## 1 Introduction  
Ghost imaging (GI), a kind of nonlocal imaging method, was firstly observed in an experiment by [PERSON] et al. using entangled photon pairs through spontaneous parametric down-conversion (SODC) in 1995 [1; 2]. Different from conventional imaging technology, the GI geometry includes two paths: signal path and reference (or idle) path. The light source is firstly split into two equal parts by the beam splitter, and two parts propagate through two different paths separately. A bucket detector with no spatial resolution collects the light intensity from the signal path where the object is placed, and, in the reference path, another detector with high spatial resolution receives the light signal. One cannot obtain the image information with only one path information, but the image can be retrieved by measuring the fourth-order correlation function (FOCF) between two detectors. Whether entangled photon pairs are necessary for GI has been debated for a long time. In 2002, [PERSON] et al. realized GI with a laser beam using a scanning galvanometer system [3]. Later, GI was experimentally demonstrated using pseudo-thermal light [4; 5], which is generated by scattering a laser beam through a rotating ground glass disk. In theory, such a source can be modeled as a typical partially coherent source, known as the Gaussian Schell-Model (GSM) beam. [PERSON] and [PERSON] studied GI with a GSM beam based on the classical optical coherence theory [6; 7], and the results revealed that the image quality and visibility closely depended on the coherence properties of the light and it is impossible to observe a ghost image with both high quality and high visibility. The quality and visibility mentioned above measure the perfectness of the image compared to the object and the ratio of the image signal to the background noise in the imaging system, respectively. Compared to entangled photon pairs, a pseudo-thermal source can be generated easily. Considerable attention has been paid to GI with a pseudo-thermal source in the past twenty years [8; 9; 10; 11; 12; 13; 14; 15]. The GI has found applications in quantum metrology, lithography, holography, secure communication, information encryption and decryption, and so on [16; 17; 18; 19; 20; 21; 22; 23]. In recent years, there is a growing interest in GI in harsh environments, i.e., the optical path contains atmospheric/oceanic turbulence or strong scattering media, owing to its important applications in many aspects, such as communication, laser radar remote sensing, and optical imaging. In 2009, [PERSON] firstly investigated GI in a turbulent atmosphere and came to the conclusion that the quality of the image was degraded [24]. However, [PERSON] et al. found in the experiment that the quality of the image was immune to atmospheric turbulence [25], which is contradictory to the results obtained by [PERSON]. Since then, the properties of GI in a turbulent atmosphere, such as quality and visibility, have been studied extensively by other researchers [26; 27; 28], and the results showed that the quality of the image cannot be immune to turbulence, but the GI can greatly reduce the turbulence-induced degeneration compared to conventional imaging system. In 2018, [PERSON] and co-workers [29] found that the different results between [24] and [25] come from different types of turbulence, i.e., monostatic turbulence and bistatic turbulence, and solve the controversy between [24] and [25]. Recently, researchers focused on the properties of the GI in a turbulent ocean. Compared to atmospheric turbulence, the oceanic turbulence is affected by three major factors: the rate of dissipation of mean square temperature, the rate of dissipation of turbulent kinetic energy per unit mass of fluid, and the relative strength of temperature salinity fluctuations, which generally are much stronger than atmospheric turbulence. In 2017, [PERSON] et al.