## 4 Experiments
### Comparison with State-of-the-Art Methods  
Our method was compared with the state-of-the-art methods: SRGAN [36], RDN [44], RCAN [45], DRN [20], TransENet [35], SwinIR [26], and ESRGCNN [46]. In terms of network structure, SRGAN is based on a generative adversarial network, TransENet is based on a convolutional neural network structure, and the rest of the methods are based on convolutional neural networks. RCAN and DRN additionally used the channel attention structure. In terms of the ill-posedness of super resolution, SRGAN and DRN discussed this problem and proposed methods to reduce the ill-posedness by deepening the network, using GAN and increasing the number of supervision, respectively.  
The visual comparison of the output of each method is shown in Figure 2. From the visual comparison, our method has the advantage in reducing both the loss of details and the appearance of pseudo-detail during super resolution. Both PSNR and the structure similarity index measure (SSIM) were used as network performance evaluation metrics. The comparison of each network performance is shown in Table 1. Except for one value, our method outperformed existing SOTA methods. In the two-times super-resolution task, our method achieved a PSNR improvement of 0.29\(\sim\)2.48 dB over the existing optimal method. In the four-times super-resolution task, our method achieved a PSNR improvement of 0.47\(\sim\)3.57 dB over the existing optimal method. It can be seen that our method has a more significant performance improvement on the four-times super-resolution task than on the two-times task. This is because the ill-posedness of four-times super resolution is more severe than two times. The four-times super resolution has a more urgent need for additional supervision to reduce the ill-posedness. Accordingly, greater gains can be obtained by using a multi-level supervision structure on four-times super-resolution tasks. This also suggests that the larger the super-resolution scale factor, the greater the multi-level supervision structure needed to introduce adequate supervision. Exploring the benefits of multi-level supervision structures in super-resolution tasks with larger scale factors could be an interesting direction for future research. To validate the statistical significance of the experiments, [PERSON]'s test, a non-parametric statistical method, was employed to compare various methods. The \(p\)-values for PSNR and SSIM were calculated separately. The \(p\)-value for PSNR is \(1.88\times 10^{-6}\), and the \(p\)-value for SSIM is \(2.08\times 10^{-5}\). These \(p\)-values are both lower than the standard threshold of 0.05, indicating significant differences among the compared methods.  
Although a two-level supervised network was used, which may bring an increase in parameters, it can be seen that the proposed network still has advantages in terms of parameter quantity and will not bring additional burden to practical applications. As shown in Table 2, the computational complexity of different methods were calculated under our datasets. It can be seen that the proposed method has certain advantages in computational complexity comparing with other comparative methods. As mentioned before, multi-level supervised networks may increase computational complexity for the purpose of improving the performance of super resolution. But it has been proven that the computational complexity of the proposed network has not become a significant drawback of the network.  
Figure 2: Comparison of the 4-times super-resolution outputs of P2P-SR and other methods [20; 26; 35; 36; 44; 45; 46]. There are seven sets of images from different scenes. In each set of results, HR is the high-resolution original image, GT is a local zoom of the HR image, and LR is a local zoom of the low-resolution input image. Also shown in each set of pictures are the results of the seven compared methods (**a–g**) as well as our method.