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In this short note we propose a simple two-stage sparse phase retrieval strategy that uses a near-optimal number of measurements, and is both computationally efficient and robust to measurement noise.
On signal reconstruction without phase
R. Balan, P. Casazza, and D. Edidin · 2006
Earlier work this paper cites.
Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
E. Candes, J. Romberg, and T. Tao · 2006
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Stable signal recovery from incomplete and inaccurate measurements
E. Candes, J. Romberg, and T. Tao · 2006
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Near optimal signal recovery from random projections: Universal encoding strategies?
E. Candes and T. Tao · 2006
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Compressed sensing
D. L. Donoho · 2006
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Signal recovery from partial information via orthogonal matching pursuit
J. Tropp and A. Gilbert · 2007
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A simple proof of the restricted isometry property for random matrices
R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin · 2008
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Graph implementations for nonsmooth convex programs
M. Grant and S. Boyd · 2008
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Random Sampling of Sparse Trigonometric Polynomials II - Orthogonal Matching Pursuit versus Basis Pursuit
S. Kunis and H. Rauhut · 2008
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Cosamp: Iterative signal recovery from incomplete and inaccurate samples
D. Needell and J. A. Tropp · 2008
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Painless reconstruction from magnitudes of frame coefficients
R. Balan, B. G. Bodmann, P. G. Casazza, and D. Edidin · 2009
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Iterative hard thresholding for compressed sensing
T. Blumensath and M. E. Davies · 2009
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Compressed Sensing and Best k k -term Approximation
A. Cohen, W. Dahmen, and R. DeVore · 2009
Cited alongside, same era.
Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit
D. Needell and R. Vershynin · 2009
Cited alongside, same era.
Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit
D. Needell and R. Vershynin · 2010
Cited alongside, same era.
Templates for convex cone problems with applications to sparse signal recovery
S. Becker, E. J. Candes, and M. Grant · 2011
Cited alongside, same era.
Cprl: An extension of compressive sensing to the phase retrieval problem
H. Ohlsson, A. Yang, R. Dong, and S. Sastry · 2012
Cited alongside, same era.
Compressive phase retrieval via generalized approximate message passing
TFOCS: Templates for first-order conic solvers, version 1.3.1
S. Becker, E. J. Candes, and M. Grant · 2014
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Solving quadratic equations via phaselift when there are about as many equations as unknowns
E. J. Candes and X. Li · 2014
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Phase retrieval: Stability and recovery guarantees
Y. C. Eldar and S. Mendelson · 2014
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Phase retrieval from very few measurements
M. Fickus, D. Mixon, A. Nelson, and Y. Wang · 2014
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CVX: Matlab software for disciplined convex programming, version 2.1
M. Grant and S. Boyd · 2014
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Compressed sensing with sparse binary matrices: Instance optimal error guarantees in near-optimal time
M. Iwen · 2014
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P. Schniter and S. Rangan · 2012
Cited alongside, same era.
Phaselift: Exact and stable signal recovery from magnitude measurements via convex programming
E. J. Candes, T. Strohmer, and V. Voroninski · 2013
Cited alongside, same era.
A Mathematical Introduction to Compressive Sensing
S. Foucart and H. Rauhut · 2013
Cited alongside, same era.
Quantum tomography under prior information
T. Heinosaari, L. Mazzarella, and M. M. Wolf · 2013
Cited alongside, same era.
Sparse phase retrieval: Convex algorithms and limitations
K. Jaganathan, S. Oymak, and B. Hassibi · 2013
Cited alongside, same era.
Sparse signal recovery from quadratic measurements via convex programming
X. Li and V. Voroninski · 2013
Cited alongside, same era.
Phase retrieval with polarization
B. Alexeev, A. S. Bandeira, M. Fickus, and D. G. Mixon · 2014
Cited alongside, same era.
SparsePR: Matlab software for sparse phase retrieval, version 1.0
M. Iwen, Y. Wang, and A. Viswanathan · 2014
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Gespar: Efficient phase retrieval of sparse signals
Y. Shechtman, A. Beck, and Y. C. Eldar · 2014
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Phase retrieval for sparse signals
Y. Wang and Z. Xu · 2014
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Fast compressive phase retrieval from fourier measurements
Ç. Yapar, V. Pohl, and H. Boche · 2014
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Technical note: A minor correction of theorem 1.3 from [1]
M. Iwen, F. Krahmer, and A. Viswanathan · 2015
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