# RETRACTED: Image Super-Resolution Algorithm Based on Dual-Channel Convolutional Neural Networks
## 3 Dual-Channel Convolutional Neural Networks
### The Network Structure of DCCNN  
The image super-resolution algorithm based on DCCNN fully considers the nonlinear mapping relationship between the low-resolution image and the super-resolution image, and the characteristics of the dual-channel are equal to those of the proposed model. The corresponding weights for each channel are not shared in DCCNN. The shallow channel is mainly used to restore the overall outline of the image. The deep channel is used to extract detailed texture information of the LR image. In the phase of feature extraction and mapping with the deep channel, the input layer of the proposed network is the three-channel LR image, which is \(48\times 48\) size of units. Figure 2 presents the dual-channel network constructed in this paper, which is divided into two sub-channels: the deep channel and the shallow channel. Firstly, the number of channels is increased to 64 through the convolutional kernel of \(3\times 3\) size, then entered into the residual block (see Figure 3). It is composed of _Conv_, _ReLU_, and _Conv_, and the _Conv_ residual block size is \(3\times 3\), while the step length is one and the padding is two. After three residual blocks, the output has \(16\leavevmode\
obreak\ 48\times 48\) characteristic graphs. At this time, the semantic information in the feature map is richer than it was previously. In the up-sampling phase, as the most important part of the network, the goal is to increase the spatial span of the \(LR\) images to \(HR\) size. After the mapping, the dimension of \(1\times 1\) is compressed from 16 to 4. Instead of using the manual interpolation method, we used deconvolution (_DeConv_) to achieve the up-sampling. The size of _DeConv_ is \(9\times 9\). For two times, three times and four times, the different scales of up-sampling by setting different steps. After deconvolution, the feature map is increased to 64. Finally, the dimension of the \(1\times 1\) filter is mapped from 64 to 4, the parameters of the \(1\times 1\) filter are effectively reduced, and the calculation complexity is also reduced. In the stage of reconstructing long-term and short-term memory, as the last stage of the network, the up-sampling phase is also the most important part, as it determines the quality of the texture information recovery from the network. Considering that it is difficult for the model to achieve long-term dependence at each stage, we used the multi-scale convolution to reconstruct the up-sampling feature space using long-term and short-term memory blocks at the beginning of the reconstruction. The long-term and short-term memory blocks, which are shown in Figure 4, consist of three residual blocks. The dimensions of the feature map range from 64 to 32, which further reduces the dimensions and enhances the nonlinear mapping ability. The size of _Conv_ in the long-term and short-term memory block is \(3\times 3\), the step length is one, the padding is two, and the output is 32 feature graphs. The \(1\times 1\) filter is then used to compress the dimensions from 32 to 16, so that the high-dimensional feature is extracted and the computational complexity is reduced. In order to effectively aggregate the local information of the 16 feature maps, multi-scale convolution is used for reconstruction. The multi-scale coiling layer contains four filters of different sizes, namely, \(1\times 1\), \(3\times 3\), \(5\times 5\) and \(7\times 7\). The four filters' convolutions in the layer are parallel. Each filter has 4 outputs in the feature graph, and then the 16 feature graphs are combined. Finally, the \(1\times 1\) filter is used as the weighted combination of multi-scale texture features. At this time, the dimension of the feature map is from 16 to 1. Correspondingly, the use of deconvolutional networks to complete the up-sampling operation involves the use of a three-layer structure similar to that of SRCNN in shallow channels.