基于弱相干光源的数字全息，由于参考光和物光夹角在非常小的范围内才能观察到干涉条纹，因此该技术一般限制在同轴全息的范围之内，即采用相移法对多幅同轴全息图采集，不利于动态物体的观测与记录。引入压缩感知理论，结合数字全息重构算法，实现对单幅弱相干光数字全息图的数值重建，能有效抑制孪生像及相干噪声的干扰。给出详细的基于压缩感知的数值重建算法框架，并以发光二极管作为弱相干光源，基于数字全息实验光路，以分辨率测试标板为样品展开实验研究，说明该方法的有效性和可行性。

Low-coherence digital holography is confined to in-line holography because the interference fringes could be observed only when the angle between the object and reference light is small enough. Therefore, phase-shifting technique is usually employed. But it is not fit for dynamic analysis for demanding more than one hologram. However, the reconstructed image according to different sections of the object will be disturbed by the twin image and the out-of-focus section image by employing the traditional numerical reconstruction method for the analysis of one single in-line digital hologram. A numerical reconstruction method according to compressive sensing theory for the analysis of single low-coherence in-line digital hologram is proposed. By this method, the twin image and the coherent noise can be inhibited. The theory is presented in detail. Experimental research on light emitting diode-based digital holography is performed to demonstrate the feasibility and validity of the method.