Deblurring Turbulent Images via Maximizing L1 Regularization

Round 1

Reviewer 1 Report

Dear Authors!

I have carefully read your work on the development of an algorithm for deburring images distorted by atmospheric turbulence. The problem you are investigating is urgent for a variety of fields, from artistic photography to astronomy and aerial photography, so I warmly approve your research.
As for the manuscript, it is written at a high scientific level. Its structure is clear and consistent, it is high quality illustrated, the necessary formulas and algorithms are given. After reading, one gets an understanding of the essence of your solution. The results of the work are inspiring, which is reflected in the description of the contribution and in the conclusions.
However, I have found a few minor flaws.
1. Formula (2) gives the reader an understanding of what ML1 regularization is, but there are no formulas for L1 and other regularizations for the non-specialist to easily see the difference.
2. If I understand correctly, in Figures 5 and 6 you show the result of the algorithms on images with different blur kernels. Thus, it looks like you have selected such kernels to make your algorithm seem more advantageous. Despite the fact that in Figures 7 and 8 you show the analysis for all types of blur nuclei and they confirm the high efficiency of your algorithm, I strongly recommend comparing the results of the algorithms in Figures 5 and 6 with the same blur kernel.
3. Figure captions must be formatted according to the MDPI template.
4. I don't understand the phrase "norms decrease as the image becomes solutions" (line 95). Please, clarify. Also, in line 247 please replace 'As' with 'In'.
4. ORCID for 1st author is wrong and consists of zeros, other authors ORCIDs are missed. To improve the visibility of your other works, please leave readers as much information about you as possible.

Author Response

We gratefully thank the reviewer for his/her time spend making his/her constructive remarks and useful suggestions, which has significantly raised the quality of the manuscript and has enabled us to improve the manuscript. Each suggested revision and comment brought forward by the reviewers was accurately incorporated and considered.

Author Response File: Author Response.pdf

Reviewer 2 Report

The work that is reported in the paper with the title "Deblurring Turbulent Image via Maximizing L1 Regularization" discusses on the problematic of removing blur artefacts from useful image data. Thus, the authors describe a suppression projected alternating minimization algorithm, which has the goal to approximate the latent sharp image data, and the blur kernel. The authors test their proposed model using a rather small synthetic image data set, which they generate. I appreciate that the authors provide an acceptable description of their proposed approach's mathematical core. Nevertheless, the synthetic data set is barely enough in order to demosntrate the model's validity as a research prototype. It offers no suggestion concerning the possible suitability of the described approach for the possible processing of large/big real world data. Additionally, the algorithmic approach that is considered in order to generate the synthetic images is not sufficiently described. The authors claim that they also assess their model on real world image data, but they essentially do not provide any description of the mentioned real world data. They should provide indications regarding the size of the respective data sets, the features of typical individual images in the data set, and also quantitative indications to demonstrate the claimed superior behaviour compared to the mentioned existing approaches. 

Additionally, the English language is rather poor, The paper should be fully proofread and re-written, in order to comply with the standards of a scientific paper.

Author Response

We gratefully thank the reviewer for his/her time spend making his/her constructive remarks and useful suggestions, which has significantly raised the quality of the manuscript and has enabled us to improve the manuscript. Each suggested revision and comment brought forward by the reviewers was accurately incorporated and considered.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

I am able to attest that the authors considered and effectively incorporated the suggested changes into their paper. Furthermore, the English language has been improved. I could mention just one significant aspect that pertains to an assertion that the authors make. Thus, they enrich their test data set, and immediately infer that this demonstrates the possible suitability of their model for the processing of larger real-world data. This does not constitute sufficient proof in order to make this assertions. Nevertheless, I appreciate that the authors' work is worth to be reported and may be considered for publication.

Author Response

We are very grateful to the reviewer for his/her valuable comment and approval of our work.

Author Response File: Author Response.pdf