## 1 Introduction  
The aim of SR is to learn a mapping function from input low-resolution (LR) images to output high-resolution (HR) images. High-resolution medical images are very important for doctors in terms of making accurate diagnoses of lesions; thus, SR for medical images has recently received a great deal of attention. However, image super-resolution remains a challenge, as LR images lose a certain amount of information as compared to HR images [1]. Many researchers have tried to find a solution to this critical issue [2; 3; 4; 5]. On the basis of deep learning, [PERSON] et al. proposed the SR convolutional neural network (SRCNN) [2], which utilizes the convolutional neural network (CNN) architecture and is vastly superior to other traditional methods. Thereafter, [PERSON] et al. proposed fast SR convolutional neural networks (FSRCNNs) [5], which up-sample feature maps using deconvolution in the last layer of the network and provide more accurate estimates with less computation. The deconvolutional layer generates HR features by enlarging feature maps. Then, the subpixel convolutional layer was proposed by [PERSON] et al. [6], which expandsthe number of feature channels in order to store more pixels and rearrange them to generate HR features. The Laplacian pyramid super-resolution network (LapSRN) [7] up-samples LR feature maps progressively, which enables it to reconstruct multi-scale SR images in one training session. To further improve SR performance, deep networks were introduced into SR. The very deep SR convolutional neural network (VDSR) [8] proposed by [PERSON] et al. is the first deep multiple-scale model. It bypasses interpolated LR images to the end by residual learning. Then, on the basis of VDSR [8], the authors proposed a deeply recursive convolutional network (DRCN) [9], which trains the network using a recursive-supervised strategy and achieves a similar performance to VDSR [8] with fewer parameters. Deep dense SR (DDSR) [10] was proposed for the SR of medical images, which uses densely connected hidden layers to obtain informative high-level features. However, it remains a challenge for deep neural networks to go deeper because of the various difficulties associated with training, such as gradient vanishing/exploding problems. Residual learning was proposed to solve these problems. The deep residual network (ResNet) [11] is a representative model, which achieves a remarkable performance based on residual learning. [PERSON] et al. [12] used residual learning and recursive learning to realize a very deep network without an enormous amount of parameters. The SR network using dense skip connections (SRDenseNet) [13] is another representative model based on residual learning. It bypasses all previous features to latter layers in blocks and densely concatenates all blocks. The enhanced deep SR network (EDSR) [14] proposed by [PERSON] et al. removes the use of batch normalization (BN), which is harmful to the final performance in SR tasks. EDSR also employs a pretraining strategy and residual scaling techniques to improve the final performance. On the basis of residual learning, for the SR of three-dimensional (3D) brain MRI images, [PERSON] et al. [15] proposed a deep 3D CNN. Above classical SR methods are all feedforward SR methods; low-frequency information is directly passed to the following layer or bypassed to the latter layers through skip connections. The feedback mechanism enables the previous layers to perceive high-frequency information from the latter layers, but no new parameters are introduced. It is widely used in the domain of computer vision [16; 17; 18; 19]. Recently, [PERSON] et al. [20] proposed error feedback for image SR, which was used in two back-projection units. Thereafter, the SR feedback network (SRFBN) [21] was proposed, which contains a feedback block that functions in a self-feedback manner. For the SR of medical images, the feedback adaptive weighted dense network (FAWDN) [22] was proposed based on an adaptive weighted dense block and feedback connection.