中文摘要：

关联成像可提供一种运用常规手段难以获得清晰图像的方法, 能够解决一些常规成像技术不易解决的问题, 是近些年来量子光学领域的前沿和热点之一.本文提出一种基于压缩感知的差分关联成像方案（简称, 差分压缩关联成像方案）, 将高斯分布的热光源强度分布作为压缩感知的测量矩阵, 差分物体信息作为被成像物体信息, 利用差分关联成像方案的高成像信噪比和压缩感知技术的低采样次数, 通过正交匹配追踪算法, 高质量地恢复出物体信息. 并以二灰度“双缝”、“NUPT”, 多灰度Lena图和Boats图为例, 数值仿真差分压缩关联成像过程; 同时将本方案350次测量的结果与差分关联成像方案30000次测量的结果进行对比, 研究结果表明针对不同的被成像物体（二灰度“双缝”、“NUPT”, 以及多灰度Lena图和Boats图）, 10次成像的均方误差平均值分别降低了97.7%, 93.9%, 92.5%和71.4%; 与压缩鬼成像方案相比, 同样测量次数条件下均方误差值对于二灰度双缝和多灰度Lena图、Boats图等目标物 体分别有50.4%, 72.9%和66.8%的降低. 差分压缩关联成像方案极大地提高了成像信噪比, 降低了成像时间.

英文摘要：

Correlated imaging offers great potentiality, with respect to standard imaging, to obtain the imaging of objects located in optically harsh or noisy environment. It can solve the problems which are difficult to solve by conventional imaging techniques. Recently, it has become one of the hot topics in quantum optics. In this paper, we propose a new scheme of correlated imaging with differential correlated imaging based on compressive sensing, named differential compressive correlated imaging. The new scheme takes advantage of the high signal-to-noise ratio of the differential correlated imaging and low-imaging sampling frequency of the compressed sensing technique. In the scheme, we utilize the intensity of the thermal light, which is in line with the Gaussian distribution, as the measurement matrix of compressive sensing. We extract the differential object information as the image object information which could be recovered via orthogonal matching pursuit algorithm with high quality. By numerical simulations, we verify the proposed scheme. Here, we select the two gray-scale images, such as double-slit and NUPT, as well as the two multi-grayscale images （Lena and Boats） as the object. We take sampling 350 times in differential compressive correlated imaging for measurement. The numerical simulation results show that for the above image objects, the average mean-square error （MSE） over 10 times for the differential compressive correlated imaging scheme is reduced by 97.7%, 93.9%, 92.5% and 71.4% respectively with respect to that of the differential correlated imaging scheme. Moreover, compared with the compressive ghost imaging, the MSE value of the same double-slit in CDGI, as well as Lena and Boats under the same conditions, is reduced by 50.4%, 72.9% and 66.8% separately, which indicates that the compressive differential correlated imaging scheme can greatly improve the signal-to-noise ratio of the imaging, and significantly reduce the imaging time.