对于同轴傅里叶数字全息，传统重构算法应用快速傅里叶逆变换算法进行重构，但采样过程需要满足香农采样定理，导致海量采样数据，大大增加了存储和传输的代价。提出了一种基于压缩传感的相移同轴傅里叶数字全息重构方法，利用马赫曾德尔干涉光路采集同轴全息图，对采集数据进行部分采样、测量；然后利用最小全变分法对采集的数据进行数值再现。数值仿真结果表明，基于压缩传感的傅里叶全息重构算法优于基于快速傅里叶逆变换的传统算法，它将全息数据的采集和压缩合为一步进行，不仅采样数据明显少于传统采样数据，而且利用约8%的数据仍然能精确地重构出原图像。

on-axis Fourier digital holography, the conventional way for image reconstruction is inverse fast Fourier transform (IFFT), but the Shannon′s sampling theory must be satisfied in the sampling process, which causes the data redundancy and greatly increases the cost of storage and transmission. A reconstruction method of phase-shifting on-axis Fourier digital holography based on compressed sensing (CS) theory is put forward. Firstly, on-axis hologram is collected in the Mach-Zehnder interferometer light path. Then the collected data are partially sampled and measured. Lastly the image is numerically reconstructed by using the minimum total variation method. The numerical simulation result shows that the reconstruction method based on CS, which takes the sampling and compression of the hologram data to one step, is superior to that based on the conventional reconstruction method. The amount of sampling data based on CS is less than that based on IFFT, but the original image can also be accurately reconstructed from just about 8% hologram data.