Application of optimization technique to noncrystalline x-ray diffraction microscopy: Guided hybrid input-output method

Chen, Chien-Chun; Miao, Jianwei; Wang, C. W.; Lee, T. K.

doi:10.1103/physrevb.76.064113

Cited by 220 publications

(109 citation statements)

References 28 publications

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“…Hence, the development of algorithms for signal recovery from magnitude measurements is still a very active field of research. Existing methods for phase retrieval rely on all kinds of a priori information about the signal, such as positivity, atomicity, support constraints, real-valuedness, and so on [18,26,27,47]. Direct methods [33] are limited in their applicability to small-scale problems due to their large computational complexity.…”

Section: Main Approaches To Phase Retrievalmentioning

confidence: 99%

Phase Retrieval via Matrix Completion

Candès

Eldar²,

Strohmer

et al. 2013

SIAM J. Imaging Sci.

665

850

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This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach, called PhaseLift, combines multiple structured illuminations together with ideas from convex programming to recover the phase from intensity measurements, typically from the modulus of the diffracted wave. We demonstrate empirically that any complex-valued object can be recovered from the knowledge of the magnitude of just a few diffracted patterns by solving a simple convex optimization problem inspired by the recent literature on matrix completion. More importantly, we also demonstrate that our noise-aware algorithms are stable in the sense that the reconstruction degrades gracefully as the signal-to-noise ratio decreases. Finally, we introduce some theory showing that one can design very simple structured illumination patterns such that three diffracted figures uniquely determine the phase of the object we wish to recover.

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Section: Main Approaches To Phase Retrievalmentioning

confidence: 99%

Phase Retrieval via Matrix Completion

Candès

Eldar²,

Strohmer

et al. 2013

SIAM J. Imaging Sci.

665

850

View full text Add to dashboard Cite

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“…When the diffraction intensity is oversampled such that the number of independently measured intensity points is more than the number of unknown variables of the sample, the phases are in principle uniquely encoded in the diffraction intensity (29) and can be directly retrieved by using iterative algorithms (30)(31)(32)(33). In this experiment, we first reconstructed projectional images from individual 2D diffraction patterns by an iterative algorithm (32), where a projectional image represents the integral of the sample along the x-ray beam direction at a certain orientation.…”

mentioning

confidence: 99%

“…The phase retrieval of each diffraction pattern was conducted by a variation of the GHIO (Guided Hybrid Input and Output) algorithm (32), which incorporates edge-preserving image regularization in order to guide the phase retrieval to the less noisy state that is concurrently consistent with experimental data. The GHIO algorithm began with 16 different random initial phase seeds and the quality of each reconstruction was monitored by an R factor (R F ),…”

mentioning

confidence: 99%

“…In this experiment, we first reconstructed projectional images from individual 2D diffraction patterns by an iterative algorithm (32), where a projectional image represents the integral of the sample along the x-ray beam direction at a certain orientation. We then computed the 3D structure of the yeast spore cell from the set of projectional images through tomographic reconstruction.…”

mentioning

confidence: 99%

“…One promising approach currently under rapid development is coherent diffraction microscopy (also termed coherent diffractive imaging or lensless imaging) in which the coherent diffraction pattern of a noncrystalline specimen or a nanocrystal is measured and then directly phased to obtain an image . The well-known phase problem is solved by using the oversampling method (29) in combination with the iterative algorithms (30)(31)(32)(33). Since its first experimental demonstration in 1999 (1), coherent diffraction microscopy has been applied to imaging a wide range of materials science and biological specimens such as nanoparticles, nanocrystals, biomaterials, cells, cellular organelles, viruses by using synchrotron radiation (2-21), high harmonic generation (22)(23)(24), soft X-ray laser sources (23,25), and free electron lasers (26)(27)(28).…”

mentioning

confidence: 99%

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Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy

Jiang

Song

Chen

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

262

153

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Microscopy has greatly advanced our understanding of biology. Although significant progress has recently been made in optical microscopy to break the diffraction-limit barrier, reliance of such techniques on fluorescent labeling technologies prohibits quantitative 3D imaging of the entire contents of cells. Cryoelectron microscopy can image pleomorphic structures at a resolution of 3-5 nm, but is only applicable to thin or sectioned specimens. Here, we report quantitative 3D imaging of a whole, unstained cell at a resolution of 50-60 nm by X-ray diffraction microscopy. We identified the 3D morphology and structure of cellular organelles including cell wall, vacuole, endoplasmic reticulum, mitochondria, granules, nucleus, and nucleolus inside a yeast spore cell. Furthermore, we observed a 3D structure protruding from the reconstructed yeast spore, suggesting the spore germination process. Using cryogenic technologies, a 3D resolution of 5-10 nm should be achievable by X-ray diffraction microscopy. This work hence paves a way for quantitative 3D imaging of a wide range of biological specimens at nanometer-scale resolutions that are too thick for electron microscopy.coherent diffractive imaging | equally sloped tomography | lensless imaging | iterative phase-retrieval algorithms | oversampling A pplication of the long penetration depth of X-rays to the imaging of large, unstained biological specimens has long been recognized as a possible solution to the thickness restrictions of electron microscopy. Indeed, using sizable protein crystals, X-ray crystallography is currently the primary methodology used for determining the 3D structure of protein molecules at near-atomic or atomic resolution. However, many biological specimens such as whole cells, cellular organelles, some viruses, and many important protein molecules are difficult or impossible to crystallize and hence their structures are not accessible by crystallography. Overcoming these limitations requires the employment of different techniques. One promising approach currently under rapid development is coherent diffraction microscopy (also termed coherent diffractive imaging or lensless imaging) in which the coherent diffraction pattern of a noncrystalline specimen or a nanocrystal is measured and then directly phased to obtain an image (1-28). The well-known phase problem is solved by using the oversampling method (29) in combination with the iterative algorithms (30-33). Since its first experimental demonstration in 1999 (1), coherent diffraction microscopy has been applied to imaging a wide range of materials science and biological specimens such as nanoparticles, nanocrystals, biomaterials, cells, cellular organelles, viruses by using synchrotron radiation (2-21), high harmonic generation (22-24), soft X-ray laser sources (23, 25), and free electron lasers (26-28). Until now, however, the radiation damage problem and the difficulty of acquiring high-quality 3D diffraction patterns from individual whole cells have prevented the successful high-resolution ...

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Coherent Diffraction Imaging of Strain on the Nanoscale

Harder

2012

Characterization of Materials

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Coherent diffraction imaging (CDI) in the Bragg geometry has gained a niche in recent years for its ability to image strain in a crystalline lattice on the nanoscale. This development is based on the realization that coherently scattered x‐rays, in the vicinity of a Bragg peak of the crystalline sample, have exquisite sensitivity to distortions of the crystal lattice. The method is dependent on the use of beams of highly brilliant x‐rays available at the third–generation synchrotrons and the new x‐ray–free electron lasers. There are several instruments at these facilities capable of such measurements. Argonne National Laboratory in the United States hosts such an instrument at the Advanced Photon Source. Computational algorithms are used to retrieve the phases lost in the measurement of the coherently scattered x‐rays and, subsequently, produce the images of the sample. These algorithms are a subject of intense development and in many cases are carefully tuned to a specific application. Phase retrieval for Bragg CDI data will be described in some detail, but similar principles are implemented in all forms of CDI.

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Application of optimization technique to noncrystalline x-ray diffraction microscopy: Guided hybrid input-output method

Cited by 220 publications

References 28 publications

Phase Retrieval via Matrix Completion

Phase Retrieval via Matrix Completion

Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy

Coherent Diffraction Imaging of Strain on the Nanoscale

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