高计算复杂度是目前制约全息显示的瓶颈，针对这一难题，提出一种基于压缩感知理论与无透镜傅里叶变换相结合的全息图编码与重现算法。利用计算机生成无透镜离轴傅里叶全息图，再用压缩感知理论对全息图进行压缩采样和恢复，最后对恢复出的全息图进行重构，并再现原始图像。该方法的优点在于只采样全息图的部分有用系数就能很好地恢复出原始图像，从而解决了传感器采样数据过大的问题，降低了计算复杂度。仿真实验表明，20%的压缩采样时，重构出的全息图的相关系数为0.85，而50%时该系数为0.9999。通过搭建的全息再现系统进行实际验证，实验结果表明能够清晰地再现出原始图像，从而证明了该方法的可行性。

High computational complexity is the bottleneck of the holographic display. Aiming at the problem, a new hologram coding and reconstruction algorithm based on compressed sensing theory and lensless Fourier transform is proposed. Lensless off-axis Fourier hologram is generated by computer, and then the hologram is sampled and reconstructed by the theory of compressed sensing. At last, the original image is reconstructed by the hologram. The advantage of this method is that only some useful sampling coefficients of the hologram is used to reconstruct the original image well, which solves the problem of large volume of sampling data of the sensor and achieves the goal of reduction of the computational complexity. Simulation results show that the correlation coefficient of reconstructed image with 20% compressive sampling rate is 0.85; when compressive sampling rate of hologram with 50%, the coefficient reaches 0.9999. In addition, a holographic reconstruction system is built to verify the hologram compression sampling theory. The experimental results indicate that the original image can be clearly reconstructed by the system, which proves the feasibility of the method.