# Experimental Investigation of Anisotropic Diffusion Applied in Ghost Imaging Reconstruction
## 1 Introduction  
Traditional imaging technology reconstructs the object image with a photosensitive panel in which each pixel corresponds to a value of light intensity of the reconstructed object, usually considered as direct imaging technology. In contrast, ghost imaging (GI), also known as correlation imaging, utilizes two spatially correlated beams to retrieve the object image. The spatially correlated beams are received by a beam splitter, which divides the optical field into the object beam and the reference beam in the GI system. The object beam is modulated by an unknown object and measured by a bucket detector with no spatial resolution; the reference beam is collected by a detector with spatial resolution. It is an indirect imaging technology in which the two detectors are not directly used for object reconstruction, but the objects can be achieved by the associative calculation of two groups of data the detectors collected [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15]. Therefore, ghost imaging technology can be applied in a variety of complex environments, such as imaging targets in a harsh surrounding, where traditional imaging technology may fail [16; 17; 18]. The quantum light source was considered to be a necessary condition for ghost imaging, because GI was originally realized by the two-photon with entangled properties. However, in recent years, thermal light [19; 20; 21], pseudo thermal light [22], neutrons [23; 24] and even X-rays [25] have all proven to be applicable to GI. With these developments, the interpretation of the ghost imaging is not limited to quantum entanglement theory; classical coherent light propagation theory can be applied [2; 3; 4; 5]. In addition, owing to its convenience and low cost, the pseudo-thermal light source is widely used in ghost imaging technology [22]. The appearance of ghost imaging with a classical light source has greatly enlarged the application prospect of ghost imaging. Ever since, researchers began focusing on how to improve the imaging quality and speed up the process of application exploration [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 26; 16; 17; 18; 19; 27; 28]. In the aspect of ghost imaging algorithms, differential ghost imaging (DGI) [6], as well as normalized ghost imaging (NGI) [7], turn attention to modifying the GI algorithm by means of weighting the speckle patterns for each measurement. DGI and NGI reduce the effect of noise in the imaging process to a certain extent. Based on the entire measurement data, the GI algorithm can be described as a matrix form. Pseudo-inverse ghost imaging (PGI) replaces the transpose of the matrix constructed by all of the intensity distribution measured by the detector with its pseudo-inverse, thereby providing a new direction of investigation for further study [8; 9]. Iterative pseudo-inverse ghost imaging (IPGI) uses the reconstruction results of PGI to construct the noise term, and then obtains better reconstruction results over several iterations [10; 11]. In binomial-theorem ghost imaging (BGI) [12], images with low-level noise can be generated by constructing a binomial formula using high-order imaging results that are acquired by reintroducing the reconstruction result back into the imaging formula repeatedly. Compressive sensing ghost imaging (CSGI) introduces compressive sensing theory into GI, which not only reduces the measurements times, but also enhances the visibility of the imaging. Nevertheless, one deficiency of CSGI is that the algorithm complexity causes very long computing time [14; 15]. For a ghost imaging system, computing ghost imaging (CGI) [26; 27] uses a spatial light modulator to generate a random phase light field, whose light field distribution can be calculated after propagating a certain distance, so the construction of the reference light path is no longer necessary.