# On Ghost Imaging Studies for Information Optical Imaging
## 3 Ghost Imaging Studies for Information Optical Imaging
### Optimizing the Encoding Mode to Reduce Unnecessary Sampling Redundancy  
The issue of unnecessary sampling redundancy of the traditional imaging mode is hard to address due to its \"direct point-to-point\" imaging architecture. In the GI system, however, since the encoding mode can be varied more flexibly during the practical imaging process, unnecessary redundancy in the detection signal can be largely reduced by designing light fields based on the information theory. From the theoretical perspective, several studies in this direction have been performed. In 2013, [PERSON] et al. [91] firstly tried to theoretically analyze the mutual information between the detection signal and the imaging object given the determined light fields in GI, and on this basis, gave the optimal parameter of Bernoulli light fields that maximizes the mutual information to perform the optimization. However, this research was restricted to designing light fields subject to some specific distributions. Besides ideas inspired by [PERSON] information theory, by combining the CS theory, light field optimization scheme via minimizing the mutual coherence between the sampling matrix (consisting of light field patterns) and the orthogonal sparsity basis was proposed [92] according to the incoherent sampling principle [93]. The effect of this scheme on improving the imaging quality was also demonstrated by practical experiments [92]. To further incorporate image statistics into the optimization, an optimization framework combined with dictionary learning [94; 95] was proposed [96]. In this framework, an over-complete sparsity basis that describes the statistics of imaging objects was given via dictionary learning, and light fields were optimized by similarly solving a mutual coherence minimization problem through a concise method. A closed-form solution of the optimal light fields was theoretically derived and experimentally applied to further enhance the imaging quality. Briefly speaking, these studies have shown that optimizing light fields with the help of information theory can essentially increase image information transmission efficiency. In addition, some heuristic encoding mode optimization studies have been proposed, which adaptively adjust the encoding mode according to precedent-acquired information [97; 98; 99; 100] to reduce the redundancy contained in subsequent samplings.  
On the other hand, the information content that the GI system can transmit is a more fundamental problem which could inspire the encoding optimization. As aforementioned, mutual information between the detection signal and the imaging object given a determined type of light fields has been analyzed [91] and applied to light-field optimization. Besides the mutual information, Fisher information [101] has also been used to analyze the information that detection signals contain about the imaging object in the GI system [102]. In this study, it was shown that signals with larger fluctuations contain more information, which is consistent with several existing studies [103; 104; 105; 106] and provides a potential idea for the encoding mode optimization.  
Generally, by utilizing fundamental information-theoretic studies, it is possible to provide a solid foundation for those research topics of the GI system such as encoding light fields optimization, resolution analysis, and performance investigation. Hence, there would be significant demands on this research direction considering that existing studies on the information content analysis of the GI system are still rather limited.