# Image Dehazing Enhancement Strategy Based on Polarization Detection of Space Targets
## 5 Image Dehazing Method Based on Full Polarization Information Inversion and Image Fusion
### Fusion Method of Space Target Dehazing Images  
In our paper, the image fusion method based on Discrete Cosine Transform (DCT) [25; 26] and Local Spatial Frequency (LSF) is used to fuse the inverted DoP image with the intensity image after dehazing to obtain the Dehazing Polarization Fusion Enhancement (DPFE) image. Compared with other fusion methods, the fusion method based on DCT and LSF has a stronger energy concentration ability for the relevant information so that more detailed features can be resolved in DPFE images. The fusion process is shown in Figure 7.  
Step 1: The method of Discrete Wavelet Transform (DWT) is used to decompose the intensity image and the inverted DoP image into low-frequency sub-images (L1, L2), high-frequency sub-images (H1, H2), vertical sub-images (V1, V2) and horizontal sub-images (D1, D2).  
Step 2: DCT is used to transform the sub-images into discrete cosine coefficient images (D\({}_{\text{L1}}\), D\({}_{\text{L2}}\), D\({}_{\text{H1}}\), D\({}_{\text{H2}}\), D\({}_{\text{V1}}\), D\({}_{\text{V2}}\), D\({}_{\text{D1}}\), D\({}_{\text{D2}}\)).  
Step 3: Compare the local spatial frequency of two discrete cosine coefficient images with the same decomposition direction and recombine the two images into one discrete cosine sub-image (D\({}_{\text{L}}\), D\({}_{\text{H}}\), D\({}_{\text{V}}\), D\({}_{\text{D}}\)) according to the fusion rules shown in Equation (30).  
\[D(i,j)=\left\{\begin{array}{l}\frac{Det_{l_{0}}+Det_{DoP}}{2},\left|Lsf_{l_{ 0}}-Lsf_{DoP}\right|\leq\xi\\ Dt_{l_{0}},\left|Lsf_{l_{0}}-Lsf_{DoP}\right|>\xi\quad\&\quad Det_{l_{0}}>D_{ DoP}\\ Dt_{DoP},\left|Lsf_{l_{0}}-Lsf_{DoP}\right|>\xi\quad\&\quad Det_{DoP}> DCT_{l_{0}}\end{array}\right. \tag{30}\]  
\(D(i,j)\) is the fusion result of the discrete cosine coefficient, and \(Det_{l_{0}}\) and \(Det_{DoP}\) represent the discrete cosine coefficients in different decomposition directions in the intensity image and DoP image, respectively. \(Lsf_{l_{0}}\) and \(Lsf_{DoP}\) are local spatial frequencies, and \(\xi\) is the screening threshold for Local Spatial Frequency. \"&\" is used to represent the 'and' in logical operation relationships. In the image fusion method proposed in our paper, the threshold \(\xi\) is set within a fixed range. The information entropy of the fused images at each threshold is calculated. After the calculation in the entire interval is completed, the threshold corresponding to the maximum is taken as the best screening threshold in the image fusion process.  
Step 4: The Inverse Discrete Cosine Transform (IDCT) is used to convert the fused discrete cosine coefficient sub-image to a low-frequency sub-image (L), high-frequency sub-image (H), vertical sub-image (V), and horizontal sub-image (D).  
Step 5: The Dehazing Polarization Fusion Enhancement (DPFE) image is obtained by Inverse Discrete Wavelet Transform (IDWT) finally.  
Validation of the Effectiveness of Image Dehazing Method Based on Full Polarization Information Inversion and Image Fusion