# A Review of Ghost Imaging via Sparsity Constraints
## 3 Applications of GISC
### GISC Spectral Camera  
Spectral imaging is a multidimensional data acquisition technology combining spectroscopic and image analysis, which captures a 3D spectral data-cube (x,y,\(\lambda\)) about a scene to be imaged. With both spatial and spectral resolving capabilities, it is extremely effective and vital for scene survey and detail information extraction. Conventional spectral imaging, with th point-to-point corresponding between the object and image planes, requires time-consumed scanning along either a spatial or wavelength axis since the 3D spectral data-cube is detected by a 2D detector [59]. Hence, its application is restricted in fields such as ultra-fast imaging [60; 61]. Recently, remarkable snap-shot spectral imaging techniques have been widely developed to acquire a 3D spectral data-cube in just a single exposure [62; 63; 64; 65; 66]. However, since the correlation between pixels and wavelengths of the 3D image data-cube is not  
Figure 2: The result of the 3D GISC LiDAR reconstruction, the color bar denotes the distance to the GISC LiDAR: (**a**) the airborne 3D GISC LiDAR system, (**b**) a photo of the target, (**c**) the structured 3D GISC reconstruction [57]. utilized in these methods, the information acquisition efficiency is lower than the Shannon limit [67; 68]. Another important category of snapshot spectral imaging approaches is the coded aperture spectral imaging, such as the coded aperture snapshot spectral imager (CASSI), which utilizes a binary-coded mask and an equilateral prism to modulate light fields and captures a spectral image with a single shot 2D measurement [69; 70; 71; 72]. Combining with the compressive sampling principle, it improves the sampling efficiency through the compressive sampling in photoelectric detection. GI with true thermal light has been demonstrated by detecting the temporal fluctuation of light fields and the imaging information was obtained from the second-order correlation of light fields in time domain [73; 74]. This scheme requires that the time resolution of detector is close to or less than the coherence time of light field, which may be as short as femtoseconds for true thermal light [8; 20; 74]. Unlike the other existing imaging methods, a GISC spectral camera modulates the image at the whole spectral band, and the true thermal light is modulated into a spatial fluctuating pseudo-thermal light field by utilizing a spatial random phase modulator. In GISC spectral camera, the spectral images of the object are obtained by the second-order spatial mutual-correlation of light fields. Therefore, high time resolution isn't required in this scheme, and the information of the object can be acquired in a single-shot measurement. As shown in Figure 3, the GISC spectral camera consists of (1) an imaging module, which projects the image of an object on the object plane '\(a\)' onto the first image plane '\(b\)', (2) a spatial random phase modulator, which disperses the image with different wavelengths as a random grating and modulates the image to generate speckle patterns in plane '\(c\)' [20; 75; 76], (3) a microscope objective, which magnifies the speckle patterns in plane '\(c\)', and (4) a CCD detector recording the magnified speckle patterns.