Deblurring of Space Targets’ Blurred Images Caused by Complex Motion of Ocean-Based Observing Platform

Propagation model of space targets’ images are built up based on angular spectrum theory, and Richardson-Lucy (RL) algorithm is employed to simulate the recovery of the blurred images numerically. In the model, blurred images of space targets caused by the relative motion between the targets and the observing equipment are simulated, and degeneration of image quality due to atmospheric turbulence and noise is considered to make the simulation comprehensive. The deblurring effect using RL algorithm is investigated. Introduction Ocean-based TT & C platform is an important component of Chinese TT & C system. The relative motion between space target and TT & C optoelectronic equipment makes the observing image blurred [1-3]. The effect of deblurring of blurred image employing blind-deblurring method is limited because of the complexity of ocean-based platform’s motion [4-6]. Furthermore, atmospheric turbulence and noise will degrade the quality of images, and make the recovery more challenging. Richardson-Lucy (RL) algorithm is a widely applied nonlinear iteration method of deblurring image, which employs maximum likelihood method to estimate the original image under the condition that the image pixels obey Poisson distribution [7, 8]. Even if the noise is unknown, RL algorithm can be used to deblur the blurred image as long as the point spread function (PSF) is obtained. Researchers mainly focus on deblurring of blurred images caused by uniform linear motion or central rotational motion between the target and the equipment. There is almost no demonstration on deblurring of blurred images caused by complex motion employing RL algorithm as far as we know. In this paper, optoelectronic propagation model based on angular spectrum (AS) theory is built up to simulate blurred images of space target observed by ocean-based TT & C system with complex relative motion. The effect of deblurring using RL algorithm is investigated, and the influence of atmospheric turbulence and noise is analyzed. Theoretical Model In linear displacement invariant system, blurred image g(x, y) can be depicted as the sum of noise n(x, y) and the convolution of original image f(x, y) and PSF h(x, y): ( ) ( ) ( ) ( ) , , , + , g x y h x y f x y n x y = ∗ (1) If PSF can be obtained, one can employ RL algorithm to estimate the original image using iteration method: ( ) ( ) ( ) ( ) ( ) ( ) 1 , , , , , , T n n n g x y f x y h x y f x y h x y f x y +   =   ∗   (2) where fn+1(x, y) and fn(x, y) are estimated images after n+1 and n iterations, respectively. It is clear that the noise n(x, y) is not necessary when estimating the original image via RL algorithm. 21 However, since the motion of ocean-based TT & C platform contains several degrees (such as pitch, roll and yaw), the relative motion track between space target and TT & C platform is usually a complex curve. Thus, the PSF is hardly to be estimated from the blurred image blindly. One feasible method is to measure the real-time parameters of platform’s motion, and built up a model describing the motion of line of sight (LOS) of observing equipment to calculate the accurate PSF. In this paper, the point of our investigation is the effect of deblurring when PSF is known, so the built-up of LOS model is not introduced. AS theory is deduced from Rayleigh-Sommerfeld integral formula without any approximation, so it can be used to calculate the propagation of light accurately [9, 10]. The light field U(x, y, z) at a distance of z can be described as below: