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This paper concerns the problem of recovering an unknown but structured signal $x \in R^n$ from $m$ quadratic measurements of the form $y_r=|<a_r,x>|^2$ for $r=1,2,...,m$.
Phase retrieval algorithms: a comparison
J. R. Fienup · 1982
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On Milman’s inequality and random subspaces which escape through a mesh in ℝ n \mathbb{R}^{n}
Y. Gordon · 1988
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A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
S. Burer and R. Monteiro · 2003
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Invited article: A unified evaluation of iterative projection algorithms for phase retrieval
S. Marchesini · 2007
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High-dimensional analysis of semidefinite relaxations for sparse principal components
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R. H. Keshavan, S. Oh, and A. Montanari · 2009
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Compressive phase retrieval from squared output measurements via semidefinite programming
H. Ohlsson, A. Y. Yang, R. Dong, and S. S. Sastry · 2011
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The convex geometry of linear inverse problems
V. Chandrasekaran, B. Recht, P. A. Parrilo, and A. S. Willsky · 2012
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On robust phase retrieval for sparse signals
K. Jaganathan, S. Oymak, and B. Hassibi · 2012
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Efficient algorithms for collaborative filtering
R. H. Keshavan · 2012
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Oracle inequalities and the isomorphic method
S. Mendelson · 2012
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I. Waldspurger, A. d’Aspremont, and S. Mallat · 2012
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Saving phase: Injectivity and stability for phase retrieval
A. S. Bandeira, J. Cahill, D. G. Mixon, and A. A. Nelson · 2013
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Complexity theoretic lower bounds for sparse principal component detection
Q. Berthet and P. Rigollet · 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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A partial derandomization of phaselift using spherical designs
D. Gross, F. Krahmer, and R. Kueng · 2013
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Sparse phase retrieval: Convex algorithms and limitations
K. Jaganathan, S. Oymak, and B. Hassibi · 2013
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K. Lee, Y. Wu, and Y. Bresler · 2013
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Sparse signal recovery from quadratic measurements via convex programming
X. Li and V. Voroninski · 2013
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Phase retrieval using alternating minimization
P. Netrapalli, P. Jain, and S. Sanghavi · 2013
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The squared-error of generalized LASSO: A precise analysis
S. Oymak, C. Thrampoulidis, and B. Hassibi · 2013
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Living on the edge: Phase transitions in convex programs with random data
D. Amelunxen, M. Lotz, M. B. McCoy, and J. A. Tropp · 2014
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Statistical guarantees for the EM algorithm: From population to sample-based analysis
S. Balakrishnan, M. J. Wainwright, and B. Yu · 2014
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Phase retrieval from coded diffraction patterns
E. J. Candes, X. Li, and M. Soltanolkotabi · 2014
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Sparse pca via covariance thresholding
Y.h Deshpande and A. Montanari · 2014
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Phase retrieval: Stability and recovery guarantees
Y. C. Eldar and Sh. Mendelson · 2014
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Improved recovery guarantees for phase retrieval from coded diffraction patterns
D. Gross, F. Krahmer, and R. Kueng · 2014
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Structured low-rank matrix factorization: Optimality, algorithm, and applications to image processing
B. Haeffele, E. Young, and R. Vidal · 2014
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Phasecode: Fast and efficient compressive phase retrieval based on sparse-graph codes
R. Pedarsani, K. Lee, and K. Ramchandran · 2014
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Global convergence of stochastic gradient descent for some nonconvex matrix problems
C. De Sa, K. Olukotun, and C. Ré · 2014
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Phase retrieval with application to optical imaging
Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev · 2014
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Algorithms and Theory for Clustering and Nonconvex Quadratic Programming
M. Soltanolkotabi · 2014
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Global optimality of local search for low rank matrix recovery
S. Bhojanapalli, B. Neyshabur, and N. Srebro · 2016
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The non-convex Burer-Monteiro approach works on smooth semidefinite programs
N. Boumal, V. Voroninski, and A. S. Bandeira · 2016
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Matrix completion has no spurious local minimum
R. Ge, J. D. Lee, and T. Ma · 2016
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Phasemax: Convex phase retrieval via basis pursuit. arxiv preprint
T. Goldstein and C. Studer · 2016
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P. Hand and V. Voroninski · 2016
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R. Sun and Z. Luo · 2014
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Simple, efficient, and neural algorithms for sparse coding
S. Arora, R. Ge, T. Ma, and A. Moitra · 2015
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Efficient compressive phase retrieval with constrained sensing vectors
S. Bahmani and J. Romberg · 2015
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Optimal rates of convergence for noisy sparse phase retrieval via thresholded wirtinger flow
T. T. Cai, X. Li, and Z. Ma · 2015
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Phase retrieval via Wirtinger flow: Theory and algorithms
E. J. Candes, X. Li, and M. Soltanolkotabi · 2015
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Solving random quadratic systems of equations is nearly as easy as solving linear systems
Y. Chen and E. Candes · 2015
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Y. Chen and M. J. Wainwright · 2015
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P. Hand and V. Voroninski · 2016
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M. A. Iwen, B. Preskitt, R. Saab, and A. Viswanathan · 2016
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Fast phase retrieval from local correlation measurements
M. A. Iwen, A. Viswanathan, and Y. Wang · 2016
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STFT phase retrieval: Uniqueness guarantees and recovery algorithms
K. Jaganathan, Y. C. Eldar, and B. Hassibi · 2016
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K. Jaganathan and B. Hassibi · 2016
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Saffron: A fast, efficient, and robust framework for group testing based on sparse-graph codes
K. Lee, R. Pedarsani, and K. Ramchandran · 2016
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Direct single-shot phase retrieval from the diffraction pattern of separated objects
B. Leshem, R. Xu, Y. Dallal, J. Miao, B. Nadler, D. Oron, N. Dudovich, and O. Raz · 2016
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Rapid, robust, and reliable blind deconvolution via nonconvex optimization
X. Li, S. Liang, T. Strohmer, and K. Wei · 2016
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A simple tool for bounding the deviation of random matrices on geometric sets
C. Liaw, A. Mehrabian, Y. Plan, and R. Vershynin · 2016
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Fast and reliable parameter estimation from nonlinear observations
S. Oymak and M. Soltanolkotabi · 2016
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Finding low-rank solutions to matrix problems, efficiently and provably
Dohyung P., Anastasios K., Constantine C., and Sujay S · 2016
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A geometric analysis of phase retrieval
J. Sun, Q. Qu, and J. Wright · 2016
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Low-rank solutions of linear matrix equations via procrustes flow
S. Tu, M. Boczar, M. Simchowitz, M. Soltanolkotabi, and B. Recht · 2016
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Phase retrieval with random gaussian sensing vectors by alternating projections
I. Waldspurger · 2016
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Solving random systems of quadratic equations via truncated generalized gradient flow
G. Wang and G. B. Giannakis · 2016
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Sparse phase retrieval via truncated amplitude flow
G. Wang, L. Zhang, G. B. Giannakis, M. Akçakaya, and J. Chen · 2016
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Provable non-convex phase retrieval with outliers: Median truncated Wirtinger flow
H. Zhang, Y. Chi, and Y. Liang · 2016
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Reshaped Wirtinger flow for solving quadratic systems of equations
H. Zhang and Y. Liang · 2016
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Q. Zheng and J. Lafferty · 2016
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The discrete sign problem: uniqueness, recovery algorithms and phase retrieval applications
B. Leshem, O. Raz, A. Jaffe, and B. Nadler · 2017
Closest in time.
F. Salehi, K. Jaganathan, and B. Hassibi · 2017
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High-Dimensional Probability
R. Vershynin · 2017
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