## 3 Method  
### Sub-Pixel Convolution  
Super-resolution reconstruction of images has been a work of great interest [35]. Sub-pixel convolution is a technique commonly used in image processing, particularly in SR reconstruction, and has achieved significant results in target detection, image segmentation, and high-resolution reconstruction of images and videos in the field of computer vision (CV) [36; 37; 38]. During the image data acquisition process in photography and other fields, images are discretized. Due to the limitations of hardware devices such as photoreactive elements, a single pixel typically represents the color of a certain area. The finer pixels that are not recorded between two adjacent pixels are referred to as sub-pixels. SR operations are often described as the process of obtaining these unknown sub-pixels. In neural network models, upsampling methods are commonly used to restore or interpolate LR images [39]. The upsampling process typically involves uniform interpolation within a specified receptive field using specific methods such as Max Pooling or Average Pooling, which are entirely composite mathematical computation operations, as shown in Figure 3.  
Contrary to upsampling operations, sub-pixel convolution effectively harnesses the information from low-resolution images when generating high-resolution images, as it can learn weight parameters during the model training process. Studies have posited that zero-padding the receptive field during the upsampling process is an ineffective practice [40], with the singular blank data being not only invalid information but also potentially detrimental to model training and gradient optimization for LR data of size \(W,~{}H\). Sub-pixel Convolution differs from mere upsampling processes in that it does not directly generate HR data through interpolation or similar methods; instead, it obtains the HR data by rearranging the feature matrices within the model's hidden layers. As shown in Figure 4, the model initially derives a feature matrix with \(r^{2}\) channels and subsequently employs periodic shuffling to produce HR data of size \(W*r,H*r\). The mathematical expression is as follows:  
\[I^{SR}=f\Big{(}I^{LR}\Big{)}=f\Big{(}F\Big{(}I^{LR}\Big{)}\Big{)} \tag{2}\]  
where \(I^{LR}\) represents the original data, and \(I^{SR}\) denotes the HR data output by the model. \(f(x)\) refers to the shuffling operation, which is the model's process of padding the feature values. Specifically, in sub-pixel convolution, LR pixels are regarded as an area of size \(r^{2}\). During upsampling, the model utilizes the features it has learned to fill this area, adjusting the output of the final convolutional layer to  
\[N*(C*r*r)*W*H\Rightarrow N*C*(W*r)*(H*r) \tag{3}\]  
Figure 3: Correspond pairs of downsampling and upsampling layers.  
In this context, \(N\) represents the Batch Size; \(C\) denotes the number of channels; \(W,H\) are the dimensions of the LR data size; \(r\) is the upscale factor. The model training process continuously adjusts feature parameters and padding methods, making the deconvolution process not entirely compliant with mathematical procedures. This approach addresses the issue of excessive hyperparameters and overt human intervention in some upsampling methods.