Research On Application Of Sensitivity Analysis And Convex Optimization Theory In Ghost Imaging

Ghost imaging can reconstruct the image of the target object by correlating the data measured by the two detectors,which breaks the thinking and limitation of traditional imaging.It has the characteristics of"off-axis imaging",which can achieve super-resolution and long-distance imaging,and has excellent anti-interference ability.Therefore,it is widely used in many fields.The object's image is obtained by calculating the data,so the quality of the image is closely related to the data sampling rate.The high-resolution image usually means a large amount of sampling data and long-time calculation,which puts forward high requirements for experimental equipment and hardware facilities,and also affects the performance of real-time imaging.Under the premise of the imaging quality,correspondence ghost imaging and compressive sensing ghost imaging can reduce the number of sampling required for image reconstruction and shorten the calculation time,which have important practical significance.Based on the above mentioned,the research contents of this paper include the following two aspects:1.Sensitivity analysis is used to explain correspondence ghost imaging.Correspondence ghost imaging can reconstruct the equal quality image by selecting the bucket sequence with large fluctuation and the corresponding reference patterns.In this paper,using sensitivity analysis,we establish the regression model on the reconstructed image and reference patterns.In this regression model,the sensitivity of the reconstructed image to reference patterns can be quantified as sensitivity coefficients.Comparing the bucket sequence with sensitivity coefficients,and combining with the study of similarity between the reconstructed image and reference patterns,we explain the reason of achieved better effect for correspondence ghost imaging.We also find that the sensitivity coefficients are more robust than the bucket sequence under noisy conditions.2.Using convex optimization theory to explore the reason that the fluctuation preprocessing can improve imaging resolution.In the image reconstruction by the compressive sensing algorithm,it is found that the fluctuation preprocessing of the two detectors'data has a positive effect on the imaging,which can improve the resolution of the reconstructed image.Based on the convex optimization theory,in this paper,the imaging resolution problem is explained by the geometric theory behind compressive sensing,which is a series of theories that the existence of unique solution for compressive sensing problem is equivalent to the number of(k-1)-faces of the high-dimensional cross-polytope remains unchanged after projection from the high-dimensional space to the low-dimensional space.The data is displayed on the sphere in the three-dimensional space,and it is found that the distribution of data after fluctuation preprocessing is more scattered and random,which also verifies our conclusion.