# An Iris Image Super-Resolution Model Based on Swin Transformer and Generative Adversarial Network
## 3 Method
### Model Architecture  
The overall structure of the generator is shown in Figure 2. A three-channel low-resolution image with a resolution of \(56\times 56\) is input and a three-channel high-resolution image with a resolution of \(224\times 224\) is output after super-resolution reconstruction. The size of the shallow feature \(\mathbf{F}_{0}\) is the same as the size of the input image \(\mathbf{I}_{\text{LR}}\). The role of the convolution kernel is to map the image from the low-dimensional space \(\mathbf{C}\) to the high-dimensional space \(\mathbf{C}^{\prime}\) to recover the image's low-frequency information. After shallow feature extraction (the feature maps shown in Figure 3), the feature maps still retain structural information. To recover the lost high-frequency information, we partition the feature map from the shallow feature extraction module into several  
Figure 1: Iris recognition system with super-resolution model. non-overlapping patch embeddings. The overall structure of the generator is shown in Figure 2.  
We first use a \(3\times 3\) convolution kernel \(f_{conv}(\cdot)\) to extract shallow features from the image using a \(3\times 3\) convolution kernel \(\mathbf{I}_{\mathbf{I}\mathbf{R}}\in\mathbb{R}^{C\times H\times W}\) for the input low-resolution image, obtaining shallow features \(\mathbf{F}_{0}\in\mathbb{R}^{C^{\prime}\times H\times W}\):  
\[\mathbf{F}_{0}=f_{conv}(\mathbf{I}_{\mathbf{I}\mathbf{R}}) \tag{1}\]  
The RSTB (Residual Swin Transformer Block) structure, depicted in Figure 4, is composed of multiple Swin Transformer layers (STL) and convolutional layers. The RSTB  
Figure 3: Shallow feature maps. From left to right and top to bottom, the obtained feature maps correspond to the increasing epochs. Figure 2: Generator structure. structure incorporates a residual connection, enabling the fusion of features from different levels and enhancing training stability. The introduction of convolutional layers aims to enhance the model's translational invariance, enabling it to better capture spatial information in the iris images. The combination of Swin Transformer layers and convolutional layers within the RSTB structure helps improve the model's feature representation capabilities. The STL divides the input into multiple non-overlapping local windows and calculates each window's standard self-attention (i.e., local attention) separately. The structure of the STL is shown in Figure 5. The STL block consists of two LayerNorm, a Multi-Headed Self-Attention (MSA) module based on shifted windows and a nonlinear layer containing a two-layer perceptron (MLP) [18]. The specific structure of the model includes the addition of LayerNorm before each MSA module and MLP module, along with the use of residual connectivity throughout. The main differences between the STL compared to the original Transformer layer are the use of local attention and shifted windows mechanisms. The transition block is set after several residual Swin Transformer blocks. This operation aims at keeping the model compactness and improving the computing efficiency, which consists of a BN layer, followed by a Conv layer with 1 \(\times\) 1 kernels and a 2 \(\times\) 2 average pooling layer. Inspired by progressive upsampling networks, we upsample the image once at each stage and gradually reconstruct the image to obtain a higher resolution. This progressive upsampling operation reduces the difficulty of learning. It adds more detailed information in each of the multiple upsampling, thus alleviating the problem of information loss during a single upsampling. For low-resolution images with quadruple downsampling, we magnify the features by a factor of two each time and execute two upsamplings. After this series of operations, we obtained the deep feature map shown in Figure 6.  
Figure 4: Residual Swin Transformer Block (RSTB) structure. Figure 5: Swin Transformer Layer (STL) structure.