## 2 Proposed Method  
In this section, we propose a deep learning method with CNNs for super-resolution image reconstruction. In the proposed method, the output of each layer group is connected to input data with a skip connection. Each skip connection has a multiplication factor (MF) with input data, which is a parameter that is also to be learned during the training process. Hence, the proposed method connects input data to layer groups through multiple skip connections at regular intervals, whereas the existing VDSR method utilizes only one skip connection. If the input image data are repetitively skipped and connected to a predetermined number of layer groups, the problem of data extinction due to ReLU operation at the output of each layer would be significantly alleviated. The first advantage of skip connections with regular intervals is that the data processed in each layer group would retain the characteristics of the input data to be learned without loss of input data information by data extinction and gradient vanishing. This phenomenon has a positive effect on learning for super-resolution reconstruction because the number of contributing units for learning in the proposed method would be greater than that in the structure without repetitive skip connections. The second advantage is that repetitive skip connections to all layer groups would maintain the features of the input image to be learned more robustly. The neural network for super-resolution reconstruction aims to improve the image quality by generating the optimum high-frequency information from the input low-resolution image. The repetitive skip connections would be advantageous to preserving the features of the input image to be learned for super-resolution reconstruction. In the proposed method, because the number of skip connections with input data is relatively large, the neural network may be overfitted as the epochs roll over during training. To transmit the information of the input data to be learned while preserving their characteristics, each skip connection is associated with an MF, which represents the weight for input data. The MF of the proposed method is a parameter that is also to be learned during the training process. The value of this parameter is to be learned like other parameters, such as filter kernels. We experimentally observed that the super-resolution image reconstruction performance is improved when the MFs are learned and set through the training process. Figure 2 shows the proposed network structure with a different skip connection for each layer group. Let \(k\) represent the number of layers in a layer group and \(n\) represent the number of layer groups. The total number of layers \(l\) is given by \(l=kn\). In Figure 2, \(\mathbf{G}_{i}\) (\(i=1,\cdots,n\)) represents layer groups, each of which is composed of \(k\) layers. Figure 2: Proposed network structure with skip connections for each layer group (\(l=20,k=5,n=4\)). Each \(\lambda_{i}\) represents the MF for layer group \(\mathbf{G}_{i}\), and the last MF \(\lambda_{n}\) is fixed to 1.0 as in the existing VDSR method. The MF values of \(\lambda_{1}\) through \(\lambda_{n-1}\) are to be learned and updated as the optimization of parameters in the training process with initialization to some values. Note that the structure of each \(L_{i}\) in the proposed method (Figure 2) is the same as that of each \(L_{i}\) in VDSR (Figure 1). Each \(L_{i}\) in the proposed method is composed of one convolution layer and one ReLU layer as each \(L_{i}\) in VDSR. There are 64 convolutions with \(3\times 3\) filter kernels in one convolution layer. The parameters relating convolution operations in the proposed method are the same as the parameters relating convolution operations in VDSR. The operation of ReLU units in the proposed method is performed as (1), which is exactly the same as the VDSR. The only different parameters are the \(\lambda_{1},\cdots,\lambda_{n-1}\) MFs in the proposed method (Figure 2), which do not exist in the VDSR (Figure 1).