# Residual Dense Swin Transformer for Continuous-Scale Super-Resolution Algorithm
## 1 Introduction  
Single-image super-resolution (SISR) refers to the technical means to restore a low-resolution image to a high-resolution image. It is widely used in the fields of medical imagery [1; 2], remote sense image [3; 4], monitoring, and security [5; 6]. Therefore, this technology has long been a research hotspot in the field of computer vision. In most of today's application scenarios, people expect to enlarge an image to any scale without losing the high-frequency details of the image. However, because a low-resolution image can correspond to multiple different high-resolution images, SISR becomes an ill posed problem. How to use the single model to approximate the optimal solution in the super-resolution space of arbitrary scale amplification is still a difficult problem. Therefore, it is of great significance to study a continuous-scale super-resolution algorithm with excellent performance. SISR algorithms can be divided into two categories: traditional methods and deep-learning-based methods. [PERSON] [7] drew on the idea of compressed sensing, performed sparse representation of low-resolution images, and used prior knowledge to complete the dictionary learning of high-resolution images to achieve super-resolution reconstruction; [PERSON] et al. [8] used locally linear embedding in manifold learning. To achieve linear mapping from low-resolution space to high-resolution space, both [PERSON] [9] and [PERSON] [10] proposed the example-based super-resolution method; the difference between the methods being that the latter transforms the patch to find a more similar patch in the low-resolution to high-resolution images. However, the super-resolution effect of these traditional methods is limited, and they struggle to meet application requirements in real life. Algorithms basedon deep learning, especially based on convolutional neural networks, exhibit excellent performance that traditional methods do not have. Since [PERSON] [11] first brought CNN into the SR field, countless SISR algorithms have been developed, and the SRCNN structure has been improved. Most of them use residual connections, dense connections, and iterative supervision to continuously deepen the CNN [12; 13; 14; 15]. Although this approach solves the problem of limited receptive field caused by CNN fixed-size convolution to a certain extent, it still does not fundamentally solve the problem of global information loss. In addition, there are very few studies on super-resolution at any scale. [PERSON] et al. [16] used multiple upsampling modules for training to achieve integer multiples of multiscale super-resolution. Refs. [17; 18] used the pooling layer and local implicit functions to achieve arbitrary scales of super-resolution, but they both focused on building modules that can achieve arbitrary scales of upsampling, while ignoring the importance of feature extraction. The development of the Transformer [19] in the field of CV, especially the emergence of the ViT [20] and Swin Transformer [21], has provided new ideas for scholars in the field of SISR. ViT was the first method to successfully apply Transformer to the computer field and achieve the same or even surpassing the effect of CNN. It slices the image and performs patch embedding, using it as the input sequence of the Transformer. Based on this, some scholars [22; 23; 24] have proposed performing super-resolution tasks and realized new SOTA performance at that time. On this basis, the Swin Transformer uses the idea of CNN to introduce a shift window to enhance the performance of network local feature extraction and reduce the amount of calculation. Based on this, ref. [25] introduced the idea of partial windows to further improve the super-resolution effect. It is obvious that none of these Transformer-based methods can make full use of the low-level and high-level information and cannot achieve image super-resolution on a continuous scale.