Paper:
Super Resolution (SR) is a fundamental and important low-level computer vision (CV) task. Different from traditional SR models, this study concentrates on a specific but realistic SR issue: How can we obtain satisfied SR results from compressed JPG (C-JPG) image, which widely exists on the Internet. In general, C-JPG can release storage space while keeping considerable quality in visual. However, further image processing operations, e.g., SR, will suffer from enlarging inner artificial details and result in unacceptable outputs. To address this problem, we propose a novel SR structure with two specifically designed components, as well as a cycle loss. In short, there are mainly three contributions to this paper. First, our research can generate high-qualified SR images for prevalent C-JPG images. Second, we propose a functional sub-model to recover information for C-JPG images, instead of the perspective of noise elimination in traditional SR approaches. Third, we further integrate cycle loss into SR solver to build a hybrid loss function for better SR generation. Experiments show that our approach achieves outstanding performance among state-of-the-art methods.

Review:
In this article, the authors propose a single image super-resolution network that can generate high-resolution images from the corresponding C-JPG images. The method contains two main parts, namely a JPG recovering step, which recovers the information from low-quality JPG images, and an SR generation step, which generates SR images from the images achieved by the recovering step. Moreover, the authors leverage a cycle loss to generate better results.
The main contribution of this work is only the integration of existing models. The authors claimed that the proposed method is lossless, while there is no evidence to demonstrate it. The authors should show more evidence about the JPG recovering step, like how much information it can recover. Moreover, the SR generation step only incorporates s-LWSR without any improvement. It makes SR in this manuscript more like an application for the JPG recovering method rather than a contribution to the SISR field. 
In the experimental section, Figure 5 makes readers confused. Does the image entitled “s-LWSR(Training)” mean the “STRAIGHT TRAINING” described in section 4.2.1? If yes, is there any perceptual difference between the result of s-LWSR and the result of ours? It is suggested that the authors should reorganize the results and provide more instructions. In Table 1, the results derived from s-LWSR32(C-JPG) and the proposed are very similar. The authors should more convincingly show the advantages of the proposed method. From the results, I observe that the SR images of the proposed model are blurry and lack much information about textures. At the same time, there are some other SISR studies, especially GAN based models like ESR-GAN, which show visual quality with more realistic and natural textures. I hope the authors can conduct more comparisons with these methods.
There are still some issues as follows:
1.	The authors should carefully check the format of the references in the whole article. For instance, in section 4.1, almost all references are in the wrong format. The same mistake happens in the caption of Figure 6. Please check the full article before submission.
2.	(Page 1, line 2 from bottom) Please add a reference to “bicubic”.
3.	(Section 3, line 1) Please add a full stop after “Challenge Formulation”.
4.	(Figure 2) Please enlarge the arrow of the red lines. They are hard to read right now.
5.	(Figure 4) The figure seems to miss the skip connect of the former five layers, which should be a part of the input added to the latter four layers (Li et al., 2019). In addition, please enlarge the arrow of the blue lines.
6.	(Section 4.2.1, line 4) “Both of the PSNR …” Does figure 5 can reflect this? Please add data instruction.