Gaur Charu, Mohan Baranidharan, Khare Kedar
J Opt Soc Am A Opt Image Sci Vis. 2015 Nov 1;32(11):1922-7. doi: 10.1364/JOSAA.32.001922.
The problem of iterative phase retrieval from Fourier transform magnitude data for complex-valued objects is known to suffer from the twin image problem. In particular, when the object support is centrosymmetric, the iterative solution often stagnates such that the resultant complex image contains the features of both the desired solution and its inverted and complex-conjugated replica. In this work we make an important observation that the ideal solution without the twin image is typically more sparse in some suitable transform domain as compared to the stagnated solution. We further show that introducing a sparsity-enhancing step in the iterative algorithm can address the twin image problem without the need to change the object support throughout the iterative process even when the object support is centrosymmetric. In a simulation study, we use binary and gray-scale pure phase objects and illustrate the effectiveness of the sparsity-assisted phase recovery in the context of the twin image problem.
从复值物体的傅里叶变换幅度数据中进行迭代相位恢复的问题，已知会受到双像问题的困扰。特别是，当物体支撑区域是中心对称时，迭代解常常会停滞，使得最终的复图像包含了期望解及其反转和复共轭副本的特征。在这项工作中，我们有一个重要发现，即在某些合适的变换域中，没有双像的理想解通常比停滞解更稀疏。我们进一步表明，在迭代算法中引入一个增强稀疏性的步骤，可以解决双像问题，即使物体支撑区域是中心对称的，在整个迭代过程中也无需改变物体支撑区域。在一项模拟研究中，我们使用二进制和灰度纯相位物体，并在双像问题的背景下说明了稀疏性辅助相位恢复的有效性。
