# Image Dehazing Enhancement Strategy Based on Polarization Detection of Space Targets
## 5 Image Dehazing Method Based on Full Polarization Information Inversion and Image Fusion
### Basic Principle of Image Dehazing Based on Full Polarization Information Inversion
#### 5.1.4 Inversion Method for the Degree of Linear Polarization of Space Targets  
In the polarization image of space targets, the DoP of space targets are determined by their own properties, and the transmittance function is related to factors such as atmospheric extinction. Therefore, the transmittance function and the DoP of space targets are statistically independent. The Pearson correlation coefficient [24] is used to construct a function expression, as shown in Equation (27); when the Pearson correlation coefficient is calculated as 0, the two variables are considered independent of each other.  
\[\mathit{Person}(t(x,y),J(x,y))=\frac{\mathrm{cov}(t_{\mathit{l}\mathit{ump}}(x,y),J(x,y))}{\sigma t(x,y)\sigma J(x,y)}=0 \tag{27}\]  
The Equations (18) and (19) are substituted into Equation (27). Solve the formula using \(\mathit{[PERSON]_{\mathrm{target}}(x,y)}\) as the only variable as shown in Equation (28).  
\[\mathit{cov}\left\{\begin{array}{c}\frac{A(x,y)[\mathit{[PERSON]_{\mathrm{target }}(x,y)-\mathit{[PERSON]_{\mathrm{target}}(x,y)}]+S_{0}(x,y)(\mathit{[PERSON]_{ \mathrm{target}}}-\mathit{[PERSON]_{\mathrm{target}}})-\mathit{[PERSON]_{\mathrm{ target}}}S_{0}(x,y)-\Delta I(x,y)}}{A(x,y)[\mathit{[PERSON]_{\mathrm{target}}(x,y)- \mathit{[PERSON]_{\mathrm{target}}}(x,y)}]}\quad,\\ \frac{A(x,y)[\Delta I(x,y)-S_{0}(x,y)\mathit{[PERSON]_{\mathrm{target}}(x,y)}]}{ \mathit{[PERSON]_{\mathrm{target}}(x,y)[A(x,y)-S_{0}(x,y),S_{0}^{T}(x,y)]-\mathit{[PERSON] _{\mathrm{target}}}(x,y)|A(x,y)+S_{0}^{T}(x,y)+\Delta I(x,y)}}\end{array} \right\}=0 \tag{28}\]  
Then convert the above formula to a function \(f(\mathit{[PERSON]_{\mathrm{target}}})\), the estimation of \(\mathit{[PERSON]_{\mathrm{target}}(x,y)}\) becomes the problem of finding the optimal solution, so the second derivative of solving for \(f(\mathit{[PERSON]_{\mathrm{target}}})\) is used to obtain the value of \(\mathit{[PERSON]_{\mathrm{target}}(x,y)}\).  
\[\frac{df^{2}(\mathit{Dolp_{\mathrm{target}}})}{\mathit{dolp_{\mathrm{target}}}}=0 \tag{29}\]  
According to the calculation result of Equation (29), the calculation of the degree of linear polarization of space targets can be completed.  
Validation of the Effectiveness of the Dehazing Method Based on Fully Polarization Information Inversion  
To preliminarily verify the effectiveness of the image dehazing method based on the introduction of full polarization information inversion, the simulated polarization image of space targets was used. After the images were restored using our method, the dehazing effect is shown in Figure 6a,b. The DoP image of space targets obtained by inversion is shown in Figure 6a, and the intensity image obtained by suppressing the effect of haze on image quality is shown in Figure 6b.  
Figure 6: Comparison results of polarization images of simulated space targets after dehazing: (**a**) Polarization image of the targets obtained by inversion, (**b**) Intensity image after dehazing.  
As shown in Figure 6a, compared with the standard DoP image shown in Figure 4, there is a certain degree of calculation error in the DoP image obtained by inversion, but the basic contour and detail information of the target are contained, indicating that the image dehazing method based on full polarization information inversion can be used to solve the polarization characteristics of space targets.  
On the other hand, it can be seen from Figure 6b that although the influence of haze on image quality can be suppressed, the image after dehazing is dark, and the effect is not satisfactory. In the DoP image of real space targets, if the target occupies a small number of pixels, the detailed features are easily submerged using this method, which is not conducive to target recognition under complex conditions. Therefore, in order to improve the quality of dehazing images further, the image fusion enhancement method in this paper is adopted to improve the image contrast and the target information dimension in a single frame.