# A Review of Ghost Imaging via Sparsity Constraints
## 3 Applications of GISC  
### GISC LiDAR  
As an important detection tool, LiDAR has been widely used in remote sensing in recent decades [38; 39]. Traditional imaging LiDAR can be classified into two types: a scanning mode and a non-scanning mode (such as flash radiography) [40; 41; 42]. In the scanning mode, a real-space image of a target is obtained by scanning the target region point-by-point with a pulsed laser [41]. Therefore, it is difficult to image a high-speed moving target. The Non-scanning mode, characterized by an imaging system with high resolution and a pulsed flash laser, can cover the whole field of the target and obtain the real-space image in a single exposure [42]. However, because the light intensity reflected by the target is divided onto many small pixels of charge-coupled device (CCD) camera, the detectionsensitivity is poor, so the detection distance of the non-scanning LiDAR is limited by the signal-to-noise ratio (SNR) of the received photons distributed on the aperture of the imaging system. Currently, it is still difficult for the traditional LiDARs to achieve high-resolution images in long ranges. In addition, all these imaging methods require sampling rate at or beyond the Nyquist limit. GISC LiDAR was proposed to obtain a high-resolution 2D or 3D image in real-space at a sampling rate significantly less than the Nyquist rate with a time-resolved single-pixel detector, which means that it has the capability of both high efficiency in information extraction and high sensitivity in detection [18; 19]. Generally speaking, GISC in real-space requires that a measurement distance (between the detector and the light source) in the reference arm equals to an illuminating distance (from the light source to the target) in the test arm, and all of the reflected intensity distribution in the test arm is collected by a bucket detector. However, in remote sensing, the distance to the target, a.k.a., illumination distance, is usually unknown, so matching the measurement distance to the illuminating distance is not a reasonable option. In addition, the optical aperture in practice is very limited, so that only a small fraction of the reflected intensity from the remote target can be collected. Therefore, two key issues should be addressed in GISC LiDAR: (1) light fields on the target and the reference detection plane should be correlated, even when the test arm is far longer than the reference arm, (2) high quality images should still be reconstructed with only a small fraction of the reflected light. The second-order longitudinal correlation length of a thermal source can be expressed as [43]  
\[\Delta l_{z}\propto\lambda\left(\frac{z}{D}\right)^{2} \tag{5}\]  
where \(\lambda\) is the wavelength, \(z\) is the illuminating distance from the light source to the target, and \(D\) is the diameter of the pseudo-thermal light source. Researches have shown that 3D GI can still be achieved as long as the difference between the illumination and measurement distances is within the spatial longitudinal correlation length of the pseudo-thermal light source [44]. In 2009, a proof of principle experiment of far-field GI in real-space was completed [45]. According to the statistical characteristics of random speckle fields, the sum of multiple speckle intensity is proportional to the sum of total speckle intensity. The intensity correlation of light fields between the reference and test arms still holds, when the receiving aperture is not much smaller than the transmission aperture, only part of the reflected light is necessary to achieve the equivalent 'bucket' detection and realize 3D images in 3D GISC LiDAR [46]. These not only give a theoretical support for 3D GISC LiDAR, but also provide a system design guide. Figure 1a presents a typical schematic of GISC LiDAR system [19]. A conjugate relationship, between the target surface and the sensitive plane of the CCD camera in the reference arm, ensures correlation properties between the intensity distributions on the corresponding target and camera planes.