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Shape transform phasing of edgy nanocrystals

ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES 2019年第2期75卷 239-259页

作者： Chen, J. P. J. Donatelli, J. J. Schmidt, K. E. Kirian, R. A. Arizona State Univ Dept Phys Tempe AZ 85287 USA Lawrence Berkeley Natl Lab Ctr Adv Math Energy Res Applicat Berkeley CA 94720 USA Lawrence Berkeley Natl Lab Dept Appl Math Berkeley CA 94720 USA

Diffraction patterns from small protein crystals illuminated by highly coherent X-rays often contain measurable interference signals between Bragg peaks. This coherent 'shape transform' signal introduces enough additional information to allow the molecular densities to be determined from the diffracted intensities directly, without prior information or resolution restrictions. However, the various correlations amongst molecular occupancies/vacancies at the crystal surface result in a subtle yet critical problem in shape transform phasing whereby the sublattices of symmetry-related molecules exhibit a form of partial coherence amongst lattice sites when an average is taken over many crystal patterns. Here an iterative phase retrieval algorithm is developed which is capable of treating this problem;it is demonstrated on simulated data.

关键词： iterative projection algorithms shape transforms shape transform phasing phase retrieval nanocrystals serial femtosecond crystallography X-ray free-electron lasers

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RECONSTRUCTION OF OBJECTS FROM THEIR AVERAGED FINITE CRYSTAL DIFFRACTION INTENSITY 26

RECONSTRUCTION OF OBJECTS FROM THEIR AVERAGED FINITE CRYSTAL...

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26th IEEE International Conference on Image Processing (ICIP)

作者： Chen, J. P. J. Schmidt, K. E. Kirian, R. A. Donatelli, J. J. Arizona State Univ Dept Phys Tempe AZ 85287 USA Lawrence Berkeley Natl Lab Dept Appl Math Berkeley CA 94720 USA Lawrence Berkeley Natl Lab Ctr Adv Math Energy Res Applicat Berkeley CA 94720 USA

ISBN: (纸本)9781538662496

We outline an image reconstruction algorithm that is capable of reconstructing an object from the averaged Fourier intensity of finite crystals of that object with arbitrary lattice occupancies. The algorithm is tested via simulations where the 3-dimensional electron density of a protein molecule is successfully reconstructed from such intensity measurements.

关键词： Phase retrieval iterative projection algorithms Constraint satisfaction problems Computational imaging Crystallography

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The phase problem for two-dimensional crystals. II. Simulations

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ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES 2018年第5期74卷 537-544页

作者： Arnal, Romain D. Zhao, Yun Mitra, Alok K. Spence, John C. H. Millane, Rick P. Univ Canterbury Dept Elect & Comp Engn Computat Imaging Grp Christchurch New Zealand Arizona State Univ Dept Phys Tempe AZ 85287 USA Univ Auckland Sch Biol Sci Auckland New Zealand

Phasing of diffraction data from two-dimensional crystals using only minimal molecular envelope information is investigated by simulation. Two-dimensional crystals are an attractive target for studying membrane proteins using X-ray free-electron lasers, particularly for dynamic studies at room temperature. Simulations using an iterative projection algorithm show that phasing is feasible with fairly minimal molecular envelope information, supporting recent uniqueness results for this problem [Arnal & Millane (2017). Acta Cryst. A73, 438-448]. The effects of noise and likely requirements for structure determination using X-ray free-electron laser sources are investigated.

关键词： phase problem phase retrieval two-dimensional crystals XFELs ab initio phasing iterative projection algorithms membrane proteins

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Simultaneous retrieval of coherently illuminated defocused objects

Simultaneous retrieval of coherently illuminated defocused o...

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International Conference on Image and Vision Computing New Zealand (IVCNZ)

作者： Chen, Joe P. J. Kirian, Richard A. Arizona State Univ Dept Phys Tempe AZ 85287 USA

ISBN: (纸本)9781538642764

It is demonstrated here that the exit wave-field of objects from two different planes along the wave propagation axis can be retrieved from their coherently summed far-field diffraction intensity. This is achieved through the application of an iterative projection algorithm developed previously in [1]. Simulations show that given such an intensity data, the algorithm can successfully retrieve the exit wave-field of the two objects simultaneously, provided the objects are translated far enough away from each other in the transverse direction to the propagation axis.

关键词： Phase retrieval iterative projection algorithms defocus image reconstruction coherent diffractive imaging

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Phase retrieval in the presence of multiplicative noise

Phase retrieval in the presence of multiplicative noise

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Conference on Unconventional and Indirect Imaging, Image Reconstruction, and Wavefront Sensing

作者： Chen, Joe P. J. Kirian, Richard A. Arizona State Univ Dept Phys Tempe AZ 85287 USA

ISBN: (纸本)9781510612785;9781510612778

An additional step to traditional iterative phase retrieval algorithms is described that allows the reconstruction of an image from the product of its sufficiently sampled far-field diffraction intensity and a second signal. The iterative phasing algorithm with this added step attempts to recover both the image and the multiplicative signal at the same time. Simulations show that reasonable reconstructions of both the original image and the multiplicative signal can be attained in many cases.

关键词： Phase retrieval multiplicative noise iterative projection algorithms

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Reconstruction of an object from diffraction intensities averaged over multiple object clusters

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JOURNAL OF OPTICS 2016年第11期18卷 114003-114003页

作者： Chen, J. P. J. Arnal, R. D. Morgan, A. J. Bean, R. J. Beyerlein, K. R. Chapman, H. N. Bones, P. J. Millane, R. P. Kirian, R. A. Arizona State Univ Dept Phys Tempe AZ 85287 USA Univ Canterbury Dept Elect & Comp Engn Computat Imaging Grp Christchurch New Zealand DESY Ctr Free Electron Laser Sci D-22607 Hamburg Germany European XFEL GmbH Albert Einstein Ring 19 D-22761 Hamburg Germany

A projection operator is derived for use in iterative phase retrieval algorithms when the Fourier intensity data is an average over the intensity from multiple clusters of identical objects. The projection operator is a generalization of the magnitude projection for conventional phase retrieval for a single object, and is applicable when the relative orientations and positions of the objects within the clusters are known. Simulations demonstrate that an iterative projection algorithm equipped with this new projection operator can successfully reconstruct an object from the averaged Fourier intensities from multiple clusters, each containing multiple copies of the object.

关键词： phase retrieval crystallography diffractive imaging iterative projection algorithms

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Volumic omit maps in ab initio dual-space phasing

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ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES 2016年第Pt 4期72卷 480-488页

作者： Oszlanyi, Gabor Suto, Andras Hungarian Acad Sci Inst Solid State Phys & Opt Wigner Res Ctr Phys POB 49 H-1525 Budapest Hungary

Alternating-projection-type dual-space algorithms have a clear construction, but are susceptible to stagnation and, thus, inefficient for solving the phase problem ab initio. To improve this behaviour new omit maps are introduced, which are real-space perturbations applied periodically during the iteration process. The omit maps are called volumic, because they delete some predetermined subvolume of the unit cell without searching for atomic regions or analysing the electron density in any other way. The basic algorithms of positivity, histogram matching and low-density elimination are tested by their solution statistics. It is concluded that, while all these algorithms based on weak constraints are practically useless in their pure forms, appropriate volumic omit maps can transform them to practically useful methods. In addition, the efficiency of the already useful reflector-type charge-flipping algorithm can be further improved. It is important that these results are obtained by using non-sharpened structure factors and without any weighting scheme or reciprocalspace perturbation. The mathematical background of volumic omit maps and their expected applications are also discussed.

关键词： omit maps iterative projection algorithms dual-space methods structure determination

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iterative projection algorithms for reconstructing compact binary images

Iterative projection algorithms for reconstructing compact b...

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Conference on Image Reconstruction from Incomplete Data V

作者： Lo, V. L. Millane, R. P. Univ Canterbury Dept Elect & Comp Engn Computat Imaging Grp Christchurch 1 New Zealand

ISBN: (纸本)9780819472960

An algorithm is described for reconstructing compact binary images from limited Fourier amplitude data. This problem arises in macromolecular crystallography where one wishes to reconstruct the molecular envelope from crystal x-ray diffraction amplitudes using a solvent contrast series. Such data are the amplitude of the Fourier transform of all object that has a constant electron density within the boundary of the molecule and zero outside. The image is thus binary and compact, but, the data are available only within a limited resolution range in Fourier space and are undersampled. The problem is solved Using all iterative projection algorithm;a class of algorithm used to solve inverse problems for which the solution is subject to a, number of constraints that, represent a priori information and the data. Unfortunately, these algorithms experience convergence difficulties if one or more of the constraints are non-convex, which is the case for all the constraint's in this problem. We solve the problem by constructing appropriate projection operators and implementing the difference map projection algorithm. Simulations axe used to study convergence behaviour of the algorithm.

关键词： Phase retrieval Image reconstruction iterative projection algorithms X-ray crystallography

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RECONSTRUCTION OF MACROMOLECULAR ENVELOPES FROM CRYSTAL X-RAY DIFFRACTION AMPLITUDES

RECONSTRUCTION OF MACROMOLECULAR ENVELOPES FROM CRYSTAL X-RA...

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15th IEEE International Conference on Image Processing (ICIP 2008)

作者： Lo, V. L. Millane, R. P. Kingston, R. L. Univ Canterbury Computat Imaging Grp Dept Elect & Comp Eng Private Bag 4800 Christchurch 1 New Zealand Univ Auckland Sch Biolog Sci Auckland 92019 New Zealand

ISBN: (纸本)9781424417650

The envelope problem in macromolecular x-ray crystallography involves determining the boundary of a molecule from measurements of amplitudes of x-rays diffracted from a crystalline specimen. This represents a highly underdetermined image reconstruction problem with a large number of degrees of freedom. We regularize the problem by applying binary and connectivity constraints to the image, and seek the solution using the method of iterated projections. However, since the constraints are highly non-convex, the usual methods of generalized projections are not effective. We use the difference map projection algorithm and show that this is effective with simulated diffraction data from a protein envelope.

关键词： X-ray crystallography phase retrieval iterative projection algorithms image reconstruction

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