# GPSR: Gradient-Prior-Based Network for Image Super-Resolution
## 4 Experiments
### Ablation Experiments
Specifically, the LR images (shown in Figure 7a,d) as the network input, the reconstructed images, and the corresponding absolute gradient intensity maps (shown in Figure 7b,e) obtained using the model without GGS, and the reconstructed images and the corresponding absolute gradient intensity maps (shown in Figure 7c,f) obtained using the model with GGS, are depicted in Figure 7. Notably, the absolute gradient intensity maps directly reflect the quality of edge and texture details of the reconstructed images by using the brightness of color. The brighter the color \begin{table}
\begin{tabular}{c c c c} \hline \(L_{grad}^{pix}\) & ✓ & & ✓ \\ \(L_{SG}^{pix}\) & & ✓ & ✓ \\ \hline PSNR & 32.54 & 32.31 & 32.61 \\ \hline \end{tabular}
\end{table} 
Table 2: Ablation experiments on gradient-guided loss, including \(L_{grad}^{pix}\) and \(L_{SG}^{pix}\). The average PSNR values are evaluated on Set5 dataset with scaling factor \(\times\)4. Figure 6: Results of gradient branch. Among them, (**a,d**) are the gradient maps of the reference HR images, (**b,e**) are the gradient maps of the corresponding LR images, and (**c,f**) are the gradient maps of the reconstructed images generated by the gradient branch. is, the sharper the structure details are. From Figure 7b,c, it can be seen that the sharpness of the whiskers in the reconstructed image is significantly improved by adopting GGS. Additionally, compared with Figure 7e, the wire on the window in Figure 7f appears sharper, which is more evident in the absolute gradient intensity map in Figure 7f. Additionally, the PSNR of the reconstructed images (i.e., Figure 7c,f) obtained by the model with GGS is significantly improved by 0.09 dB and 0.38 dB, respectively, compared to the baseline. It indicates that the proposed GGS not only strengthens the edge and texture details, but also alleviates the geometric distortion well. **Analysis on effects of CRFS, CRFS, and GGS:** We conduct ablation experiments to analyze the effectiveness of CRFS, CRFS, GGS and their combinations, and report the results in Table 3. Compared with the baseline, the models with only CRFS or LRSAM achieve better results by up to 0.06 dB and 0.06 dB in terms of the PSNR metric, respectively. These results demonstrate that fusing the contextual residual feature can provide more advanced features for SR task, and spatial attention mechanisms with large-sized receptive fields can effectively explore valuable spatial content. At the same time, compared with the baseline, the PSNR obtained by the model with only GGS improves by 0.15 dB. It can be seen that our GGS possesses the highest contribution to performance improvement. This is because GGS provides the beneficial gradient prior for the SR process, which facilitates the guidance of the GPSR model to restore sharp high-frequency details. Furthermore, the improvement of the model with both CRFS and LRSAM is significant, with a PSNR improvement of 0.17 dB over the one with only CRFS, which indicates that LRSAM is able to effectively promote the feature representation ability of CRFS. Finally, we obtained the highest gain (0.28 dB) by the model with LRSAM, CRFS, and GGS simultaneously, which is the GPSR model. \begin{table}
\begin{tabular}{c c c c c c c c} \hline LRSAM & ✓ & & & ✓ & ✓ & & ✓ \\ CRFS & & & ✓ & & ✓ & & ✓ \\ GGS & & & ✓ & & ✓ & ✓ & ✓ \\ \hline PSNR & 32.46 & 32.52 & 32.52 & 32.61 & 32.63 & 32.70 & 32.67 & 32.74 \\ \hline \end{tabular}
\end{table} 
Table 3: Investigations of LRSAM, CRFS, and GGS. We observe that the proposed GPSR, that is, the model that uses LRSAM, CRFS, and GGS simultaneously, achieves the best super-resolution performance on Set5 dataset with scaling factor \(\times\)4. Figure 7: Visual comparison of the baseline with and without the Gradient-Guided Strategy (GGS). We present the LR images, the reconstructed images, and the absolute gradient intensity maps corresponding to the reconstructed images.