# Improvement of a Subpixel Convolutional Neural Network for a Super-Resolution Image
## 2 Materials and Methods  
In the ESPCN model, low-resolution images are directly used to extract feature maps. The model combines the feature image set from the previous feature map as input in the last layer, and the pixels corresponding to the same point in each channel are brought together to form the new image by shifting the pixels on the new image. In the ESPCN model, 64 convolutional kernels of 5 \(\times\) 5 size are firstly used for the convolutional layer. After inputting the first subpixel convolutional layer with kernels of 5 \(\times\) 5 size, the datasets are transformed into 64-channel datasets. Next, the second group of datasets with kernels of 3 \(\times\) 3 size are transformed into 32-channel datasets, and the subpixel convolutional layer finally produces 9-channel datasets, which means the length and width of the image data are increased by 3 times respectively. The last layer generates a high-resolution image directly from the low-resolution feature maps with a boost filter for each feature map. Given a training set of 1, \(\ldots\), N high-resolution image samples, the corresponding low-resolution images are generated, and the pixel-wise mean square error (MSE) of the reconstruction is calculated as an objective function to train the network [17]. \[l(W_{1,\text{L}},b_{1,\text{L}})=\frac{1}{r^{2}HW}\sum_{x=1}^{rH}\sum_{x=1}^{ rW}\left(\text{I}_{x,y}^{HR}-f_{x,y}^{LR}\left(\text{I}^{LR}\right)\right)^{2} \tag{1}\]  
In the model, the activation function is inspired by the experimental results, and tanh is used instead of relu. When no improvement is observed by using 100 epochs in the training of the model, the processes are stopped. The initial learning rate of the model is determined as 0.01, the training is updated to the final learning rate as 0.0001, and the cost function is gradually updated when the improvement is smaller than a threshold value. The peak signal-to-noise ratio (PSNR) and the structural similarity index measure (SSIM) are used as performance metrics to evaluate the model. In this article, inspired by the three-layer ESPCN model, a super-resolution image reconstruction method based on subpixel convolutional neural networks, which we call R-ESPCNs, is proposed by remodeling the model with a deep network. Figure 4 shows the flowchart of the ESPCN model. The proposed model is five layered, as shown in Figure 5, and consists of 6 layers, including the last boosting layer. First, a low-resolution image is given to the network system. In order to obtain more information from the images, 2 convolutional layers are modeled for feature extraction in the first part, 2 nonlinear mapping layers are modeled in the second part, and a subpixel convolution layer is modeled in the last layer to obtain  
Figure 4: Flow chart of the ESPCN [17]. a high-resolution image from a low-resolution image. Our proposed model has 5 layers, and the input and output channel numbers of each layer are defined. Another parameter defined in parentheses between the layers indicates the size of the filter convolution kernel in Figure 5. In our proposed model, unlike the ESPCN model, 32 convolutional kernels of 3 \(\times\) 3 size are used for the convolutional layer. In this way, the computational cost is tried to be reduced compared to the ESPCN model. Tanh is preferred as the activation function in the model. In the training of the model, 100 epochs are used, the initial learning rate is determined as 0.01, and the learning rate is updated as 0.0001 during the training period. The improvement of the cost function is updated gradually when it is smaller than a threshold value. The structural similarity index measure (SSIM) and the peak signal-to-noise ratio (PSNR) are used as performance measures to evaluate the model. In general, network models that obtain super-resolution images do not use low-resolution images as input, and this situation negatively affects the network as it increases the convolution calculation process.