相移数字全息图用传统数字再现可以消除零级像与共轭像, 但数字全息术记录的全息图及数字再现像的分辨率被CCD的分辨率所限制。将新兴的压缩感知算法用于数字全息图的稀疏重建, 以实现由部分全息图数据得到高分辨率再现像。分析了压缩感知用于重建数字相移全息图的原理, 并利用该算法对计算机模拟的相移全息图进行了重建。结果表明, 压缩感知算法能够对数字全息图稀疏重建, 利用50%的部分全息图数据重建出了较高质量的再现像, 并消除了零级像和共轭像。当选用合适的观测器如数字微反射镜器件或随机位相片实现随机观测矩阵时, 可以实现单像素成像, 从而突破记录全息图CCD分辨率的限制。

The zero-order diffraction image and the conjugate image can be eliminated using the phase-shifting digital holography. However, the resolution of the hologram and the reconstructed image is limited by the resolution of the CCD used in the digital holography. To reconstruct a higher resolution image from part information of a hologram, the novel compressive sensing algorithm is applied to the sparse reconstruction of digital holograms. The theory of applying the compressive sensing algorithm to reconstruct digital holograms is analyzed. A digital hologram acquired by simulation in computer is reconstructed using this algorithm. The experimental results show that digital holograms can be reconstructed using the compressive sensing algorithm. A high-quality image is reconstructed from the 50% data of the hologram. The zero-order diffraction image and the conjugate image are eliminated. When random measurement is realized by an appropriate measurement device such as a DMD or a random phase plate, digital holograms can be recorded by a single pixel camera to break the limitation of the CCD resolution.