Extending X-Ray Crystallography to Allow the Imaging of Noncrystalline Materials, Cells, and Single Protein Complexes

Miao, Jianwei; Ishikawa, Tetsuya; Shen, Qun; Earnest, Thomas

doi:10.1146/annurev.physchem.59.032607.093642

Cited by 227 publications

(163 citation statements)

References 92 publications

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“…Over the last century or so, this field has developed a wide array of techniques to recover Bragg peaks from missing-phase data. Of course, the phase retrieval problem permeates many other areas of imaging science, and other applications include diffraction imaging [12], optics [65], astronomical imaging [20], microscopy [49], to name just a few. In particular, X-ray tomography has become an invaluable tool in biomedical imaging to generate quantitative 3D density maps of extended specimens on the nanoscale [21].…”

Section: The Phase Retrieval Problemmentioning

confidence: 99%

Phase Retrieval via Matrix Completion

Candès

Eldar²,

Strohmer

et al. 2013

SIAM J. Imaging Sci.

655

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: The Phase Retrieval Problemmentioning

confidence: 99%

Phase Retrieval via Matrix Completion

Candès

Eldar²,

Strohmer

et al. 2013

SIAM J. Imaging Sci.

655

850

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“…The oversampling concept (i.e., sampling the Fourier slice at a frequency finer than the Nyquist interval) has been widely used to solve the phase problem in coherent diffraction imaging. [34][35][36] In the EST method, we implemented oversampling by padding each projection with zeros. These zeros do not provide extra information about the object but allow us to define a support in real space to facilitate the reconstruction process.…”

Section: Iib the Est Methodsmentioning

confidence: 99%

Radiation dose reduction in medical x‐ray CT via Fourier‐based iterative reconstruction

et al. 2013

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Purpose: A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry. Methods: EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). In each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method. helical cone-beam CT data suggest that the combination of EST and ASSR produces reconstructions with higher image quality and lower noise than the Feldkamp Davis and Kress (FDK) method and the conventional ASSR approach. Conclusions: A Fourier-based iterative method has been applied to the reconstruction of fan-bean CT data with reduced x-ray fluence. This method incorporates advantageous features in both real and Fourier space iterative schemes: using a fast and algebraically exact method to calculate forward projection, enforcing the measured data in Fourier space, and applying physical constraints and flexible regularization in real space. Our results suggest that EST can be utilized for radiation dose reduction in x-ray CT via the readily implementable technique of lowering mAs settings. Numerical experiments further indicate that EST requires less computation time than several other iterative algorithms and can, in principle, be extended to helical cone-beam geometry in combination with the ASSR method.

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“…By shortening the working wavelength or increasing the NA of the system, the resolution of the microscope can be improved to some extent. Based on this principle, the prototype ultraviolet microscope was constructed by Köhler 7 in 1904, while X-rays 8,9 were later introduced into the micro-imaging system. The natural progression of this work was the realization of electron microscopy, 10 where electrons with a critically shorter de Broglie wavelength are used for imaging.…”

Section: Introductionmentioning

confidence: 99%

From microscopy to nanoscopy via visible light

Hao

Kuang

et al. 2013

Light Sci Appl

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The resolution of conventional optical equipment is always restricted by the diffraction limit, and improving on this was previously considered improbable. Optical super-resolution imaging, which has recently experienced rapid growth and attracted increasing global interest, will result in applications in many domains, benefiting fields such as biology, medicine and material research. This review discusses the contributions of different researchers who identified the diffractive barrier and attempted to realize optical super-resolution. This is followed by a personal viewpoint of the development of optical nanoscopy in recent decades and the road towards the next generation of optical nanoscopy.

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Extending X-Ray Crystallography to Allow the Imaging of Noncrystalline Materials, Cells, and Single Protein Complexes

Cited by 227 publications

References 92 publications

Phase Retrieval via Matrix Completion

Phase Retrieval via Matrix Completion

Radiation dose reduction in medical x‐ray CT via Fourier‐based iterative reconstruction

From microscopy to nanoscopy via visible light

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