深空探测的不断发展对光学成像系统的观测能力提出了极高的要求，0.01角秒的分辨率需要的口径达到百米量级，目前的加工技术难以满足需求。光学合成孔径成像通过多个小孔径克服单一孔径的局限，是达到高分辨率成像的有效途径。然而光学合成孔径成像系统由于其子孔径离散化分布，整个成像系统的实际透光面积只占等效单子径系统透光面积的一部分。当系统填充因子较小时，采集到的图像中高频阶段频域信息损失严重，甚至出现中高频信息缺失的现象，使得最终的成像效果出现退化模糊现象，图像分辨率降低。因此本文对低填充比光学合成孔径成像系统图像复原算法展开研究，提高图像分辨率，获取像质较好的图像。

本文首先对低填充比光学合成孔径成像系统退化图像中高频信号进行分析，提出了一种改进对数螺旋变阵方法，实现了图像中高频信号的增强。然后改进了维纳滤波算法，通过提出的综合评价指标Q自适应确定维纳滤波的参数K值，提高了算法的自适应性和图像成像质量。最后提出了一种频域组合滤波方法，有效提高了图像分辨率，实现了低填充比情况下的高质量图像复原。具体工作内容如下：

针对低填充比光学合成孔径成像系统退化图像中高频信息缺失的问题，提出了一种阵列改进对数螺旋变阵方法。以现有的阵列对数螺旋变阵为基础，利用阿基米德螺旋线等间距向外扩散的特点改进其中高频离散化，均匀性差的问题。提高了综合阵列及其调制传递函数的中高频频域覆盖，综合阵列中高频特性提升了17.35%，从而实现了退化图像中高频信号的增强。仿真结果表明Golay3阵列通过改进对数螺旋变阵可得到低填充比情况下中高频频域信息较充分的退化图像。

针对光学合成孔径成像系统得到的退化图像成像质量不理想，图像分辨率和对比度下降的问题，提出了一种改进维纳滤波算法。首先通过现有评价方法对复原图像进行单独评价分析，综合全参考和无参考评价方法，给出一个新的综合评价指标Q，解决了单个评价指标很难准确评价图像复原效果的问题。然后，基于综合评价指标Q，通过自迭代的方式对维纳滤波的参数K值进行自适应确定，使算法不需要人为地对先验信息进行估计而能得到最适宜的复原结果。仿真结果表明综合评价指标Q能够提高评价的准确性，改进维纳滤波算法提高了算法的自适应性且能够更准确地选取到合适的K值，得到较好的复原效果。

针对改进维纳滤波算法存在的局限性，获得的图像依旧存在低频背景信号强，高频细节信号弱的特征，在改进维纳滤波的基础上，提出一种频域组合滤波方法。根据高低频信号的特点，分别用不同滤波算法对高低频进行处理。首先通过无振铃现象的高斯高通滤波器来区分高低频区域，并根据综合评价指标Q找到其划分高低频的最优截止频率。对于低频部分，利用双边滤波算法保边去噪的特点进行平滑背景处理；对于高频部分，利用高频强调滤波进行突出强调细节处理。最后通过傅里叶反变换得到最终的复原图像。仿真结果表明该算法能够有效提高图像分辨率，相较于改进维纳滤波提高了3.77%，实现了低填充比情况下的高质量图像复原。

The continuous development of deep space exploration has posed extremely high requirements on the observation capabilities of optical imaging systems. A resolution of 0.01 arcseconds requires an aperture of hundreds of meters in size, which is currently beyond the capability of existing processing technologies. Optical synthetic aperture imaging overcomes the limitations of a single aperture by using multiple small apertures and is an effective way to achieve high-resolution imaging. However, due to the discretized distribution of sub-apertures, the actual aperture area of the entire imaging system only accounts for a portion of the equivalent single-aperture system. When the filling factor of the system is small, the high-frequency phase domain information in the collected image is severely lost, and the phenomenon of missing mid-to-high frequency information occurs, resulting in degraded and blurred imaging effects and reduced image resolution. Therefore, this paper investigates image restoration algorithms for low filling ratio optical synthetic aperture imaging systems to improve image resolution and obtain higher-quality images.

This paper first analyzes the high-frequency signal in degraded images of low fill-factor optical synthetic aperture imaging systems, and proposes an improved logarithmic spiral transformation method to enhance the high-frequency signal in the image. Then, the Wiener filtering algorithm is improved by proposing a comprehensive evaluation index Q to adaptively determine the parameter value K of the Wiener filter, thereby improving the adaptability of the algorithm and the imaging quality of the image. Finally, a frequency domain-based combined filtering method is proposed, which can simultaneously smooth the low-frequency background and enhance the high-frequency details, achieving high-quality image restoration under low fill-factor conditions. The specific work is as follows:

To address the problem of missing high-frequency information in degraded images of low fill-factor optical synthetic aperture imaging systems, an array-based improved logarithmic spiral transformation method is proposed. Based on the existing array logarithmic spiral transformation, the method improves the problem of poor uniformity of high-frequency discretization by utilizing the characteristic of Archimedean spiral spreading outward at equal intervals. This improves the coverage of the mid-to-high frequency domain of the composite array and its Modulate Transfer Function, thus achieving enhancement of high-frequency signals in degraded images. Simulation results show that the Golay3 array can obtain degraded images with more sufficient mid-to-high frequency domain information under low fill-factor conditions through improved logarithmic spiral transformation.

Aiming at the problem of low contrast between high and low frequency components in degraded images caused by array transformation and the resulting suboptimal imaging quality, an improved Wiener filtering algorithm is proposed. Firstly, a new comprehensive evaluation index Q is given by analyzing the restored image separately through existing evaluation methods, integrating full-reference and no-reference evaluation methods to solve the problem of difficult and inaccurate evaluation of image restoration effects with a single evaluation index. Then, based on the comprehensive evaluation index Q, the adaptive determination of the parameter K of the Wiener filter is achieved through self-iteration, which eliminates the need for prior estimation of information and enables the algorithm to obtain the most suitable restoration results. Simulation results show that the comprehensive evaluation index Q can improve the accuracy of evaluation, and the improved Wiener filtering algorithm has higher adaptability and can more accurately select the appropriate value of K to achieve better restoration effects.

A frequency-domain combination filtering method is proposed to address the limitations of the improved Wiener filtering algorithm, which still produces images with strong low-frequency background signals and weak high-frequency detail signals. Based on the characteristics of high and low frequency signals, different filtering algorithms are applied to process them. Firstly, a Gaussian high-pass filter without ringing is used to distinguish between high and low frequency regions, and the optimal cut-off frequency for separating them is determined based on the comprehensive evaluation index Q. For the low-frequency part, a bilateral filtering algorithm is used to smooth the background while preserving edges and removing noise. For the high-frequency part, a high-frequency emphasis filter is used to enhance the details. Finally, the restored image is obtained by inverse Fourier transform. The simulation results show that the proposed algorithm can effectively improve the image resolution, which is 3.77% higher than that of the improved Wiener filter, and achieves high-quality image restoration in the case of low fill ratio.