## 1 Introduction  
Single image super-resolution (SISR) reconstruction is the development of high-resolution (HR) images with richer details and clearer texture from low-resolution (LR) images or degraded images and has wide applications in the field of image processing [1; 2; 3; 4; 5]. At present, reconstruction techniques are divided into three main categories: interpolation-based, reconstruction-based, and learning-based methods. The interpolation reconstruction method proposed here includes nearest interpolation, bilinear interpolation, and bicubic interpolation. Further proposed reconstruction-based methods are iterative back projection (IBP) [6], projection onto convex sets (POCS) [7], and maximum a posteriori (MAP) [8]. Some learning-based methods have been proposed, including the early collar neighbor embedding (NE) [9] algorithm and the sparse representation-based classification algorithm [10]. Deep resolution reconstruction methods based on deep learning are gaining more attention. The super-resolution convolutional neural network (SRCNN) [11] algorithm introduceddeep learning methods to SISR for the first time. In order to improve the network convergence speed of SRCNN, accelerating the super-resolution convolutional neural network (FSRCNN) [12] was developed. Efficient sub-pixel convolutional neural network (ESPCNN) [13] was also proposed to further improve the efficiency of computation. In order to further recover the high-frequency detail of images, [PERSON] [14] et al. proposed a deep learning method called data-driven external compensation guided deep networks for image superresolution. Traditional deep learning methods can optimize image quality by making the network structure deeper, to obtain more image features. The introduction of generative adversarial networks (GAN) [15] is a new direction for SISR. Super-resolution generative adversarial network (SRGAN) [16] applied GAN to SISR for the first time. The images generated by SRGAN are clearer and more detailed than those produced using similar reconstruction methods. However, there are also shortcomings, such as edge blurring, image artifacts, excessive numbers of network parameters, and difficulty in achieving convergence of the neural network. The Wasserstein GAN [17] uses a gradient penalty to try to solve the problems of neural network training. In this paper, we propose a GAN based on depthwise separable convolution dense blocks, which can improve computational efficiency by greatly reducing the number of parameters. It also reduces algorithm complexity, reduces reliance on hardware resources, and extends the range of applications. For the better restoration of image edges and improvement of the quality of super-resolution images, we introduce a new loss function for generative networks: the frequency energy similarity loss function. This new loss function is used to constrain the generator network so that the image quality is better and the edges are clearer. In image super-resolution reconstruction experiments using the benchmark datasets Set5 and Set14, the performance of the depthwise separable convolution super-resolution generative adversarial network (DSCSRGAN) algorithm according to the objective indicators peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and mean square error (MSE), was better than that of similar algorithms. In terms of subjective visual evaluation, the super-resolution algorithm made the image edges clearer, the details richer, and according to comprehensive subjective and objective evaluation, the reconstruction algorithm described in this paper achieved good results. We describe the DSCSRGAN architecture, energy similarity loss function, and the DSC Dense Block in Section 3. The visual illustrations are provided in Section 4. The paper concludes with a discussion in Section 5. In summary, we would like to make the following technical contributions:  
* We propose DSCSRGAN. This is the first time that depthwise separable convolution has been used for SISR.