Color Image Recovery Using Generalized Matrix Completion over Higher-Order Finite Dimensional Algebra

Round 1

Reviewer 1 Report

This work presents a recovery method based on generalized high-order scalars to improve the accuracy of color image completion with missing entries. Please address the following comments and questions:  

1.       On line 61, it should be “For example, Zeng introduced …”.

2.       How is the proposed higher-order t-matrix model validated in the study?  

3.       What are the drawbacks of this color image recovery technique, and how to improve them? Please address this question in detail in the Conclusions section.

4.       How difficult is it to commercialize this technique?   

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript discusses an image recovery method to enhance the accuracy of color image completion with missing entries. The proposed approach extends from the traditional second-order matrix model to a higher-order matrix model "t-matrix." Through the proposed method, standard matrix and tensor completion algorithms can apply to higher-order computations. The comparative experiments show that the proposed method outperforms the lower-order tensor and conventional matrix method. 
The manuscript is detailed and the review recommends acceptance once comments regarding writing/language and other reviewers' comments are properly addressed. 

The paper is well-written with good-quality grammar and mechanics. However, I recommend paying closer attention to details and conducting another round of proofreading. For instance, line 61 on page 2/22,  there needs to be a space before "Zeng introduced...". 

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

This paper extends a tensor completion algorithm to the higher-order version, which incorporates spatial information of the image for the local constraint. This paper presents various discussions on the model. Experiments on simulated and real data sets demonstrate the effectiveness of the design. My comments are:

 1. The authors provide a literature review in the Introduction. However, it is unclear the real motivations of this work. Which problems are addressed exactly?  

2. It is not clear what is the objective function to be optimized with Algorithm 4. The authors need to indicate clearly the model in the paper.

 3. In Section 4.2, the authors give some discussions on the higher-order rand and its variants. Which one is adopted in the model? What is the definition?

 4. The authors can compare with more recent SOTA methods to validate the effectiveness of the model. 

5. In the experiments, it is better to show the ground truth and the restored images within one figure. Also, the authors can highlight the differences between different methods. 

6. The authors can report the running time of different methods, which is very interesting.

 7. In the introduction, some references are missing. For instance, the method proposed by Lu (line 91). 

8. There are a number of techniques developed to process high-dimensional data. The following SOTA methods should be mentioned, including DOI: 10.1109/TKDE.2021.3087517, DOI: 10.1109/TGRS.2021.3127536, DOI: 10.1109/TCYB.2020.3023973.

 9. There are a few typos in the paper. For instance, line 60: “For example,Zeng”; line 91; “Our model is inspired by and ….. data”; line 340: “An RGB image”.

See my comments.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Thanks for the revision. I have no more comments.