# GPSR: Gradient-Prior-Based Network for Image Super-Resolution
## 4 Experiments
### Results with Bicubic (BI) Degradation
#### 4.3.1 Quantitative Metrics  
For quantitative comparison, we compare the PSNR and SSIM metrics of different methods for the SR task with scaling factors \(\times\)4 and \(\times\)8. Table 4 lists the comparison of \(\times\)4 and \(\times\)8 quantitative results on the five commonly benchmark datasets, including Set5, Set14, BSD100, Urban100, and Manga109, where the optimal and suboptimal metrics are highlighted in red and blue, respectively, and where '-' means that the result is not available. Params and FLOPs denote the total number of parameters and floating-point operations, respectively. Noted that each the efficiency proxy FLOPs is measured under the setting of upscaling reconstructed images to the size of 1280 \(\times\) 720 on the scaling factors \(\times\)4 and \(\times\)8. It should be noted that we derive the results of the methods used for comparison from their pre-trained models, released code, or their original paper. It is worth noting that some comparison methods, including HAN, RDN, EDSR, PA-EDSR, and NLSN, do not offer experimental results for \(\times\)8 SR. Therefore, we retrained these models on the \(\times\)8 scaling factor with their official source codes. In addition, for a fair comparison, we retrained DRN on the DIV2K dataset, as it originally used the DF2K dataset as the training set.  
For convenience to quantitative comparisons, we take Set5 (\(\times\)4) as an example. From Table 4, we observe that SR models #1 with deeper network structures and more extensive connections, including DBPN, RDN, and EDSR, obtain approximately 0.9 dB of PSNR gains compared to LapSRN. Further, SR models #2 with attention mechanisms, including HAN, SAN, PA-EDSR, and NLSN, can adaptively emphasize useful feature information for more accurate image reconstruction. The PSNR gains of models #2 over #1 range from 0.12 dB to 0.19 dB. However, the above models ignore the potential of the gradient prior for image SR. In contrast, the proposed GPSR makes full use of the gradient map to restore sharp high-frequency details, and obtains the highest quantitative metrics. It is worth noting that the proposed GPSR achieves a performance advantage of 0.09 dB with fewer parameters (18% parameters of PA-EDSR) and FLOPs (34% Flops of PA-EDSR) compared to PA-EDSR, which obtains sub-optimal SR results.This indicates that the proposed GPSR takes into account the computational efficiency while pursuing performance.  
From Table 4, we can see that GPSR shows superior performance for both \(\times\)4 and \(\times\)8 SR tasks. GPSR+ achieves the optimal results on all test datasets. Compared with the nine state-of-the-art methods, the PSNR and SSIM metrics obtained by our GPSR are optimal in most test datasets. Specifically, our GPSR performs optimally on all datasets for both \(\times\)4 and \(\times\)8 SR tasks, except for the suboptimal SSIM metric on BSD100 for the \(\times\)4 SR task. Consequently, Table 4 provides adequate evidence that the proposed GPSR achieves the optimal super-resolution performance in the SR tasks with large scaling factors. Furthermore, Table 4 also presents the number of parameters and FLOPs for different SR methods. Overall, the proposed GPSR achieves a better tradeoff between computational efficiency and the super-resolution performance.  
We also present an illustrated comparison in terms of the PSNR metric and the number of parameters for both the \(\times\)4 and \(\times\)8 SR tasks in Figure 8. As can be seen from Figure 8, compared with other SR models used for comparison, the proposed GPSR achieves the highest PSNR with a small number of parameters on the Set5 dataset for both the \(\times\)4 and \(\times\)8 SR tasks, indicating its optimal super-resolution performance.