Nonlinear diffusion noise reduction in astronomical images

From ancient times, celestial bodies have been used by travelers and scientists for positioning and routing. By developing sciences, it was found that the celestial bodies form an accurate inertial system to use in navigation applications. In this system, each star is considered as a reference point in determining reference coordinate frame of the system. Due to the visibility of the satellite motion trace and the fundamental need to determine and modify satellites’ orbital parameters as well as to identify and locate espial satellites, determining the positional parameters of the satellite is also one of the modern and important applications of vision-based astronomical systems. In the modern vision-based astronomical systems, data collection is done using charge-coupled device (CCD) array. During the process of light collision to the surface of the CCD and then reading and measuring the number of photoelectrons as well as converting them to the digital numbers to store them as grey degree in each pixel, the smallest mistakes that result in lost or added electrons on each pixel can lead to distortion and noise in the image. The process of noise elimination should not only eliminate or reduce the noise but also avoid blurring the image and removing or relocating the edges of the image. To determine the primary orbit of the satellite using an optical method, the streak of the satellite must be extracted accurately because the misdiagnosis of the beginning and end points of the streak directly affects the accuracy of the determined orbit. Therefore, we need to find noise elimination methods that impose the lowest possible effects to the key complications of the astronomical images such as star and satellite streak. In this study, it is attempted to eliminate the noises using diffusion equation and solving it numerically. On the other hand, to identify the accurate position of the edges, the gradient is calculated by through convoluting the main image by the Gaussian filter. In this study, a numerical method is used to solve diffusion equation. Heat diffusion equation is an iteration-based method. It is obvious that the more the paces and iterations in the equation, the smoother the image. This factor must be chosen such that the image brightness does not exceed the main range. For this purpose, the noise must be eliminated from the image by choosing appropriate number of iterations. In this research, the structural similarity index (SSI) is used to select the optimum number of iterations. As a result, in this research, it is attempted to use noise elimination methods that impose the lowest changes to the existing satellite’s streak.