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The problem of recovering a signal from its phaseless Fourier transform measurements, called Fourier phase retrieval, arises in many applications in engineering and science.
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https://www.nobelprize.org/nobel_prizes/medicine/laureates/1962/
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The question of phase retrieval in optics
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A practical algorithm for the determination of phase from image and diffraction plane pictures
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Phase retrieval algorithms: a comparison
James R Fienup · 1982
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The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform
Monson H Hayes · 1982
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Reducible polynomials in more than one variable
Monson H Hayes and James H McClellan · 1982
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Signal reconstruction from short-time Fourier transform magnitude
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Reconstruction of a complex-valued object from the modulus of its fourier transform using a support constraint
James R Fienup · 1987
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Phase retrieval and image reconstruction for astronomy
James R Fienup and Chris Dainty · 1987
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Almost unique specification of discrete finite length signal: from its end point and Fourier transform magnitude
Lei Xu, Pingfan Yan, and Tong Chang · 1987
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The phase retrieval problem in X-ray crystallography
Wooshik Kim and Monson H Hayes · 1991
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Phase problem in crystallography
Robert W Harrison · 1993
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Phase retrieval using a window function
Wooshik Kim and Monson H. Hayes · 1993
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Matching pursuits with time-frequency dictionaries
Stéphane G Mallat and Zhifeng Zhang · 1993
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Fundamentals of speech recognition
Lawrence Rabiner and Biing-Hwang Juang · 1993
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Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating
Rick Trebino and Daniel J Kane · 1993
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Frequency-resolved optical gating with the use of second-harmonic generation
KW DeLong, Rick Trebino, J Hunter, and WE White · 1994
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Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
Michel X Goemans and David P Williamson · 1995
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Diffraction gratings and applications
Erwin G Loewen and Evgeny Popov · 1997
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Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating
Rick Trebino, Kenneth W DeLong, David N Fittinghoff, John N Sweetser, Marco A Krumbügel, Bruce A Richman, and Daniel J Kane · 1997
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Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens
Jianwei Miao, Pambos Charalambous, Janos Kirz, and David Sayre · 1999
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Reconstruction of the shapes of gold nanocrystals using coherent X-ray diffraction
Ian K Robinson, Ivan A Vartanyants, GJ Williams, MA Pfeifer, and JA Pitney · 2001
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Phase retrieval, error reduction algorithm, and fienup variants: a view from convex optimization
Heinz H Bauschke, Patrick L Combettes, and D Russell Luke · 2002
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Hybrid projection–reflection method for phase retrieval
Heinz H Bauschke, Patrick L Combettes, and D Russell Luke · 2003
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Phase retrieval by iterated projections
Veit Elser · 2003
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Solution of the crystallographic phase problem by iterated projections
Veit Elser · 2003
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Log-det heuristic for matrix rank minimization with applications to Hankel and Euclidean distance matrices
Maryam Fazel, Haitham Hindi, and Stephen P Boyd · 2003
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Blind channel estimation via combining autocorrelation and blind phase estimation
Buyurman Baykal · 2004
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Relaxed averaged alternating reflections for diffraction imaging
D Russell Luke · 2004
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Nontrivial ambiguities for blind frequency-resolved optical gating and the problem of uniqueness
Birger Seifert, Heinrich Stolz, and Manfred Tasche · 2004
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On signal reconstruction without phase
Radu Balan, Pete Casazza, and Dan Edidin · 2006
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Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
Emmanuel J Candès, Justin Romberg, and Terence Tao · 2006
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Femtosecond diffractive imaging with a soft-X-ray free-electron laser
Henry N Chapman, Anton Barty, Michael J Bogan, Sébastien Boutet, Matthias Frank, Stefan P Hau-Riege, Stefano Marchesini, Bruce W Woods, Saša Bajt, W Henry Benner, et al · 2006
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Compressed sensing
David L Donoho · 2006
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Multilevel Gauss-Newton methods for phase retrieval problems
Birger Seifert, Heinrich Stolz, Marco Donatelli, Dirk Langemann, and Manfred Tasche · 2006
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Application of optimization technique to noncrystalline X-ray diffraction microscopy: Guided hybrid input-output method
Chien-Chun Chen, Jianwei Miao, CW Wang, and TK Lee · 2007
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Invited article: A unified evaluation of iterative projection algorithms for phase retrieval
Stefano Marchesini · 2007
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CVX: Matlab software for disciplined convex programming, 2008
Michael Grant, Stephen Boyd, and Yinyu Ye · 2008
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Principal components generalized projections: a review [invited]
Daniel J Kane · 2008
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Phase reconstruction by a multilevel iteratively regularized Gauss-Newton method
Dirk Langemann and Manfred Tasche · 2008
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Phase retrieval in X-ray imaging based on using structured illumination
YJ Liu, B Chen, ER Li, JY Wang, A Marcelli, SW Wilkins, H Ming, YC Tian, KA Nugent, PP Zhu, et al · 2008
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Ptychography and related diffractive imaging methods
JM Rodenburg · 2008
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High numerical aperture tabletop soft X-ray diffraction microscopy with 70-nm resolution
Richard L Sandberg, Changyong Song, Przemyslaw W Wachulak, Daisy A Raymondson, Ariel Paul, Bagrat Amirbekian, Edwin Lee, Anne E Sakdinawat, La-O Chan, Mario C Marconi, et al · 2008
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Multiple wavelength diffractive imaging
Bo Chen, Ruben A Dilanian, Sven Teichmann, Brian Abbey, Andrew G Peele, Garth J Williams, Peter Hannaford, Lap Van Dao, Harry M Quiney, and Keith A Nugent · 2009
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Phase retrieval: An overview of recent developments
Kishore Jaganathan, Yonina C Eldar, and Babak Hassibi · 2015
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Alternating projection, ptychographic imaging and phase synchronization
Stefano Marchesini, Yu-Chao Tu, and Hau-tieng Wu · 2015
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Simultaneously structured models with application to sparse and low-rank matrices
Samet Oymak, Amin Jalali, Maryam Fazel, Yonina C Eldar, and Babak Hassibi · 2015
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Phase retrieval with application to optical imaging: a contemporary overview
Yoav Shechtman, Yonina C Eldar, Oren Cohen, Henry Nicholas Chapman, Jianwei Miao, and Mordechai Segev · 2015
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Sparsity-based super-resolved coherent diffraction imaging of one-dimensional objects
Pavel Sidorenko, Ofer Kfir, Yoav Shechtman, Avner Fleischer, Yonina C Eldar, Mordechai Segev, and Oren Cohen · 2015
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Multilevel phase reconstruction for a rapidly decreasing interpolating function
Dirk Langemann and Manfred Tasche · 2009
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Nanoscale imaging using deep ultraviolet digital holographic microscopy
Ahmad Faridian, David Hopp, Giancarlo Pedrini, Ulrike Eigenthaler, Michael Hirscher, and Wolfgang Osten · 2010
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A century of nature: twenty-one discoveries that changed science and the world
Laura Garwin and Tim Lincoln · 2010
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Superresolution imaging via ptychography
Andrew M Maiden, Martin J Humphry, Fucai Zhang, and John M Rodenburg · 2011
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Compressive phase retrieval from squared output measurements via semidefinite programming
Henrik Ohlsson, Allen Y Yang, Roy Dong, and Shankar S Sastry · 2011
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Vectorial phase retrieval for linear characterization of attosecond pulses
Oren Raz, Osip Schwartz, Dane Austin, AS Wyatt, Andrea Schiavi, Olga Smirnova, Boaz Nadler, Ian A Walmsley, Dan Oron, and Nirit Dudovich · 2011
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Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing
Yoav Shechtman, Yonina C Eldar, Alexander Szameit, and Mordechai Segev · 2011
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Phase recovery, maxcut and complex semidefinite programming
Irène Waldspurger, Alexandre d’Aspremont, and Stéphane Mallat · 2015
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Experimental robustness of Fourier ptychography phase retrieval algorithms
Li-Hao Yeh, Jonathan Dong, Jingshan Zhong, Lei Tian, Michael Chen, Gongguo Tang, Mahdi Soltanolkotabi, and Laura Waller · 2015
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Non-negativity constraints in the one-dimensional discrete-time phase retrieval problem
Robert Beinert · 2016
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One-dimensional phase retrieval with additional interference measurements
Robert Beinert · 2016
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Enforcing uniqueness in one-dimensional phase retrieval by additional signal information in time domain
Robert Beinert and Gerlind Plonka · 2016
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Robust recovery of stream of pulses using convex optimization
Tamir Bendory, Shai Dekel, and Arie Feuer · 2016
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Non-convex phase retrieval from STFT measurements
Tamir Bendory and Yonina C Eldar · 2016
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Phase retrieval from Gabor measurements
Irena Bojarovska and Axel Flinth · 2016
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Nonconvex phase synchronization
Nicolas Boumal · 2016
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Optimal rates of convergence for noisy sparse phase retrieval via thresholded wirtinger flow
T Tony Cai, Xiaodong Li, Zongming Ma, et al · 2016
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The projected power method: An efficient algorithm for joint alignment from pairwise differences
Yuxin Chen and Emmanuel Candès · 2016
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Phaseless super-resolution in the continuous domain
Myung Cho, Christos Thrampoulidis, Weiyu Xu, and Babak Hassibi · 2016
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Phasemax: Convex phase retrieval via basis pursuit
Tom Goldstein and Christoph Studer · 2016
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Phase retrieval from 1D Fourier measurements: Convexity, uniqueness, and algorithms
Kejun Huang, Yonina C. Eldar, and Nikos D. Sidiropoulos · 2016
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Mark A Iwen, Brian Preskitt, Rayan Saab, and Aditya Viswanathan · 2016
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Fast phase retrieval from local correlation measurements
Mark A. Iwen, Aditya Viswanathan, and Yang Wang · 2016
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STFT phase retrieval: Uniqueness guarantees and recovery algorithms
Kishore Jaganathan, Yonina C Eldar, and Babak Hassibi · 2016
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Kishore Jaganathan and Babak Hassibi · 2016
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Phaseless super-resolution using masks
Kishore Jaganathan, James Saunderson, Maryam Fazei, Yonina C Eldar, and Babak Hassibi · 2016
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On the 2D phase retrieval problem
Dani Kogan, Yonina C Eldar, and Dan Oron · 2016
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Direct single-shot phase retrieval from the diffraction pattern of separated objects
Ben Leshem, Rui Xu, Yehonatan Dallal, Jianwei Miao, Boaz Nadler, Dan Oron, Nirit Dudovich, and Oren Raz · 2016
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Message-passing algorithms for synchronization problems over compact groups
Amelia Perry, Alexander S Wein, Afonso S Bandeira, and Ankur Moitra · 2016
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Robust phase retrieval algorithm for time-frequency structured measurements
Goetz E Pfander and Palina Salanevich · 2016
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Single-shot ptychography
Pavel Sidorenko and Oren Cohen · 2016
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Ptychographic reconstruction algorithm for frequency-resolved optical gating: super-resolution and supreme robustness
Pavel Sidorenko, Oren Lahav, Zohar Avnat, and Oren Cohen · 2016
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DOLPHIn-—dictionary learning for phase retrieval
Andreas M Tillmann, Yonina C Eldar, and Julien Mairal · 2016
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Phase retrieval with random gaussian sensing vectors by alternating projections
Irène Waldspurger · 2016
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Solving systems of random quadratic equations via truncated amplitude flow
Gang Wang, Georgios B Giannakis, and Yonina C Eldar · 2016
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Sparse phase retrieval via truncated amplitude flow
Gang Wang, Liang Zhang, Georgios B Giannakis, Mehmet Akçakaya, and Jie Chen · 2016
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Tightness of the maximum likelihood semidefinite relaxation for angular synchronization
Afonso S. Bandeira, Nicolas Boumal, and Amit Singer · 2017
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Sparse phase retrieval of one-dimensional signals by Prony’s method
Robert Beinert and Gerlind Plonka · 2017
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Robust recovery of positive stream of pulses
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Bispectrum inversion with application to multireference alignment
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