related works in the section introduction.

[1] Nonlocal low-rank regularized tensor decomposition for hyperspectral image denoising. IEEE Transactions on Geoscience and Remote Sensing 57.7 (2019): 5174-5189.

[2] Hyperspectral Image Restoration via Global L1-2 Spatial-Spectral Total Variation Regularized Local Low-Rank Tensor Recovery. IEEE Trans. Geosci. Remote. Sens. 59(4): 3309-3325 (2021)

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

I have found this manuscript clear and well written.
Its content suggests interesting and original ideas to improve the efficiency of the MUSIC algorithm.
This is achieved by means of a pre-projection technique employed to remove the adverse effect of the pure noise subspace.
The underlying ideas are not necessarily original but their combination in this denoising context is relevant.
The Authors have provided a well-structured exposition of their material with a gradual description of the underlying ideas fully appreciable.
The content is self-explanatory and described with a sufficient level of detail to understand the topic, techniques and results.
The experimental part is well described and offers a clear illustration of the contribution of the proposed method.
The analysis provided is well conducted and corresponding results are fully appropriate to the text and its content.
The list of references to the literature related to the field is also quite appropriate.

Nevertheless, I have some questions of detail that need to be developed for a better clarity.

1) Please justify better the reasons why the signal components always exist in the set of non-zero delay SCMs when the number of received samples is insufficient

2) Explain further why the choice of (8) is beneficial instead of the ideal non-zero delay SCM

3) Why is (9) an approximation?

4) How to choose appropriately the value of K defining the "fused matrix" in (11)? In other words, what is the minimum value of K for which the risk of not having B(k) as a full rank matrix is corrected? Note that 10 non-zero delay sample covariance matrices are constructed in the simulation

5) More details are needed in (12) to justify the deletion of the terms in the penultimate line.

6) I think that the resolution of (13) would benefit from being described in the form of a pseudo algorithm, specifying the input and output data and showing the internal iterations (this can be done in addition to what is already described in textual form).

7) How can the initial value of P be estimated appropriately?

8) Figs. 3 and 4 show the number of iterations of the proposed algorithm only.
With these two figures alone, it is difficult to consider that the new algorithm needs more iterations to reach the convergence condition in the low
input SNR region.
 
9) Beyond the figures and tables that focus fully on the quantitative evaluation of the proposed method, it would be interesting to illustrate an example that shows a better separation between signal and noise
 
Typo(s):
the smallest eigenvalues of R are away uniform
[1,3,5]is

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The paper has addressed my comments, which can be considered to accept.

Reviewer 2 Report

The Authors have corrected their manuscript in accordance with my requests and expectations.
The content of the revised manuscript has been improved.
In my opinion, it is now in a form acceptable for publication