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Volume 11
Issue 3
10.3390/axioms11030101
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Article
Peer-Review Record

Truncated Fractional-Order Total Variation for Image Denoising under Cauchy Noise

Axioms 2022, 11(3), 101; https://doi.org/10.3390/axioms11030101
by Jianguang Zhu 1, Juan Wei 1, Haijun Lv 1,* and Binbin Hao 2,*
Reviewer 1: Anonymous
Reviewer 2: Anonymous
Axioms 2022, 11(3), 101; https://doi.org/10.3390/axioms11030101
Submission received: 24 January 2022 / Revised: 13 February 2022 / Accepted: 16 February 2022 / Published: 25 February 2022

Round 1

Reviewer 1 Report

Would you please explain any difference of your paper and the following published one? 

10.1109/ICNC.2008.172

Author Response

Point 1: Would you please explain any difference of your paper and the following published one?

 10.1109/ICNC.2008.172

Response 1:  Thanks very much for your comments. According to the suggestion, I will explain the differences between these two articles from two aspects.

  On the one hand, our paper is mainly about the removal of Cauchy noise subject to Cauchy distribution, while the published paper is about the removal of Gaussian noise subject to Gaussian distribution. This results in different data fidelity terms in the model between our paper and the published paper.

  On the other hand, the fractional-order total variation regularization term is used in the published articles, while our model uses truncated fractional-order total variation regularization term. Truncated fractional-order total variation regularization not only keeps the advantages of fractional-order total variation, but also can better preserve the edge and suppress the staircase effect.

  In short, our work uses truncated fractional-order total variation regularization term to remove Cauchy noise, while the paper published uses fractional-order total variation regularization term to remove Gaussian noise. 

Point 2: English language and style are fine/minor spell check required.

Response 2: Thanks very much for your comments. According to the suggestion, we have carefully checked and improved the English writing in the revised manuscript.

Reviewer 2 Report

In this paper, the authors proposed a model/method to removing Cachy noise from figures with the use of a fractional-order variation.
This paper is well written, and it is easy to understand the main motivation and the results. 
The most strong point of this paper is a detailed numerical experiments section.
Throughout this paper, the examples and results are correct. The obtained results are new and meaningful. This paper is, manly, very useful for those who need to work with image processing.

Author Response

Point 1: In this paper, the authors proposed a model/method to removing Cachy noise from figures with the use of a fractional-order variation.This paper is well written, and it is easy to understand the main motivation and the results. The most strong point of this paper is a detailed numerical experiments section.Throughout this paper, the examples and results are correct. The obtained results are new and meaningful. This paper is, manly, very useful for those who need to work with image processing.

Response 1: Thanks for your valuable feedback.

Point 2: English language and style are fine/minor spell check required.

Response 2: Thanks very much for your comments. According to the suggestion, we have carefully checked and improved the English writing in the revised manuscript.

Author Response File: Author Response.docx

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