# Multi-Scale Factor Image Super-Resolution Algorithm with Information Distillation Network
## 1 Introduction  
In computer vision, single image super-resolution (SISR) is currently a hot research topic, which reconstructs a high-resolution (HR) image from a low-resolution (LR) image through image processing methods in the same scene [1]. SISR is widely used in the fields of medicine, transportation, and remote sensing. Since one LR image can generate several HR images, SISR has no unique solution [2]. To address this problem, numerous image SR methods based on deep neural network architectures have been proposed and have shown prominent performance. Since deep learning shows strong advantages in various computer vision tasks, [PERSON] et al. [3, 4] achieved feature extraction, nonlinear matching, and image reconstruction by a three-layer network. VDSR [5] expanded dramatically the depth of the network to 20 by stacking multiple layers to enhance the receptive field. At the same time, [PERSON] et al. [6] proposed DRCN for the first time to apply recursive learning to SR tasks. [PERSON] et al. [7] first adopted a DRRN to reduce parameters. In addition, [PERSON] et al. [8] used a persistent memory network (Mem-Net) that stacks with a densely connected structure to resolve the dependency problem. EDSR [9] removed the batch normalization (BN) layer and used the residual scaling to speed up the training. [PERSON] et al. [10] added densely connected blocks to the residual to form a residual dense network (RDN). The RDN makes full use of global and local features to enhance SR performance. GFSR [11] used a gradient-guided and multi-scale feature network for image super-resolution. HRFFN [12] designed an enhanced residual block (ERB) containing multiple mixed-attention blocks (MABs) to boost the representative ability of the network. The above algorithms all increased the network depth to upgrade the quality of images [13]. [PERSON] proposed twolightweight neural networks with a hybrid residual and dense connection structure to improve the super-resolution performance [14]. However, they usually ignore the problems such as memory consumption and the network is prone to overfitting. As for the upsampling methods, most use post-upsampling, and need to train a single model for each magnification. [PERSON] et al. first upscaled the resolution as the output size in SRCNN [3; 4]. Then they proposed FSRCNN [15], which used a transposed convolution at the end of the network to finish the upsampling operation. Afterwards, [PERSON] et al. [16; 17] believed that when the scale factor is large (\(\times\)8), it is difficult to restore image texture through a one-step operation. So, they proposed Lap-SRN [16; 17], which progressively extracted image features and achieved image super-resolution. [PERSON] et al. [18] first used the sub-pixel convolution to upscale the size of feature map for reducing computation. In recent years, many methods have used sub-pixel convolution, such as EDSR [1] and RCAN [19]. However, these SISR methods only consider certain integer scale factors (\(\times\)2, \(\times\)4, \(\times\)8). We need to train a module for each scale factor. LESRCNN [20] can obtain a high-quality image by a model for different scales. Few previous works have discussed how to implement super-resolution of the arbitrary scale factor. Meta-SR [21] first proposed to use a single model to achieve multiple magnification. To solve the above problems, we propose a multi-factor image super-resolution network based on information distillation (IDMF-SR) to realize arbitrary scale SR with the smallest parameters. IDMF-SR mainly includes two parts: a feature learning block and a multi-scale factor upsampling block. The feature learning block is a collection of several information distillation modules. In the information distillation structure, four 3 \(\times\) 3 convolutions are used to extract image features. After each convolutional layer, a channel split operation divides the extracted features into two parts, and one part is sent to the next convolutional layer, while another part of the feature is retained.