Solution of the crystallographic phase problem by iterated projections.
TLDR
An algorithm for determining crystal structures from diffraction data is described which does not rely on the usual reciprocal-space formulations of atomicity, and implements atomicity constraints in real space as well as intensity constraints in reciprocal space by projections that restore each constraint with the minimal modification of the scattering density.Abstract:
An algorithm for determining crystal structures from diffraction data is described which does not rely on the usual reciprocal-space formulations of atomicity. The new algorithm implements atomicity constraints in real space, as well as intensity constraints in reciprocal space, by projections that restore each constraint with the minimal modification of the scattering density. To recover the true density, the two projections are combined into a single operation, the difference map, which is iterated until the magnitude of the density modification becomes acceptably small. The resulting density, when acted upon by a single additional operation, is by construction a density that satisfies both intensity and atomicity constraints. Numerical experiments have yielded solutions for atomic resolution X-ray data sets with over 400 non-hydrogen atoms, as well as for neutron data, where positivity of the density cannot be invoked.read more
Citations
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Phase Retrieval with Application to Optical Imaging: A contemporary overview
TL;DR: The goal is to describe the current state of the art in this area, identify challenges, and suggest future directions and areas where signal processing methods can have a large impact on optical imaging and on the world of imaging at large.
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Phase recovery and holographic image reconstruction using deep learning in neural networks
TL;DR: It is demonstrated that a neural network can learn to perform phase recovery and holographic image reconstruction after appropriate training, and this deep learning-based approach provides an entirely new framework to conduct holographic imaging by rapidly eliminating twin-image and self-interference-related spatial artifacts.
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Beyond crystallography: Diffractive imaging using coherent x-ray light sources
TL;DR: The revolutionary advances that are transforming x-ray sources and imaging in the 21st century are reviewed.
Journal ArticleDOI
Ab initio structure solution by charge flipping.
G. Oszlányi,Andras Suto +1 more
TL;DR: In this paper, an extremely simple structure solution method termed charge flipping is presented, which works ab initio on high-resolution X-ray diffraction data in the manner of Fourier recycling.
References
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Journal ArticleDOI
Phase retrieval algorithms: a comparison.
TL;DR: Iterative algorithms for phase retrieval from intensity data are compared to gradient search methods and it is shown that both the error-reduction algorithm for the problem of a single intensity measurement and the Gerchberg-Saxton algorithm forThe problem of two intensity measurements converge.
Journal ArticleDOI
The design and implementation of SnB version 2.0
TL;DR: This paper introduces SnB version 2.0, which incorporates a graphical user interface written in Java, a dynamic histogram display, and an interactive Java/VRML-based visualization facility and provides the user with several utility routines and a variety of new algorithmic options.
Journal ArticleDOI
SnB: crystal structure determination via shake‐and‐bake
TL;DR: The focus of this paper is on the details of the SnB program, including its structure, system requirements, running times and the rationale for coding in a combination of C and Fortran.
BookDOI
Direct methods for solving macromolecular structures
TL;DR: This work focuses on the application of Direct Methods to Macro-Molecular Structures to solve the Phase Problem and the challenges of integrating Direct Methods with Experimental Phase Information.