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Your manuscript entitled "A novel method ''has been reviewed and requires major revision. The reviewer comments are enclosed. Please address the questions and comments of both referees, and revise the manuscript accordingly or respond to the remarks.

I have carefully read the comments of the reviewers and the Associate Editor's recommendation. On balance I find myself most closely aligned with the comments of Reviewer 2 - all of the points he/she raises require some rethinking and re-writing. This is more than a minor revision. The authors need to reduce the size and number of figures and have the manuscript carefully edited for the English usage as well. Some thought could go into including some of the discussion and some of the less important of the figures into an on-line "Supporting Information" file.

In addition to the referees' concerns, there are some revisions needed to conform with journal style requirements for printing.
1) Please remove the embedded figures from the manuscript text file. The individual figure files are used for the printing process.
2) Please add a list of figure captions on a separate page at the end of the manuscript file, following the list of references.
3) Please move the tables and their captions to the end of the manuscript text file following the list of figure captions.
4) Each figure should be complete in one figure file, e.g., Figure 2(a),(b), and (c) should be arranged in one figure file, with the three panels stacked in one vertical column. Similarly, the multiple panels for Figures 4, 6, 8, 13, 15, 16, and 17 should be combined in one file for each figure.
5) In Figure 5, second box from top, "calcuate" should be "calculate".
6) In Figure 7, "controled" should be "controlled".

I have attached the color printing agreement form for you to complete and return to have figures printed in color.

When you submit your revision please include a rebuttal letter detailing all the changes that were made, referring by number to the referees' comments. Please note that if your revision is submitted within six months, it will be handled normally; beyond that period, it will be treated as a new submission and given a new number.

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I look forward to receiving your revised manuscript.

Best regards,
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The University of British Columbia
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Associate Editor Evaluations:
Recommendation: publishable following minor revisions

Associate Editor (Comments for the Authors):

Please address the reviewers' comments and work to reduce the length of the manuscript without sacrificing content. Please refer to literature references where appropriate that would guide the readers to mathematical formulations.


Reviewer #1 Evaluations:
Novelty: Good
Significance of Results: Good
Conclusions Supported: Good
Of interest to readers: Good
Length Appropriate: Yes
Clarity organization/writing: Adequate
Quality figs/tables: Good
Recommendation: publishable following minor revisions

Reviewer #1 (Comments for the Authors):

This paper is an interesting contribution to resolve overlapped peaks in  data processing. The aim of the paper is to show how to improve the spectral resolution of the overlapped peaks with the simulations and experiments. I suggest the publication of the paper after minor revisions given as follows:

(1) High value of S/N ratio is a crucial condition for obtaining sufficient quality. What is the S/N ratio in the experiment?

(2) Is the error caused by subtraction of baseline involved in this study?

(3) The laser fluence is commonly used as ablation parameter. I suggest using this parameter instead of the laser energy.

(4) How many laser pulses used for the measurement?

(5) How do the authors expect that this data processing technique for the sample with matrix effect?

(6) Page 26, line 423: The authors use "noise" in the text. Does it mean the continuum background or spectral background?

(7) Page 26, Fig. 15: The X-axis "the concentration ratio" needs to be specified.

(8) Page 26, Fig. 15 and page 28, Fig. 17: Maybe it is clear to insert the equations show the slope and interception of the calibration curves.

In summary, I encourage the authors to slightly improve the presentation along the comments above.



Reviewer #2 Evaluations:
Novelty: Adequate
Significance of Results: Adequate
Conclusions Supported: Good
Of interest to readers: Good
Length Appropriate: No
Clarity organization/writing: Adequate
Quality figs/tables: Adequate
Recommendation: publishable only after major revisions

Reviewer #2 (Comments for the Authors):

Comments on MS. # 12-06822

This work presents an algorithm for deconvolution of LIBS signals. From the algorithmic point of view there are some novel aspects in this paper. However, there are many shortcomings that have to be resolved before reconsideration of this paper for publication .

Novelty of work: Fair
Significance of the results: Fair
Are the conclusions well supported? Yes
Of interest to readers of Applied Spectroscopy? Yes
Clarity of organization and writing: Fair
Quality of figures and tables: Reasonable
Is the length appropriate? No

Detailed comments are listed below:

Major points

1- One of my main concerns about this manuscript is the considered objective function. Although the authors used different mathematical tools and non-linear optimization tools, the objective function is linear. Considering the norm of differences between original and reconstructed data does not justify the reliability of the method. As the authors may know, deconvolution methods are biased and different numbers of components by different shapes may give same values for objective function. Please clarify it.
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2- Another problem is related to the chemical rank determination (determination of the number of chemical constituents in each region). The analyzed data are univariate and determining the number of components in this type of signals is very difficult. They can get just an estimation of the real number of components in each spectral section. How could the authors be sure about the chemical rank?
Õâ¸öÎÒÔÚÎÄÕÂÀïÌáµ½ÁËÈçºÎÈ·¶¨£¬ÎªºÎËûÓÐÒÉÎÊ¡£ÎÒÐèÒªÔÙÖØнâÊÍ
3- The authors claimed the present method outperforms classical methods but the proofs for this are not enough. It would be worth it if they compare methods performance with more details. I think this is an important aspect that should be clarified.

4- The English level of the manuscript does not meet the required standard of this journal. I found many spelling and grammatical errors in the whole text. I strongly recommend the authors to improve the English level of the text.

5- The length of the manuscript is too long and there are too many Figures and Tables. The authors could reduce the length of the text and omit the redundant Figures and Tables from the manuscript. Please do that.


6- Theory section is again too long and it seems more like a thesis than an academic paper. Please rewrite this part with the emphasis on the important aspects of the calculations for the LIBS signal processing. Additionally, give some proper references for the rest.

7- Page 22: for the signal in Figure 12, please show the results for two and four components analyses to confirm that indeed there are three components.



Minor points

1- Line 43: I'm not sure about this statement. With the advent of good quality computers (i.e. PC and laptop), computational time for ANN is not too long. In addition, the proposed method in this work is not so easy from mathematical point of view compared to ANN.

2- Line 49: change word "reliability" to 'reliably'.


3- Line 156: Relocate the position of Figure 3 to Figure 2. The authors have to consider the order the Figures according to their appearance in the text.

4- Line 382: References are needed.
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