## 1 Introduction  
Space cameras play a crucial role in various fields, such as Earth observation and astronomical exploration, due to their advantages of being less affected by atmospheric disturbances and not being limited by geographical locations [1; 2; 3]. With the increasing demand for detecting faint celestial objects in space, cameras often require a longer integration time. Space cameras mounted on satellites face challenges when taking photographs due to the orbital motion and attitude motion of the satellite. During the integration time, there is a relative motion between the target and the camera that results in image blur. Therefore, the image motion compensation (IMC) technique is needed to enhance image clarity and resolution [4; 5]. This is particularly true for cameras that require long integration times to capture faint and weak targets. The commonly used methods for IMC include the optical IMC method, the image-based IMC method, and the mechanical IMC method. Optical IMC methods involve rotating or moving optical components in the optical path to change the direction of light and to compensate for image motion in accordance with the principle of matching the image motion speed on the camera focal plane [6]. A common approach is to compensate for forward image motion by rotating a reflecting mirror that is located in front of the objective lens. In [7], a novel IMC method was proposed to compensate for both image rotation and image translation simultaneously using a scan mirror. In [8], a two-axis, fast steering mirror was designed for aerial dynamic scans and a state imaging system. The effectiveness of the fast steering mirror and IMC algorithm was verified by the dynamic imaging test in the laboratory and flight tests. Through adopting the optical IMC method, the mirror-reflected optical paths faced issues such as inconsistency between the center and the edges of the field of view, deviations in the optical axis, and even defocusing caused by compensation. It was challenging to completely eliminate the image motion in the resulting images. Another approach is to compensate for image motion through digital image processing algorithms. These algorithms, such as image registration and motion estimation, are used to correct the image motion and motion blur in the captured images [9]. In [10], an improved Wiener filtering algorithm was proposed to restore the blurred image. Experimental results showed that the absolute average error of the image for improved algorithms decreased by 9.31%, and the peak signal-to-noise ratio increased by 13.98% when compared to the traditional Wiener filter method. Ref. [11] proposed a blind image restoration method using the Huber-Markov prior model to both regularize the image and the blur parameters. Experiments were performed to demonstrate the effectiveness of the proposed approach. Ref. [12] proposed a new blind deblurring learning framework that utilizes alternating iterations of shrinkage thresholds, and they proposed a learnable blur kernel proximal mapping module to improve the accuracy of blur kernel reconstructions. The experiments demonstrated that the proposed framework yields superior image restoration quality for blurred images with varying levels of deterioration. However, due to the blurring during the imaging process, some of the information in the image may have been lost, resulting in limited compensation accuracy through digital image processing algorithms. The mechanical IMC method utilizes a mechanical structure to move the camera in the direction of the image motion during exposure [13; 14]. The compensation speed for each point on the image plane was consistent, enabling two-axis compensation. This method is commonly used in ground or airborne cameras, but less frequently employed in space cameras. In space cameras, two-axis pointing platforms are often used to increase the pointing range, but they are rarely used to compensate for image motion [15].