Results 1  10
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28
Highresolution ab initio threedimensional xray diffraction microscopy
 Journal of the Optical Society of America A
, 2006
"... Coherent Xray diffraction microscopy is a method of imaging nonperiodic isolated objects at resolutions only limited, in principle, by the largest scattering angles recorded. We demonstrate Xray diffraction imaging with high resolution in all three dimensions, as determined by a quantitative anal ..."
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Cited by 24 (4 self)
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Coherent Xray diffraction microscopy is a method of imaging nonperiodic isolated objects at resolutions only limited, in principle, by the largest scattering angles recorded. We demonstrate Xray diffraction imaging with high resolution in all three dimensions, as determined by a quantitative analysis of the reconstructed volume images. These images are retrieved from the 3D diffraction data using no a priori knowledge about the shape or composition of the object, which has never before been demonstrated on a nonperiodic object. We also construct 2D images of thick objects with infinite depth of focus (without loss of transverse spatial resolution). These methods can be used to image biological and materials science samples at high resolution using Xray undulator radiation, and establishes the techniques to be used in atomicresolution ultrafast imaging at Xray freeelectron laser sources. OCIS codes: 340.7460, 110.1650, 110.6880, 100.5070, 100.6890, 070.2590, 180.6900 1.
Finding best approximation pairs relative to a convex and proxregular set in a Hilbert space
 SIAM J. Optim
"... Abstract. We study the convergence of an iterative projection/reflection algorithm originally proposed for solving what are known as phase retrieval problems in optics. There are two features that frustrate any analysis of iterative methods for solving the phase retrieval problem: nonconvexity and i ..."
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Cited by 19 (5 self)
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Abstract. We study the convergence of an iterative projection/reflection algorithm originally proposed for solving what are known as phase retrieval problems in optics. There are two features that frustrate any analysis of iterative methods for solving the phase retrieval problem: nonconvexity and infeasibility. The algorithm that we developed, called Relaxed Averaged Alternating Reflections (RAAR), was designed primarily to address infeasibility, though our strategy has advantages for nonconvex problems as well. In the present work we investigate the asymptotic behavior of the RAAR algorithm for the general problem of finding points that achieve the minimum distance between two closed convex sets in a Hilbert space with empty intersection, and for the problem of finding points that achieve a local minimum distance between one closed convex set and a closed proxregular set, also possibly nonintersecting. The nonconvex theory includes and expands prior results limited to convex sets with nonempty intersection. To place the RAAR algorithm in context, we develop parallel statements about the standard alternating projections algorithm and gradient descent. All the various algorithms are unified as instances of iterated averaged alternating proximal reflectors applied to a sum of regularized maximal monotone mappings.
Phase Retrieval with Application to Optical Imaging
, 2015
"... The problem of phase retrieval, i.e., the recovery of a function given the magnitude of its ..."
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Cited by 18 (6 self)
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The problem of phase retrieval, i.e., the recovery of a function given the magnitude of its
Blurkernel estimation from spectral irregularities
 IN: COMPUTER VISION–ECCV 2012
, 2012
"... We describe a new method for recovering the blur kernel in motionblurred images based on statistical irregularities their power spectrum exhibits. This is achieved by a powerlaw that refines the one traditionally used for describing natural images. The new model better accounts for biases arisin ..."
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Cited by 13 (0 self)
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We describe a new method for recovering the blur kernel in motionblurred images based on statistical irregularities their power spectrum exhibits. This is achieved by a powerlaw that refines the one traditionally used for describing natural images. The new model better accounts for biases arising from the presence of large and strong edges in the image. We use this model together with an accurate spectral whiteing formula to estimate the power spectrum of the blur. The blur kernel is then recovered using a phase retrieval algorithm with improved convergence and disambiguation capabilities. Unlike many existing methods, the new approach does not perform a maximum a posteriori estimation, which involves repeated reconstructions of the latent image, and hence offers attractive running times. We compare the new method with stateoftheart methods and report various advantages, both in terms of efficiency and accuracy.
Duality and Convex Programming
, 2010
"... We survey some key concepts in convex duality theory and their application to the analysis and numerical solution of problem archetypes in imaging. ..."
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Cited by 6 (4 self)
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We survey some key concepts in convex duality theory and their application to the analysis and numerical solution of problem archetypes in imaging.
Alternating Projection, Ptychographic Imaging and Phase Synchronization. ArXiv eprints
, 2014
"... Abstract. We demonstrate necessary and sufficient conditions of the global convergence of the alternating projection algorithm to a unique solution up to a global phase factor. Additionally, for the ptychographic imaging problem, we discuss phase synchronization and connection graph Laplacian, and ..."
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Cited by 5 (1 self)
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Abstract. We demonstrate necessary and sufficient conditions of the global convergence of the alternating projection algorithm to a unique solution up to a global phase factor. Additionally, for the ptychographic imaging problem, we discuss phase synchronization and connection graph Laplacian, and show how to construct an accurate initial guess to accelerate convergence speed to handle the big imaging data in the coming new light source era. 1.
Ultrafast singleshot diffraction imaging of nanoscale dynamics
 Nature Photonics
, 2008
"... nanoscale dynamics ..."
Biological physics
, 2002
"... Xray diffraction microscopy on frozen hydrated specimens ..."
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Cited by 4 (0 self)
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Xray diffraction microscopy on frozen hydrated specimens
XXXXXXXXXX Ab initio compressive phase retrieval
, 809
"... Any object on earth has two fundamental properties: it is finite, and it is made of atoms. Structural information about an object can be obtained from diffraction amplitude measurements that account for either one of these traits. Nyquistsampling of the Fourier amplitudes is sufficient to image sin ..."
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Cited by 2 (0 self)
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Any object on earth has two fundamental properties: it is finite, and it is made of atoms. Structural information about an object can be obtained from diffraction amplitude measurements that account for either one of these traits. Nyquistsampling of the Fourier amplitudes is sufficient to image single particles of finite size at any resolution. Atomic resolution data is routinely used to image molecules replicated in a crystal structure. Here we report an algorithm that requires neither information, but uses the fact that an image of a natural object is compressible. Intended applications include tomographic diffractive imaging, crystallography, powder diffraction, small angle xray scattering and random Fourier amplitude measurements.