## 4 Experiments and Discussion
### Simulation Experimental Principles and Results  
A flowchart of the simulation image experiment is shown in Figure 7.  
First, an image only containing stars and space targets with a uniform background was simulated and generated according to the Tycho-2 Catalogue and the relevant parameters of the optical system with a 80\({}^{\circ}\)\(\times\) 35\({}^{\circ}\) field of view. Tycho-2 Catalogue contains a large number of stars and has a limiting magnitude V-11 and mean sky density of 60 objects per square degree. It was used as a surveillance image without a nonuniform background, as shown in Figure 8a. In the simulation process, the parameter of the GSENSE6060 detector produced by Gpixel incorporation were referenced, which has a 10 \(\upmu\)m pixel size and 3 s exposure time. Typical PSF (point spread function) could be fitted to a gaussian function. Then, we simulated the two types of stray light backgrounds described in Section 2 by ray tracing, as shown in Figure 2, which are synthesized with the simulated uniform surveillance image. Two types of simulation surveillance images with nonuniform backgrounds are shown in Figure 8b,c. Finally, different algorithms are used to eliminate the two types of stray light nonuniform backgrounds in the simulated surveillance images. The experimental results are shown in Figures 9 and 10.  
Figure 8: Simulated surveillance images with (**a**) a uniform background; (**b**) the first type of stray light background; and (**c**) the second type of stray light background.  
Figure 7: Flowchart of the simulation image experiment.  
Figure 9: Elimination result for the first type of stray light background. (**a–d**) Simulated original surveillance images; (**e–h**) nonuniform backgrounds estimated by the THT, MIE, INTHT and IBSGM methods, respectively; and (**i–l**) background elimination results of the THT, MIE, INTHT, and IBSGM methods, respectively.  
For the evaluation of the reference image, we use the root mean square error (RMSE) to evaluate the effect of nonuniform background elimination. Here, \(O\) and \(I\) are the simulated  
Figure 10: Elimination result for the second type of stray light background. (**a–d**) Simulated original surveillance images; (**e–h**) nonuniform backgrounds estimated by the THT, MIF, INTHT, and IBSGM methods, respectively; and (**i–l**) background elimination results of the THT, MIF, INTHT, and IBSGM methods, respectively.  
surveillance images with a uniform background and the processed surveillance image, respectively.  
\[RMSE=\sqrt{\frac{1}{m\times n}{\sum_{i=1}^{m}\sum_{j=1}^{n}(O(i,j)-I(i,j))^{2}}} \tag{15}\]  
where \(m\) and \(n\) refer to the rows and columns of \(O\) and \(I\), respectively.  
The smaller the RMSE value, the closer the corrected image is to the original image with a uniform background, and the better the ability of the algorithm to eliminate the stray light nonuniform background. The RMSE results are shown in Table 1.  
Combining the results of Figures 9 and 10 and Table 1, the proposed IBSGM method has higher accuracy in eliminating both types of stray light nonuniform backgrounds. Therefore, the image processed image by our method is closer to the original simulated image with a uniform background. Since more complex situations cannot be studied by simulation, we used real images to further verify the performance of IBSGM and analyze its advantages in comparison with other methods in the next subsection.