压缩感知重构算法在“鬼”成像中的应用研究

“鬼”成像（GI）提供了一种用常规手段很难达到的特殊的获取图像方法，在量子光学领域是近些年来的前沿和热点之一。本文中，主要研究压缩感知（CS）的重构算法在“鬼”成像中的应用。我们使用具有高斯分布的热光源强度分布，来作为压缩感知的测量矩阵，分别以离散余弦变换(DCT)和离散小波变换(DWT)作为压缩感知中图像物体的稀疏矩阵，利用正交匹配追踪算法，最终获得基于压缩感知重构算法的“鬼”成像。研究结果表明，压缩比为0.5时，基于离散余弦变换基的压缩“鬼”成像（DCT-CS）和基于小波变换基的压缩“鬼”成像(DWT-CS)，比“鬼”成像原始重建算法有超过10dB的峰值信噪比提升；同时，基于DCT-CS算法的重建质量要优于DWT-CS算法。 

Application of compressed sensing in ghost imaging system

Ghost Imaging(GI) provides a special method to get an image, when it is difficult using conventional methods. Which has become one of the hot topics in quantum optics recently. In this paper, we discuss the application of Compressed Sensing (CS) in GI system. We utilize the intensity distribution of the thermal light distributed like Gaussian distribution as the measurement matrix of CS, select the Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT) as the sparse matrix of the image object, adopt the Orthogonal Matching Pursuit (OMP) algorithm as CS reconstruction algorithm, and obtain the reconstructed image. The result shows that the quality of GI with CS using DCT and DWT has enhanced to more than 10dB in Peak Signal-to-Noise Ratio(PSNR) to the result with original GI algorithm when the compression rate is 0.5. At the same time, the quality of DCT-CS algorithm has a little improvement to that of DWT-CS algorithm.