鬼成像是一种与传统成像方式不同的通过光场涨落的高阶关联获得图像信息的新型成像方式。近年来,相比传统成像方式,鬼成像所拥有的一些优点如高灵敏度、超分辨能力、抗散射等,使其在遥感、多光谱成像、热X射线衍射成像等领域得到广泛研究。随着对鬼成像的广泛研究,数学理论和方法在其中发挥的作用愈显突出。例如,基于压缩感知理论,可以进行鬼成像系统采样方式优化、图像重构算法设计及图像重构质量分析等研究工作。本文旨在探索鬼成像中的一些有趣的数学问题,主要包括:系统预处理方法、光场优化及相位恢复问题。对这些问题的研究既可以丰富鬼成像理论,又能推动它在实际应用中的发展。

Ghost imaging (GI) is a novel imaging technique which is different from conventional imaging techniques, which extracts image information via high-order correlation of light-field fluctuations. In recent years, compared with conventional imaging techniques, GI has some advantages such as high sensitivity, super-resolution ability and anti-scattering,which make it widely studied in remote sensing, multi-spectral imaging, thermal X-ray diffraction imaging, and other fields. With these developments, mathematical theory and methods play a more prominent role in GI. For example, based on compressed sensing (CS) theory, we can optimize the sampling mode of GI system, design the algorithm of image reconstruction and analyze the quality of image reconstruction. In this paper, we discuss a few interesting mathematical problems in GI, including preconditioning, optimization of light fields, and phase retrieval. Studying these problems can be useful for enriching the theory of GI and promoting its practical applications.