# GPSR: Gradient-Prior-Based Network for Image Super-Resolution
## 4 Experiments
### Ablation Experiments  
We analyze the effectiveness of the proposed modules, including GGS, LRSAM, and CRFS, via ablation experiments. The baseline model is built upon the proposed GPSR by removing the GB and replacing the RS3 AM-SR modules, which consist of CRFS and LRSAM, of the SR branch with the plain residual modules [10]. **Analysis on the gradient branch:** To verify the effectiveness of the GB, we visualize the output of the GB. Figure 6 illustrates the visual results of the GB. As can be seen from Figure 6a,d, the gradient maps of the HR images, which not only contain the sharp edge, but also effectively reflect the spatial structure relationship, are obtained by performing gradient feature extraction on the original HR images. This motivates us to design a detail-preserving GB to generates the gradient maps of the reconstructed images containing sharp geometric structures, and provides the essential gradient guidance for the SR process. Specifically, through the introduced GB, the gradient maps of the LR images (shown in \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **Number of Images** & **Size** & **Main Content** & **Function** \\ \hline DIV2K [41] & 900 & 5.8 GB & Humans, animals, and landscapes & Training \\ Set5 [42] & 5 & 1.30 MB & Humans and animals & Testing \\ Set14 [43] & 14 & 7.44 MB & Humans and animals & Testing \\ BSD100 [44] & 100 & 38.87 MB & Landscapes and animals & Testing \\ Urban100 [45] & 100 & 194 MB & Buildings & Testing \\ Manga109 & 109 & 219 MB & Manga & Testing \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of the dataset used for experiments. Figure 6b,e) were converted to the gradient maps of the reconstructed images (shown in Figure 6c,f). It can be observed that the gradient maps of the LR images are blurred and smooth in general, while the spatial structure details contained in the gradient maps of the reconstructed images (shown in Figure 6c,f) are significantly sharper and highly similar to the gradient maps of the HR images (shown in Figure 6a,d). This experimental result shows that the proposed GB possesses the ability to restore high-fidelity edge and texture information. This is because the proposed GB is able to generate the gradient maps at different scales and simultaneously transmit them as gradient priors for each upsampling stage on the SR branch to complement the multi-scale spatial structure features. **Analysis on gradient-guided loss:** We analyze the effectiveness of gradient-guided (GG) loss by removing \(L_{grad}^{pix}\) or \(L_{SG}^{pix}\) from the baseline model with the GGS, and report the results in Table 2. Here, \(L_{grad}^{pix}\) is used to supervise the outputs of the GB to ensure the accuracy of the multi-scale gradient maps. Additionally, \(L_{SG}^{pix}\) is used to supervise the gradient map of the final SR image. When \(L_{grad}^{pix}\) is removed, the GB of the corresponding model cannot be optimized, and it outputs unreliable multi-scale gradient maps, resulting in SR performance degrading from 32.61 dB to 32.31 dB. When \(L_{SG}^{pix}\) is removed, the SR performance of the corresponding model is reduced from 32.61 dB to 32.54 dB. It is because \(L_{grad}^{pix}\) can effectively avoid the SR model from blindly restoring high-frequency information. From the above analysis, optimizing \(L_{grad}^{pix}\) and \(L_{SG}^{pix}\) jointly is essential. Consequently, the proposed gradient-guided loss can guide the network to reconstruct accurate high-frequency details by taking full advantage of \(L_{grad}^{pix}\) and \(L_{SG}^{pix}\). **Analysis on gradient guidance strategy:** We visually compared the baseline with and without the GGS, including the GB and the GG loss.