# RETRACTED: Image Super-Resolution Algorithm Based on Dual-Channel Convolutional Neural Networks
## 3 Dual-Channel Convolutional Neural Networks
### Residual Blocks and Long-Term and Short-Term Memory Block  
(1) Residual Blocks  
The residual blocks' network design is inspired by the 152-level ResNet network proposed by [PERSON] et al. [31]. The recognition performance on the ImageNet dataset was improved with the increase of the number of network layers, and its performance on computer vision problems [22; 23; 26] from low to high tasks is excellent. The original residual block, which is shown in Figure 3a, is composed of a feed-forward convolutional network and a jump around a number of layers. The stacked residuals form the final residual networks. Compared with a smooth network, the residual network exhibits lower convergence loss and a lack of overfitting due to the disappearance of the gradient, which makes the network easier to optimize. The dimensions of the feature map progressively increase to ensure the ability to express the output features. Since the original batch normalization layer (BN) [35] is used to normalize the characteristics of the coiling output layer, this will affect the distribution of features learned by the convolution layer and cause the loss of important information from the feature graph. Moreover, the batch positive layer has the same number of parameters as the previous convolutional layer and thus consumes a lot of memory. In their image deblurring task, [PERSON] et al. [36] deleted the \(BN\) layer in the residual block, with the result that the network performance was greatly improved. Therefore, in this paper, we used the residual block to delete the batch regularization layer in order to reduce the color's offset in the output, while maintaining the training stability. Each residual block in the present paper contained two \(3\times 3\) convolutional layers and the ReLU layer. The structure of the residual block in the present paper is shown in Figure 3b. Figure 3: The processing construction with improved residual blocks described in the paper. (**a**) Original Residual Blocks; (**b**) Improved Residual Blocks in the Paper. The residual block can be expressed by Equation (1):  
\[X_{l+1}=X_{l}+F(X) \tag{1}\]  
Here, \(\mathbf{X_{I}}\) and \(\mathbf{X_{l+1}}\) represent the input and output vectors of residual blocks, respectively. The function \(F(X)\) denotes residual mapping. The residual block in this paper contained only the convolutional layer and the ReLU layer. The modified linear unit (ReLU) has unilateral suppression and sparsity. In most cases, the ReLU gradient is a constant term, avoiding the problem of gradient disappearance to a certain extent. The relevant mathematical expression can be expressed by Equation (2):  
\[f(x)=\max(0,x_{i}) \tag{2}\]  
In this paper, the activation function of the convolutional layer outside the residual block is the Parametric Rectified Linear Unit (PReLU) [34]. The use of PReLU is mainly designed to avoid the \"dead angle\" [37] caused by the zero gradient in the ReLU. It is increased by the correction of parameters to a certain extent. It can have a regularizing effect and can also improve the generalization ability of the model. The difference between the proposed model and _ReLU_ is mainly reflected in the negative part, and the mathematical expression is shown in Equation (3):  
\[f(x)=\max(0,x_{i})+a_{i}\min(x_{i},0) \tag{3}\]  
Here, \(\mathbf{x_{i}}\) is the input signal of the \(i\)th layer, and \(a_{i}\) is the coefficient of the negative part. In Equation (3), the parameter \(a_{i}\) is set to zero, but the negative part of PReLU can be learned. Finally, the output of the activation function can be expressed by Equation (4):  
\[f_{l}(x)=f(W_{l}*f_{l-1}(x)+B_{l}) \tag{4}\]  
Here\(f_{l}\) is the final output feature graph and \(B_{l}\) is the offset of the \(l\)th layer. (2) Long-Term and Short-Term Memory Block  
It is difficult to achieve long-term dependence at each stage, resulting in lower dependence on the up-sampling phase in the reconstruction phase and more loss of important high-frequency information in the up-sampling phase.