## 1 Introduction  
In recent years, with the impact of the Internet boom and the rapid development of information technology, people's requirements for signal and information processing have gradually increased, and image processing is an important part of information processing. Additionally, image super-resolution (SR) technology is particularly important in image processing. The principle is to pass one or more low-resolution (LR) images to the final high-resolution (HR) image through information processing technology. The traditional method is to enlarge the LR small image to the required size by interpolation,and then use the reconstruction algorithm to obtain an HR image. The super-resolution reconstructed image has clear details and contains plenty of information, so it can be widely used [1; 2]. For example, in the crime scene video, HR images provide more favorable evidence for the public security organs' investigation. In satellite imaging applications such as remote sensing and resource detection, HR images can easily distinguish between two or more similar objects. In medicine, HR images can provide doctors with a more accurate basis for diagnosis, and, thereby, greatly improves diagnostic accuracy. Therefore, an image super-resolution algorithm has great research value. At present, there are many algorithms for super-resolution (SR). In the research of interpolation-based image super-resolution reconstruction algorithms, the input LR image is mainly denoised, deblurred, and up-sampled to improve the image resolution. Among them, the more classic interpolation algorithms include: the nearest neighbor interpolation, the linear interpolation, the bicubic interpolation, and the spline interpolation [3]. The most classic dictionary-based sr algorithm is sparse encoding [4], which seeks a sparse representation of LR input image blocks and then uses the coefficients of this sparse representation to generate HR output. The LapSRN [5] model based on the pyramid algorithm was proposed by [PERSON] et al. It is special in that it introduces a hierarchical network. Each level only doubles the original image and adds the residuals to get a result. The learning-based image super-resolution algorithm mainly learns the similarity between high-resolution and low-resolution image blocks, and generates low-resolution image blocks to be processed into corresponding high-resolution image blocks. It is mainly learned through convolutional neural networks. First, [PERSON] et al. applied a convolutional neural network to image super-resolution reconstruction, which is called a super-resolution convolutional neural network (SRCNN) [6]. The network well implements end-to-end image reconstruction. The hidden layer of the convolutional neural network (CNN) completes all feature extraction and aggregation, but SRCNN does not consider any self-similarities. Since then, more people have proposed image super-resolution algorithms based on CNN. For example, another algorithm a Accelerating the Super-Resolution Convolutional Neural Network (FSRCNN) proposed by [PERSON] et al. [7]. Compared with SRCNN, this algorithm does not need to use interpolation to enlarge the original LR images, but process these directly. Its advantage is to shorten the training time by reducing the picture size. In addition, [PERSON] et al. proposed the Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network (ESPCN) [8] model. This model is based on small images for training. The experimental results of super-resolution processing of real-time video are very ideal. The Accurate Image Super-Resolution Using Very Deep Convolutional Networks(VDSR) [9] model was proposed by [PERSON] et al. Its input is divided into two parts. One part is to take the entire original images as input, and the other part is to train the residuals and get input. We add the two parts together to get HR images, which greatly speeds up the training and converges better.