scholarly journals A Composite Initialization Method for Phase Retrieval

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2006
Author(s):  
Qi Luo ◽  
Shijian Lin ◽  
Hongxia Wang
Keyword(s):  
Gradient Descent ◽  
Phase Retrieval ◽  
Correlation Method ◽  
Current Phase ◽  
True Solution ◽  
Vector Method ◽  
Spectral Matrix ◽  
Symmetrical Form ◽  
Maximal Correlation ◽  
Lower Error Bound

Phase retrieval is a classical inverse problem with respect to recovering a signal from a system of phaseless constraints. Many recently proposed methods for phase retrieval such as PhaseMax and gradient-descent algorithms enjoy benign theoretical guarantees on the condition that an elaborate estimate of true solution is provided. Current initialization methods do not perform well when number of measurements are low, which deteriorates the success rate of current phase retrieval methods. We propose a new initialization method that can obtain an estimate of the original signal with uniformly higher accuracy which combines the advantages of the null vector method and maximal correlation method. The constructed spectral matrix for the proposed initialization method has a simple and symmetrical form. A lower error bound is proved theoretically as well as verified numerically.

scholarly journals Three-dimensional propagation in near-field tomographic X-ray phase retrieval

2016 ◽  
Vol 72 (2) ◽  
pp. 215-221 ◽  
Author(s):  
Aike Ruhlandt ◽  
Tim Salditt
Keyword(s):  
Phase Retrieval ◽  
Near Field ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Current Phase ◽  
Computationally Efficient ◽  
X Ray ◽  
Reconstruction Quality ◽  
Consistency Constraints

This paper presents an extension of phase retrieval algorithms for near-field X-ray (propagation) imaging to three dimensions, enhancing the quality of the reconstruction by exploiting previously unused three-dimensional consistency constraints. The approach is based on a novel three-dimensional propagator and is derived for the case of optically weak objects. It can be easily implemented in current phase retrieval architectures, is computationally efficient and reduces the need for restrictive prior assumptions, resulting in superior reconstruction quality.

scholarly journals Three-dimensional coherent X-ray diffraction imaging via deep convolutional neural networks

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Longlong Wu ◽  
Shinjae Yoo ◽  
Ana F. Suzana ◽  
Tadesse A. Assefa ◽  
Jiecheng Diao ◽  
...  
Keyword(s):  
Transfer Learning ◽  
Phase Retrieval ◽  
Three Dimensional ◽  
Current Phase ◽  
X Ray Diffraction ◽  
Deep Convolutional Neural Networks ◽  
X Ray ◽  
Model Combining ◽  
Diffraction Imaging ◽  
Improved Performance

AbstractAs a critical component of coherent X-ray diffraction imaging (CDI), phase retrieval has been extensively applied in X-ray structural science to recover the 3D morphological information inside measured particles. Despite meeting all the oversampling requirements of Sayre and Shannon, current phase retrieval approaches still have trouble achieving a unique inversion of experimental data in the presence of noise. Here, we propose to overcome this limitation by incorporating a 3D Machine Learning (ML) model combining (optional) supervised learning with transfer learning. The trained ML model can rapidly provide an immediate result with high accuracy which could benefit real-time experiments, and the predicted result can be further refined with transfer learning. More significantly, the proposed ML model can be used without any prior training to learn the missing phases of an image based on minimization of an appropriate ‘loss function’ alone. We demonstrate significantly improved performance with experimental Bragg CDI data over traditional iterative phase retrieval algorithms.

scholarly journals Retrieval of the atomic displacements in the crystal from the coherent X-ray diffraction pattern

2014 ◽  
Vol 21 (4) ◽  
pp. 774-783 ◽  
Author(s):  
A. A. Minkevich ◽  
M. Köhl ◽  
S. Escoubas ◽  
O. Thomas ◽  
T. Baumbach
Keyword(s):  
Diffraction Pattern ◽  
Phase Retrieval ◽  
Real Space ◽  
Retrieval Algorithm ◽  
X Ray Diffraction ◽  
True Solution ◽  
X Ray ◽  
Spatially Resolved ◽  
Atomic Displacements ◽  
Space Image

The retrieval of spatially resolved atomic displacements is investigatedviathe phases of the direct(real)-space image reconstructed from the strained crystal's coherent X-ray diffraction pattern. It is demonstrated that limiting the spatial variation of the first- and second-order spatial displacement derivatives improves convergence of the iterative phase-retrieval algorithm for displacements reconstructions to the true solution. This approach is exploited to retrieve the displacement in a periodic array of silicon lines isolated by silicon dioxide filled trenches.

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