# GPSR: Gradient-Prior-Based Network for Image Super-Resolution
###### Abstract  
Recent deep learning has shown great potential in super-resolution (SR) tasks. However, most deep learning-based SR networks are optimized via pixel-level loss (i.e., L1, L2, and MSE), which forces the networks to output the average of all possible predictions, leading to blurred details. Especially in SR tasks with large scaling factors (i.e., \(\times\)4, \(\times\)8), the limitation is further aggravated. To alleviate this limitation, we propose a Gradient-Prior-based Super-Resolution network (GPSR). Specifically, a detail-preserving Gradient Guidance Strategy is proposed to fully exploit the gradient prior to guide the SR process from two aspects. On the one hand, an additional gradient branch is introduced into GPSR to provide the critical structural information. On the other hand, a compact gradient-guided loss is proposed to strengthen the constraints on the spatial structure and to prevent the blind restoration of high-frequency details. Moreover, two residual spatial attention adaptive aggregation modules are proposed and incorporated into the SR branch and the gradient branch, respectively, to fully exploit the crucial intermediate features to enhance the feature representation ability. Comprehensive experimental results demonstrate that the proposed GPSR outperforms state-of-the-art methods regarding both subjective visual quality and objective quantitative metrics in SR tasks with large scaling factors (i.e., \(\times\)4 and \(\times\)8). super-resolution; deep learning; gradient prior; feature representation; spatial attention +
Footnote †: journal:  
an SISR task and successfully proposed NLSN [13] and PA-EDSR [14], which fully utilize numerous highly similar textures within the image to synthesize the high-fidelity images. However, most deep learning-based SR methods are optimized via pixel-level loss (i.e., L1, L2, and MSE), which guides the SR process by minimizing the pixel-to-pixel distance between the reconstructed images and the HR reference ones. Under such a constraint, the SR model tends to output the average of all possible predictions, resulting in blurred details of the reconstructed images. More seriously, the limitation is further aggravated in SR tasks with large scaling factors (i.e., \(\times\)4 and \(\times\)8). Therefore, it is important to improve the high-frequency detail reconstruction capability of the pixel-level loss-based SR models. Considering that the gradient map of an image can reflect the spatial distribution of the high-frequency information, but also identify the local regions where the high-frequency components exist, we attempt to exploit the gradient map to guide the network to restore the appropriate edge and texture details at the suitable positions. To this end, we fully explore the potential of the gradient prior for the SR task and then propose a detail-preserving Gradient-Guided Strategy (GGS) to attain sharp edge and texture details, and to preserve the geometric invariance of the reconstructed images. Specifically, on the one hand, due to the strong correlation between the gradient information and high-frequency components, the gradient information can be transformed into the sharp edge and texture features. Thus, we introduce an additional gradient branch in the classical network with a single SR branch. The introduced gradient branch works as a feature selector that adaptively extracts structural features to provide a gradient prior for the SR branch. On the other hand, we propose a compact Gradient-Guided (GG) loss function to avoid blindly restoring high-frequency details by constraining the spatial structure of the reconstructed images. The proposed GGS facilitates the suppression of undesired geometric distortions while preventing over-smoothing or over-sharp recovery. Furthermore, the benefit from multi-level contextual residual features, which are hierarchical with different receptive fields, can provide valuable cues for SR task from different perspectives.