# On Ghost Imaging Studies for Information Optical Imaging
###### Abstract
Hence, in those studies on both optical information capacity analysis [5; 6; 7] and the resolution description of traditional imaging systems, only the 2-D spatial DOF is involved, and the generalized resolution description in a higher-dimensional light-field domain as well as the influence of multiple-dimensional information on the 2-D spatial resolution are hard to analyze for traditional imaging systems. Additionally, information theory has been used to analyze and design traditional optical imaging systems. Roughly from the information-theoretic perspective, studies in the field of image compression [21; 22] have shown that for most images, the trivial image representation is a redundant one [23]. Since typical traditional imaging systems use the \"direct point-to-point\" imaging mode that directly performs one-to-one signal mapping from the object to the detection plane, corresponding detected signals actually contain considerable redundancy, which is unnecessary in high-SNR detection. On the other hand, for those non-imaging tasks, such as object tracking and classification, though a task-specific information measure was proposed [24], since the image information acquisition mode is largely fixed, the traditional imaging system design according to information theory could only perform the optimization of system parameters [25; 26; 27; 28], rather than accordingly designing different optical transmission functions. Different from those traditional imaging systems that realize the 2-D spatial domain \"direct point-to-point\" optical transmission function by using optical elements and are thus diffraction limited by the system aperture, the coherent diffraction imaging (CDI) technique [29] performs \"direct point-to-point\" information mapping in the Fourier domain by using light propagation without optical elements. Hence, diffraction imaging is rather suitable for imaging with light sources of wavebands where corresponding high-precision imaging elements are hard to manufacture, such as X-rays [30; 31], and the resolution can theoretically reach the order of the wavelength. However, in practice, the resolution of this type of imaging mode is empirically proportional to the quarter root of the intensity of coherent radiation sources [32]. Since it is hard to obtain a highly bright coherent radiation source for X-ray and Fermions (such as neutrons and electrons), an extension on its ability of ultra-high resolution in practical applications is greatly limited. In addition, the information transmission mode in CDI is also largely fixed, thus it is hard to be optimized according to information theory to address issues such as weak signal processing in noisy circumstances for a higher resolution. Through information-theoretic studies and analyses on traditional imaging systems, a series of theories, concepts, and methods has been developed, which promotes the integration of information theory and optical imaging techniques, and sets up the basic framework of information optical imaging. However, limitations of traditional imaging systems due to the \"direct point-to-point\" image information acquisition mode are also revealed, including the following:  
1. Multiple-dimensional light-field information is degenerated into the 2-D domain;
2. Resolution analysis is also restricted to the 2-D spatial domain;
3. Detection signals usually contain unnecessary redundant image information;
4. For specific tasks where the whole image information is not necessary, (over)sampling on the full-resolution image is still performed first;
5. For diffraction imaging systems, it is hard to achieve a resolution at the order of the wavelength without highly bright coherent sources since methods for weak signal detection developed in modern information science cannot be applied.