# On Ghost Imaging Studies for Information Optical Imaging
## 4 Outlook
### X-ray Diffraction Gi  
On the basis of the already-realized X-ray diffraction GI experiment, in the near future, the main goal of X-ray diffraction GI will be to demonstrate an imaging resolution up to the order of 10 nm on the table-top-X-ray-device-based experimental facility. This is expected to be realized by fully exploiting the ability of the non-local encoding scheme on greatly improving the imaging quality without increasing the radiation exposure of the sample. Next, it is expected that performing exploratory studies will challenge the possibility of realizing a higher, near-atom-scale resolution by conducting experiments on the X-ray free-electron laser system. These will put forward further demands on both the non-local encoding mode design as well as recovery algorithms. Furthermore, for diffraction GI, it would be rather fascinating to realize diffraction imaging with thermal Fermion sources. Though compressed sensing [142; 143] and deep learning [144; 145; 146; 147] have both been applied to retrieve the image information in GI, it should still be an important research theme to adopt and develop befitting signal processing methods which can not only more efficiently utilize the detected signal and the prior information about the imaging scene by taking the advantage of GI, but also be more naturally compatible with task-oriented imaging mode as well as the quantum detection theory. The retrieval methods currently used in GI (including correlation-based, compressed sensing and deep learning algorithms) almost all perform information retrieval after obtaining the sampling data. However, this processing mode is not in line with the task-oriented imaging mode, since in many task-oriented scenes, it is required to judge in real time whether the already measured information is sufficient for the task or more samplings are needed. The confidence and uncertainty of the task information retrieved from these methods can hardly be immediately determined from a theoretical viewpoint. Nevertheless, for imaging systems based on light-field correlation (coincidence imaging, GI, etc.) that perform encoding on the image information via light-field fluctuations, it is possible to formulate the image information acquisition procedure into a (stochastic) dynamical system by arranging the measured encoded signals in a certain way. Then, Bayesian estimation methods for dynamical systems could be applied to obtain the probability distribution function (PDF) of the retrieved image information, resulting in a complete description about the retrieval accuracy of the imaging information [148; 149; 150]. By doing this, one of the advantages is that it is a recursive procedure, namely, the estimation of the image information as well as its uncertainty can be updated immediately by incorporating newly measured signals [151; 152; 153], and hence the sampling can be terminated once the desired information precision is achieved. This is more suitable for the task-oriented imaging mode compared with those \"measurement-before-processing\" modes, where oversampling or undersampling commonly exists. Additionally, since the PDF of the image information can be obtained, more complete information-theoretical description and analysis could be further performed. In addition, as a statistical method, it is also convenient to be combined with the quantum detection theory. As a matter of fact, in those very early studies of GI, it was believed that GI is a pure quantum effect [154; 155], until the demonstration of GI experiments with classical light sources [156; 157]. Currently, existing studies in GI focus more on systems with classical sources since they have more general application prospects and can thus be further targeted at various specific imaging demands. Nonetheless, quantum GI techniques exploiting non-classical sources as well as the quantum description of the interaction between lights and objects may bring a wonderful sight that has never been seen before [158].