压缩感知鬼成像中观测矩阵构造

为了提高压缩感知鬼成像(CSGI)的成像效果,解决 现阶段观测矩阵存在的稳定性差、数据庞大和不 满足非负性等问题,对观测矩阵的构造方法进行研究。首先,介绍确定性随机序列 的产生方法和 性质,可以用作观测矩阵,满足有限等距要求。针对光强的非负性,提出利用偶次幂的余弦 函数产生确定 性随机序列的方法,构造观测矩阵并证明其性质；然后,通过仿真验证该观测矩阵的正确性 ,研究了序列 的初始值和函数的幂对矩阵重构性能的影响；最后,搭建实验平台,对比常用的高斯随机矩 阵(GM),分析本文方 法的适用性和优缺点。实验结果表明,在鬼成像中,利用本文所构造的随机矩阵,重 构图像峰值信 噪比(PSNR)与GM相当,但存储的数据量大大 减少,可满足鬼成像系统的快速高效、简单方便和成本低等要求。

Construction of measurment matrix in compressive sensing g host imaging

In order to enhance the image quality of compressive sensing ghost Imaging (CSGI ) and solve the existing problems of measurement matrix in this stage,a new cons truction method of measurement matrix is presented in this paper.First,the princ iples and properties of deteiministic random sequences are introduced,which can be used as meas urement matrix and satisfy the restricted isometry property (RIP).Aiming at the nonnegativeness of light intensity,based on the deteiministic random sequences achieved by even quadratic cosine function ,a new construction method of measurement matrix is applied.Then,according to the theory of logistic map,the properties and accuracy of deteiministic random matrix are proved by simulation and the inf luences of initial value and the power of cosine function on the reconstruction property are analyzed.Finally,compared with Gaussian matrix,the experimental system platform is built,and the applicability and merit of deteiministic random matrix are analyzed.Experimental results indicate that the peak signal to noise ratio (PSNR) of the reconstructed image is 38.7dB and t he amount of data is reduced by 4096times compared with Gaussian matrix.It can satisfy the system requirements of stabilization,convenie nce and rapid speed in ghost imaging.