# Image Dehazing Enhancement Strategy Based on Polarization Detection of Space Targets
## 3 Hybrid Multi-Channel Interpolation Method Based on Regional Correlation Analysis
Taking the pixel with the polarization direction of 0\({}^{\circ}\) as an example, the calculation process diagram of the HMIRCA algorithm is shown in Figure 2.  
The calculation method is shown in Equations (4)-(6), where \(\delta\) represents the correlation coefficient of the two groups of 3 \(\times\) 3 regions (\(\delta=\delta_{1}+\delta_{2}+\ldots+\delta_{\text{n}}\)). \[I_{135}(i,j)=\sum_{m=-1}^{1}I_{135}(i+m,j)\times\left\{ \begin{array}{l}\dfrac{ \delta_{1}}{\delta},(m=-1)\\ \dfrac{\delta_{2}}{\delta},(m=1)\end{array} \right.+\dfrac{1}{4}I_{0}(i,j)- \dfrac{1}{8}(I_{0}(i-2,j)+I_{0}(i+2,j))\quad(m\
eq 0) \tag{5}\]  
\[I_{45}(i,j)=\sum_{m=-1}^{1}I_{45}(i,j+m)\times\left\{ \begin{array}{l}\dfrac{ \delta_{1}}{\delta},(m=-1)\\ \dfrac{\delta_{2}}{\delta},(m=1)\end{array} \right.+\dfrac{1}{4}I_{0}(i,j)- \dfrac{1}{8}(I_{0}(i,j-2)+I_{0}(i,j+2))\quad(m\
eq 0) \tag{6}\]  
To verify the validity of the HMIRCA method, a simulated space target polarization detection experimental platform is used to acquire the test images. The platform consists of a target, a controllable light source, a polarization detection system based on the [PERSON] telescope, and a smooth background plate. Target detection experiments are conducted under low ambient illumination conditions to simulate the real detection environment. Different interpolation methods are used to obtain DoP images for simulated space target images, including bilinear interpolation [19], nearest neighbor interpolation [20], spline interpolation [21], and the HMIRCA method. Subjectively, the comparison results are shown in Figure 3.  
From the subjective comparison results, it can be seen that the use of the nearest neighbor interpolation method and spline interpolation method will lead to a pseudo polarization edge phenomenon in DoP images and wrong target polarization information is obtained. Although the bilinear interpolation method can effectively suppress the pseudo polarization edge to a certain extent, part of the target information is lost. Compared with other methods, the image acquired by using our method is clearer, the target contour feature is more complete, and the pseudo polarization edge is better suppressed. In order to evaluate the effect of different interpolation algorithms from the objective perspective, the Root Mean Squared Error (RMSE) was selected as the evaluation index, and the intensity image containing complete target features was used as the reference image. The calculation method of RMSE is shown in Equation (7), where \(M\) and \(N\) are the width and height of the image,\(f(i,j)\) is the image to be evaluated, and \(r(i,j)\) is the reference  
Figure 2: Schematic diagram of the interpolation method proposed in this paper. image. The smaller the RMSE, the better the retention effect of the target edge feature. The comparison results are shown in Table 1.  
\[RMSE=\frac{1}{M\times N}\sum_{i=1}^{M}\sum_{j=1}^{N}\left(f(i,j)-r(i,j)\right)^{2} \tag{7}\]  
As shown in Table 1, it can be seen that the maximum interpolation error is introduced by using the nearest neighbor interpolation method, and the Bilinear and Spline methods are slightly better, but due to the insufficient consideration of the correlation between polarization components in different detection directions, their ability to maintain detailed information is poor. The RMSE of the polarization images obtained by the HMIRCA method is the lowest, indicating that the polarization information has the highest restoration accuracy. The reason is that the accuracy of image restoration is improved by using the HMIRCA method according to the correlation between different polarization components. The detailed features of the target are better maintained, so the HMIRCA method is more suitable for the acquisition of target images in dark and weak conditions. In the subsequent analysis of space target images for haze degradation, the HMIRCA method is used to solve the DoP images to improve the accuracy of target solving in the preprocessing process.