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Reviewer: 1

Recommendation: Reject (updates required before resubmission)

Comments:
The authors proposed a face super-resolution (FSR) network based on a gradient information compensation module. This paper believes that the gradient information is beneficial to the performance of FSR, and designed a special module to extract the gradient information of the feature maps. I think this article is interesting and looks good, but there are still some issues that need to be revised (unordered):
(1) In order to prove the effectiveness of the proposed method, the authors conducted a series of ablation studies. However, ablation research must follow some principles. For example, when authors prove that their GRBs are beneficial to improve the performance of the network, they should not prove by reducing the number of GRBs. Because it is not clear whether the performance loss is due to the reduction in the number of parameters or the lack of gradient information. Considering that the gradient layer is an artificial design without any learnable parameters, and its computational complexity is negligible. So it seems more reasonable to delete the gradient layer directly and observe the network performance.
(2) The author declares "Since only the test code of FSRNet was released, we re-implement FSRNet with Pytorch". I would suggest highlighting this difference in Table 1 with ¡®*¡¯ or similar symbols.
(3) When comparing the proposed method with the SOTA method, the computational complexity and parameter amount of each method should also be listed, which will help to study the efficiency of the network.
(4) I think the author missed some existing methods, especially the SOTA method since 2020. I think the author needs to add several recent SOTA methods and compare the proposed method.

Comments:
This manuscript should be resubmitted after being revised according to the follows as
Comment 1£ºThe overall framework of Figure 1 needs to be properly described. And some symbols in the figure are confused.

Comment 2£ºRCAB is used in the proposed method, but its introduction and implementation details are missing.

Comment 3£ºIn page 6, the GFNet is compared with state-of-the-art methods and achieves better results. However, the comparison methods are put forward from 2014 to 2019. References are not the recent one and some appropriate key studies are missing.

Comment 4£ºIn Abstract, ¡°the proposed network is able to reconstruct fine face images with a performance improvement of 0.3 dB PSNR and 0.82 dB PNSR¡±. This is really confusing. What is the comparison method? How do you get the results of 0.3 dB PSNR and 0.82 dB PNSR? These are not mentioned in the text.

Comment 5£ºThe format of references is incorrect, such as [1], [12], [14], [15], [20], etc.

Comment 6£ºTo have an unbiased view in the paper, there should be some discussions on the limitations of the method.

Comment 7£ºThe grammar needs to be carefully revised. There are many spelling mistakes, such as "dsuper-resolution" on page 2.
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