Second-Order Gradient Loss Guided Single-Image Super-Resolution

With the development of deep learning, convolutional neural networks for single-image super-resolution have been proposed and achieved great success. However, most of these methods use L1 loss to guide network optimization, resulting in blurry restored images with sharp edges smoothed. This is because L1 loss limits the optimization goal of the network to the statistical average of all solutions within the solution space of that task. To solve this problem, this paper designs an image super-resolution algorithm based on second-order gradient loss. This algorithm imposes additional constraints on the optimization of the network from the high-order gradient level of the image so that the network can focus on the recovery of fine details such as texture during the learning process, and alleviate the problem of restored image texture over-smoothing to a certain extent. During network training, we extract the second-order gradient map of the generated image and the target image of the network and minimize the distance between them, this will guide the network to pay attention to the high-frequency detail information in the image to generate a high-resolution image with clearer edge and texture. It is worth mentioning that our proposed loss function has good embeddability, which can be easily integrated with existing image super-resolution networks. Experimental results show that the second-order gradient loss can significantly improve both Learned Perceptual Image Patch Similarity(LPIPS) and Frechet Inception Distance score(FID) performance of existing image super-resolution deep learning models.