## 2 Super-Resolution Methods
### Reconstruction Method  
\(I_{\theta_{i}-1,2,3,4}^{\text{M/2}\times\text{N/2}}\) is a low-resolution image. If \(I_{\theta_{i}-1,2,3,4}^{\text{M}\times\text{N}}\) in the same scene is solved, the \(DP\) and \(AP\) of full-resolution images can be solved using Formulas (3) and (4). Consequently, the Stokes vector needs to be calculated. The calculation process involves finding the difference between two groups of orthogonal light intensities. It is important to note that the different image is significantly influenced by the displacement of the target. Based on the experimental findings in [19], displacement-induced pseudo-polarization has a substantial impact on subjective perception. Therefore, our reconstruction method is expressed in the following equation:  
\[ \begin{split}&\alpha^{*}=\underset{\alpha}{\text{arg}\ \underset{\alpha}{\text{min}}\left\lVert\alpha\right\rVert_{0}\ S.T.\ \ \ \ \left\lVert GD_{LR}\alpha-GI_{LR}\right\rVert_{2}^{2}<\varepsilon}\\ & I_{LR}=\left\{S_{0 LR},\left(S1/S0\right)_{LR},\left(S2/S0\right) _{LR}\right\}\\ & I_{SR}=D_{SR}\alpha^{*}\end{split}  \tag{13}\]  
\(S0_{LR}\) is reconstructed as \(S0_{SR}\) through the use of super resolution. Subsequently, \(\left(S1/S0\right)_{LR}\) and  
The light intensity captured by the detector encompasses both natural and fully polarized light components, which can be derived using Malus' law:  
\[I^{\theta}=\frac{1}{2}I_{N}+I\times P\times\cos^{2}(\theta-A) \tag{14}\]  
In the formula above, \(I^{\theta}\) represents the intensity of partially polarized light at a given declination angle \(\theta\). This can also be interpreted as the light intensity received by the detector at that angle. \(I^{N}\) represents natural light, while \(I^{N}\) represents the total light intensity. \(I^{N}\) denotes the degree of polarization, while \(A\) represents the polarization angle. The orthogonal difference of polarization is defined [31] as:  
\[I^{\theta}_{\perp}=I^{\theta}_{\perp}-I^{\theta+\frac{\pi}{2}}_{\perp}=I(1-P) \times(\cos^{2}(\theta-A)-\cos^{2}(\frac{\pi}{2}+\theta-A)) \tag{15}\]  
In the formula above, when \(\theta=0^{\circ}\), \(I^{\theta}_{\perp}=S1\), and \(\theta=45^{\circ}\), \(I^{\theta}_{\perp}=S2\). The Stokes representation of the total light intensity \(I\) is denoted as S0. Therefore, \(\left(S1/S0\right)_{LR}\) and \(\left(S2/S0\right)_{LR}\) are influenced by the polarization degree and polarization angle. By reconstructing them, it is possible to achieve better restoration of the \(DP\) and \(AP\) images at full resolution, instead of directly reconstructing the \(DP\) and \(AP\) low-resolution images from the high-resolution S0, \(DP\), and \(DP\) images. The proposed method does not take the entire image as input. Instead, a sliding window reconstruction is performed on a low-resolution image. The window size is set at \(5\times 5\), with a step length of 1. During the reconstruction process, the number of overlapping pixels is calculated, and the reconstructed \(\widetilde{I}_{SR}\) is divided by the overlap coefficient \(W\). The operational details are presented in the figure below. As shown in Figure 1, the red segment illustrates a pixel-level reconstruction process where each pixel is reconstructed once, using a weight factor of \(W=1\). The yellow part represents another reconstruction process. It is important to clarify that this specific depiction of traversing during the second step is not obligatory, as any traversal with a step size of 1 covering the entire image would be sufficient. It is worth noting that there is an overlap between the yellow and red segments. In terms of pixel-level analysis, the overlapping region carries a weight coefficient of \(W=2\). The resulting reconstructed \(I_{SR}\) is then divided by the overlap coefficient \(W\). Additionally, the Iterative Back Projection (IBP) algorithm is employed to enhance image details and minimize the reconstruction error of the reconstructed \(\widetilde{I}_{SR}\).