三维复杂场景的菲涅耳全息图频域压缩重建

Frequency Domain Compressive Reconstruction of Fresnel Hologram for Complex Three-Dimensional Object

针对三维物体计算机产生全息图信息的相似性和冗余性问题,提出了一种基于三维总变分稀疏模型复杂三维场景的菲涅耳全息图频域压缩重建方法。首先通过计算获得了三维物体的菲涅耳全息图,然后利用概率密度函数服从指数分布的非相干变密度频域下采样模式对菲涅耳全息图的频域进行频域下采样操作,最后利用压缩感知重构算法对下采样后的全息图频域信息进行频域压缩重建。模拟实验验证了该方法的可行性,相比于传统的利用高斯随机测量矩阵对全息图空域的下采样模式,所提方法能够显著提高重构图像的峰值信噪比,这方法尤其适用于低采样率情况下。

Aiming at the problem of similarity and redundancy of information of three-dimensional（3D）object hologram generated by computer,a method which based on3 D total variation sparse model to realize frequency domain of Fresnel hologram′s reconstruction of complex 3D object is proposed in this paper.Firstly,the Fresnel hologram of3 D object is obtained by using computation;then,the frequency domain of Fresnel hologram is sub-sampled by using the incoherent variable density sub-sampling pattern of frequency domain with probability density function obeying exponential distribution;finally,the sub-sampling frequency domain of hologram can be reconstructed by using compressive sensing reconstruction algorithm.Simulation experiments verify the feasibility of the method,compared with the traditional method of using Gauss random measurement matrix to subsample the spatial domain of hologram,the method proposed in this paper can improve the peak signal to noise ratio of the reconstructed image,especially in the condition of low-sampling rate.