Rodriguez Jose A, Xu Rui, Chen Chien-Chun, Zou Yunfei, Miao Jianwei
Department of Biological Chemistry, UCLA-DOE Institute for Genomics and Proteomics, University of California, Los Angeles, California 90095, USA ; Howard Hughes Medical Institute (HHMI), Chevy Chase, Maryland 20815-6789, USA.
J Appl Crystallogr. 2013 Apr 1;46(Pt 2):312-318. doi: 10.1107/S0021889813002471. Epub 2013 Feb 23.
Coherent diffraction imaging (CDI) is high-resolution lensless microscopy that has been applied to image a wide range of specimens using synchrotron radiation, X-ray free-electron lasers, high harmonic generation, soft X-ray lasers and electrons. Despite recent rapid advances, it remains a challenge to reconstruct fine features in weakly scattering objects such as biological specimens from noisy data. Here an effective iterative algorithm, termed oversampling smoothness (OSS), for phase retrieval of noisy diffraction intensities is presented. OSS exploits the correlation information among the pixels or voxels in the region outside of a support in real space. By properly applying spatial frequency filters to the pixels or voxels outside the support at different stages of the iterative process ( a smoothness constraint), OSS finds a balance between the hybrid input-output (HIO) and error reduction (ER) algorithms to search for a global minimum in solution space, while reducing the oscillations in the reconstruction. Both numerical simulations with Poisson noise and experimental data from a biological cell indicate that OSS consistently outperforms the HIO, ER-HIO and noise robust (NR)-HIO algorithms at all noise levels in terms of accuracy and consistency of the reconstructions. It is expected that OSS will find application in the rapidly growing CDI field, as well as other disciplines where phase retrieval from noisy Fourier magnitudes is needed. The (The MathWorks Inc., Natick, MA, USA) source code of the OSS algorithm is freely available from http://www.physics.ucla.edu/research/imaging.
相干衍射成像（CDI）是一种高分辨率无透镜显微镜技术，已被应用于使用同步辐射、X射线自由电子激光、高次谐波产生、软X射线激光和电子对各种样本进行成像。尽管最近取得了快速进展，但从噪声数据中重建诸如生物样本等弱散射物体的精细特征仍然是一项挑战。本文提出了一种有效的迭代算法，称为过采样平滑法（OSS），用于对有噪声的衍射强度进行相位恢复。OSS利用实空间中支撑区域之外的像素或体素之间的相关信息。通过在迭代过程的不同阶段对支撑区域之外的像素或体素适当地应用空间频率滤波器（平滑约束），OSS在混合输入输出（HIO）算法和误差减少（ER）算法之间找到平衡，以在解空间中搜索全局最小值，同时减少重建中的振荡。具有泊松噪声的数值模拟和来自生物细胞的实验数据均表明，在重建的准确性和一致性方面，OSS在所有噪声水平下均始终优于HIO、ER - HIO和噪声稳健（NR） - HIO算法。预计OSS将在快速发展的CDI领域以及其他需要从有噪声的傅里叶幅度中进行相位恢复的学科中得到应用。OSS算法的（美国马萨诸塞州纳蒂克市MathWorks公司）源代码可从http://www.physics.ucla.edu/research/imaging免费获取。
