Microseismic Signal Denoising via Empirical Mode Decomposition, Compressed Sensing, and Soft-thresholding
Round 1
Reviewer 1 Report
The paper has been strongly revised according to the previous comments.
Author Response
Dear Reviewers and Editors,
Thank you very much for your useful comments and suggestions on the content and language of our manuscript. Your comments are very valuable and helpful for revising and improving our work.
Thank you for your recognition of our work.
Once again, we appreciate for your warm work, and would like to extend our thanks for the valuable comments. We are looking forward to receiving your approval. Many thanks.
Best regards,
Yours sincerely,
Nuwen Xu
Reviewer 2 Report
General remarks
The authors improved the overall quality of the manuscript however it would be valuable to compare the proposed approach with the classic method presented in the work
Kopsinis, Y., & McLaughlin, S. (2009). Development of EMD-based denoising methods inspired by wavelet thresholding. IEEE Transactions on Signal Processing, 57(4), 1351-1362.
The main difference is that in the above algorithm the soft thresholding technique is performed directly on IMF functions. While the proposed method uses an additional discrete wavelet transform which (unnecessary) complicates algorithm.
Detailed remarks
Lines 117-118: The sentence “It is suitable for signal analysis with non-linear and non-stationary” should be corrected. It seems to be uncompleted.
Author Response
Dear Reviewers and Editors,
Thank you very much for your useful comments and suggestions on the content and language of our manuscript. Your comments are very valuable and helpful for revising and improving our work. We have seriously considered each comment and modified the manuscript accordingly. The detailed corrections are listed below:
1) Lines 117-118: The sentence “It is suitable for signal analysis with non-linear and non-stationary” should be corrected. It seems to be uncompleted.
Thanks for the comments.
Huang et al. (1998). A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the ‘empirical mode decomposition’ method with which any complicated data set can be decomposed into a finite and often small number of ‘intrinsic mode functions’ that admit well-behaved Hilbert transforms. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and non-stationary processes. We can view the research papers of Huang et al. through this website. (https://doi.org/10.1098/rspa.1998.0193)
2) Kopsinis, Y., & McLaughlin, S. (2009). Development of EMD-based denoising methods inspired by wavelet thresholding. IEEE Transactions on Signal Processing, 57(4), 1351-1362. The main difference is that in the above algorithm the soft thresholding technique is performed directly on IMF functions. While the proposed method uses an additional discrete wavelet transform which (unnecessary) complicates algorithm.
Thanks for the comments.
Reviewer may have some misunderstanding of the proposed method. The research purpose of this paper is to introduce compressed sensing technology to the denoising of microseismic signals, because compressed sensing technology has absolute advantages in signal acquisition and storage, which is convenient for later signal processing and storage. In view of the poor performance of compressed sensing theory in low signal-to-noise signals, this paper not only relies on the denoising capabilities of compressed sensing theory, but also uses EMD and ST algorithms. The proposed method greatly improves the signal-to-noise ratio of microseismic signals. At the same time, compared with some classic methods, the proposed method is better in realizing signals at different noise levels. Discrete wavelet transform is a kind of wavelet transform, and it is also a method to sparse the signal in compressed sensing theory. One of the prerequisites of compressed sensing theory is that the signal must be sparse or sparse in a certain transform domain. To perfectly integrate the application of ST algorithm, discrete wavelet variation was selected as a part of compressed sensing.
The answers to the above questions are mainly to explain and discuss with the reviewers. If there is any explanation that is not in place, please put it forward again.
There are instructions on the original manuscript, so no further changes are made to the manuscript.
Once again, we appreciate for your warm work, and would like to extend our thanks for the valuable comments. We are looking forward to receiving your approval. Many thanks.
Best regards,
Yours sincerely,
Nuwen Xu
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
The paper deals with a new method for microseismic signal denoising via 2 empirical mode decomposition, compressed sensing, 3 and soft-thresholding.
It is well written and easy to follow.
However, I have some comments:
(1) main (innovative) contributions need to be summarized/listed in the introduction (2) more related works on CS theory to the reconstruction of seismic data need to be included. (3) Overall organization of the paper needs to be indicated at the end of the introduction (4) Discussion of results needs to be significantly improved. In particular, the method here proposed needs to be compared to recent state-of-the-art. (5) the authors state"CS theory has been widely used in information theory, image optimization, and other fields."(line 115) However, the potential of Compressive sensing in the mentioned and other fields (such as (i) health care, (ii) inverse scattering problems) needs to be discussed here and in the introduction. In this sense the authors can refer to: (i) "Compressibility of High-Density EEG Signals in Stroke Patients"; "Brain network analysis of compressive sensed high-density EEG signals in AD and MCI subjects"- (ii) "Non-Linear Inverse Scattering via Sparsity Regularized Contrast Source Inversion"; "Boundary Indicator for Aspect Limited Sensing of Hidden Dielectric Objects". (6) Fig.4 needs to be briefly described in the caption in order to give the reader a better understanding of the methodology. (7) Conclusion can be improved and future directions need to be included
Reviewer 2 Report
The submitted article is focused on removing the noise from the microseismic signals by projecting the high frequency intrinsic mode functions (IMF) of the signal on a sparse space, soft thresholding the wavelet coefficients and recombining with the remaining IMFs, and reconstructing the denoised signal. The proposed hierarchy of methods is a sound combination for the intended application. The article has tested the method with simulated data and a real microseismic signal from an underground cavern.
However, the submission does not meet the minimum publishing requirements, for at least two reasons. The first problem is the language on both the grammar level and the scientific writing style. A few examples of the language problems are listed in the second part of this review. The second problem regards the lack of contribution and the experiment design. This is further explained below.
The method is a combination of steps, each of which are existing algorithms. These steps are explained properly in details. Also, the combination, as shown by the experiments, is a sound proposal. However, as a whole, there is not enough novelty in the method. This could be compensated, nonetheless, by providing reasonable justification for the choice of parameters, the tuning, and the application. But, the article does not provide this information for some of the key steps (examples below).
[L.151] Why Gaussian matrix is used as the measurement matrix basis? Are there any alternatives? Why Gaussian is suitable for this case.
[L.155] Discrete wavelet transform is selected over a few other options (without much explanation), but nowhere in the article it is mentioned which wavelets are actually used. From the description at [L.230] it seems that the Matlab implementation is used for this purpose, but the setting is not reported.
[L.173] Why soft thresholding is chosen over hard thresholding? Is there an advantage here?
[L.181] It seems that the waveform of the Ricker Wavelet is used to simulate an actual microseismic signal. However, the name is reported as Picker wavelet in [L.181] and [L.249].
[L.185] What kind of noise with what model (distribution) and what model parameters is added. Is there any model for the noise in microseismic signals? In fact, the noise level and model could be the focus point of the experiments. The methods could be tested under different levels of noise.
[Figure.2.d] The figure shows some amplified residual noise. It is not clear if this noise is in fact due to the NF phenomenon. Showing the aliased frequency range in the frequency space could be helpful in this case.
Quality Metrics: Three quality metrics are used to evaluate the methods: SNR, SD, and CC. The idea behind these metric (specifically SNR and SD) is very similar, as it can be seen from the formulas. Other evaluation methods and metrics could be added to show the efficiency of the methods in removing the noise.
Opponent Methods: The proposed EMD-CS-ST method is compared to EMD, WD, and EMD-WD. All of these opponent methods are basically steps of the proposed method. As opponents, other denoising methods with different approaches could be used to better demonstrate the advantages and the shortcomings of the method. Comparing a method to its own steps does not necessarily justify that method.
[L.48] Is the categorization (the 3 categories) suggested by the article? If not, a reference should be offered. If yes, the next paragraph is expected to give examples of each category. For examples, each of the references 5 to 11 on line 11 should be classified as one of those categories?
[L.71] The whole paragraph that starts on this line is almost completely restating what was said already in the abstract. It can be either removed, or be given some new information.
The Case Study: the information given in sections 4.1 and 4.2 are irrelevant to the work in this article. A brief mention, in a few sentences, would be enough to introduce the source of the dataset. Figures 9 and 10 are probably used from another source without reference(?) The only useful information of these paragraphs might be on [L.278] and [L.299].
[L.2] Phrases such as “new method”, “novel technique”, and similar terms are not informative in an article’s title. As new methods emerge every day, these terms lose their meaning very soon after publication. In this case, “A new method for” could be removed entirely from the title, making it shorter, without losing any information.
The language of the article (both in grammar and style) is not adequate for publication. A few of the problems are pointed out below:
Usage of etc. : The term “etc.” in scientific writing should be used only when all of the items are already enumerated and known to the reader. In this article, this term is overly used, and in many cases it is not clear what are the items that are being referred to with “etc”. For example, in none of the lines [L.41], [L.45], [L.155] it is clear to reader what other items “etc” is referring to.
[L.24] “… compared by comparing…” unnecessary wording
[L.51] The word “theory” is used at least 3 times in a short sentence.
[L.57] “Hypothesis” is a noun not a verb
[L.88] “have local symmetry” not “are…”
[L.97] “absorbs the advantage” not a correct expression
[L.100] “… with non-linear non-stationary” what? Those words are adjectives and should be followed by nouns.
[L.124] “to sparsification” wrong grammar
[L.179] The sentence is incorrectly constructed (“it faces”?)
[L.199] The sentence is incorrectly constructed.
[L.203] “the behind one component” does not express what it is intended to mean.
[Conclusion] Using adjectives such as “better” “greatly” “weak” and so on is not encouraged. They are unclear (how much better? Better than what? How great? …) and should be replaced by objective results.
