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We demonstrate necessary and sufficient conditions of the local convergence of the alternating projection algorithm to a unique solution up to a global phase factor.
The Specular Reflection of X-rays
W. L. Bragg · 1912
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The crystal structure of bixbyite and the c-modification of the sesquioxides
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Molecular structure of nucleic acids
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Beugung im inhomogenen Primärstrahlwellenfeld. I. Prinzip einer Phasenmessung von Elektronenbeungungsinterferenzen
W. Hoppe · 1969
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Optical holography
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Phase determination for image and diffraction plane pictures in the electron microscope
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Phase retrieval algorithms: a comparison
J. R. Fienup · 1982
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The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform
M. Hayes · 1982
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Uniqueness of solutions to two-dimensional fourier phase problems for localized and positive images
R.H.T. Bates · 1984
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Image restoration by the method of generalized projections with application to restoration from magnitude
A. Levi and H. Stark · 1984
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Mathematical considerations for the problem of Fourier transform phase retrieval from magnitude
J.L.C. Sanz · 1985
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Harmonic Analysis in Phase Space
G.B. Folland · 1989
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Method of successive projections for finding a common point of sets in metric spaces
P. L. Combettes and H. J. Trussell · 1990
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Hubble space telescope characterized by using phase-retrieval algorithms
J. R. Fienup, J. C. Marron, T. J. Schulz, and J. H. Seldin · 1993
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Resolution beyond the ’information limit’ in transmission electronmicroscopy
P. D. Nellist, B. C. McCallum, and J. M. Rodenburg · 1995
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Phase-retrieval x-ray microscopy by wigner -distribution deconvolution
H. N. Chapman · 1996
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Introduction to Fourier Optics
J.W. Goodman · 1996
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Phase–contrast x–ray computed tomography for observing biological soft tissues
A. Momose, T. Takeda, Y. Itai, and K. Hirano · 1996
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Algebraic geometry
R. Hartshorne · 1997
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The protein data bank
H. M. Berman, J. Westbrook, Z. Feng, G. Gilliland, T. N. Bhat, H. Weissig, I. N. Shindyalov, and P. E. Bourne · 2000
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Structural basis of transcription: Rna polymerase II at 2.8 Angstrom resolution
P. Cramer, D. A. Bushnell, and R. D. Kornberg · 2001
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Phase retrieval, error reduction algorithm, and Fienup variants: a view from convex optimization
H. H. Bauschke, P. L. Combettes, and D. R. Luke · 2002
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Optical wavefront reconstruction: Theory and numerical methods
D. R. Luke, J. V. Burke, and R. G. Lyon · 2002
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The complex gradient operator and the CR-calculus
K. Kreutz-Delgado · 2003
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X-ray image reconstruction from a diffraction pattern alone
S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C.H. Spence · 2003
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Heat Kernels and Dirac Operators
N. Berline, E. Getzler, and M. Vergne · 2004
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Relaxed averaged alternating reflections for diffraction imaging
R. Luke · 2005
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On signal reconstruction without phase
R. Balan, P. Casazza, and D. Edidin · 2006
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Superresolution imaging via ptychography
A. M. Maiden, M. J. Humphry, F. Zhang, and J. M. Rodenburg · 2011
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Iterative Algorithms for Ptychographic Phase Retrieval
C. Yang, J. Qian, A. Schirotzek, F. Maia, and S. Marchesini · 2011
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Ranking and sparsifying a connection graph
F. Chung, W. Zhao, and M. Kempton · 2012
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Disputed discovery: the beginnings of X-ray diffraction in crystals in 1912 and its repercussions
M. Eckert · 2012
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Phase retrieval with random phase illumination
A. Fannjiang and W. Liao · 2012
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Role of the illumination spatial-frequency spectrum for ptychography
M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel · 2012
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The pilatus 1m detector
Ch. Broennimann, E. F. Eikenberry, B. Henrich, R. Horisberger, G. Huelsen, E. Pohl, B. Schmitt, C. Schulze-Briese, M. Suzuki, T. Tomizaki, H. Toyokawa, and A. Wagner · 2006
Cited alongside, same era.
High-resolution ab initio three-dimensional x-ray diffraction microscopy
H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C.H. Spence, et al · 2006
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Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources
F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David · 2006
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Science of microscopy
P. W. Hawkes and J. C. H. Spence, editors · 2007
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Algorithmic methods in diffraction microscopy
P. Thibault · 2007
Cited alongside, same era.
Local Linear Convergence for Alternating and Averaged Nonconvex Projections
A. S. Lewis, D. R. Luke, and J. Malick · 2008
Cited alongside, same era.
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Vector diffusion maps and the connection Laplacian
A. Singer and H.-T. Wu · 2012
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Alternating direction methods for classical and ptychographic phase retrieval
Z. Wen, C. Yang, X Liu, and S. Marchesini · 2012
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Invertibility and robustness of phaseless reconstruction
R. Balan and Y. Wang · 2013
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A Cheeger Inequality for the Graph Connection Laplacian
A. S. Bandeira, A. Singer, and D. A. Spielman · 2013
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Progress toward an ultimate storage ring light source
M. Borland · 2013
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Phase retrieval via matrix completion
E. J. Candes, Y. C. Eldar, T. Strohmer, and V. Voroninski · 2013
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Phaselift: Exact and stable signal recovery from magnitude measurements via convex programming
E. J. Candes, T. Strohmer, and V. Voroninski · 2013
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An algebraic characterization of injectivity in phase retrieval
A. Conca, D. Edidin, M. Hering, and C. Vinzant · 2013
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Fourier phasing with phase-uncertain mask
A. Fannjiang and W. Liao · 2013
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Soft x-ray spectromicroscopy using ptychography with randomly phased illumination
A.M. Maiden, G.R. Morrison, B. Kaulich, A. Gianoncelli, and J.M. Rodenburg · 2013
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Augmented projections for ptychographic imaging
S. Marchesini, A. Schirotzek, C. Yang, H.-T. Wu, and F. Maia · 2013
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Spectral convergence of the connection laplacian from random samples
A. Singer and H.-T. Wu · 2013
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Phase recovery, maxcut and complex semidefinite programming
I. Waldspurger, A. dÕAspremont, and S. Mallat · 2013
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Phase retrieval for sparse signals
Y. Wang and Z. Xu · 2013
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Phase retrieval with polarization
B. Alexeev, A. S. Bandeira, M. Fickus, and D. G. Mixon · 2014
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Saving phase: Injectivity and stability for phase retrieval
A. S. Bandeira, J. Cahili, D. G. Mixon, and A. A. Nelson · 2014
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Graph connection Laplacian and random matrices with random blocks
N. El Karoui and H.-T. Wu · 2015
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Graph connection Laplacian methods can be made robust to noise
N. El Karoui and H.-T. Wu · 2015
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