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The problem of signal recovery from its Fourier transform magnitude is of paramount importance in various fields of engineering and has been around for over 100 years.
A. L. Patterson, “A Fourier series method for the determination of the components of interatomic distances in crystals,” Physical Review (1935), 46(5), 372
1935
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A. Walther, “The question of phase retrieval in optics,” Journal of Modern Optics 10.1 (1963): 41-49
1963
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A. Hajnal and E. Szemeredi, “Proof of a Conjecture of Erdos,” In Combinatorial Theory and Its Applications, Vol. 2, 1970
1970
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R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237 (1972)
1972
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M. Stefik, “Inferring DNA structures from segmentation data,” Artificial Intelligence 11 (1978)
1978
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J. R. Fienup, “Phase retrieval algorithms: a comparison,” Applied optics 21, no. 15 (1982): 2758-2769
1982
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M. Hayes and J. McClellan, “Reducible Polynomials in more than One Variable,” Proceedings of the IEEE 70, no. 2 (1982): 197-198
1982
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J. R. Fienup, T. R. Crimmins, and W. Holsztynski, “Reconstruction of the support of an object from the support of its autocorrelation,” Journal of the Optical Society of America Vol. 72, Issue 5, pp. 610-624 (1982)
1982
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P. Lemke and M. Wermano, “On the complexity of inverting the autocorrelation function of a finite integer sequence, and the problem of locating n points on a line, given the unlabeled distances between them,” unpublished manuscript (1988)
1988
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R. P. Millane, “Phase retrieval in crystallography and optics,” JOSA A 7.3 (1990): 394-41
1990
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L. Rabiner and B. H. Juang, “Fundamentals of Speech Recognition,” Signal Processing Series, Prentice Hall, 1993
1993
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T. Dakic, “On the Turnpike Problem,” PhD Thesis, Simon Fraser University, 2000
2000
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A. H. Sayed and T. Kailath, “A survey of spectral factorization methods,” Numerical Linear Algebra with Applications (2001)
2001
Cited alongside, same era.
H. H. Bauschke, P. L. Combettes and D. R. Luke, “Phase retrieval, error reduction algorithm, and Fienup variants: a view from convex optimization,” JOSA A 19, no. 7 (2002)
2002
Cited alongside, same era.
M. Fazel, H. Hindi, and S. Boyd, “Log-det Heuristic for Matrix Rank Minimization with Applications to Hankel and Euclidean Distance Matrices,” American Control Conference, vol. 3, pp. 2156-2162, 2003
2003
Cited alongside, same era.
E. J. Candes and T. Tao, “Decoding by linear programming,” Information Theory, IEEE Transactions on 51, no. 12 (2005): 4203-4215
2005
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E. J. Candes, M. B. Wakin, S. P. Boyd, “Enhancing Sparsity by Reweighted
2008
Cited alongside, same era.
E. J. Candes, Y. Eldar, T. Strohmer and V. Voroninski, “Phase retrieval via matrix completion,” SIAM Journal on Imaging Sciences 6.1 (2013): 199-225
2013
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E. J. Candes, T. Strohmer, and V. Voroninski, “Phaselift: Exact and stable signal recovery from magnitude measurements via convex programming,” Communications on Pure and Applied Mathematics 66, no. 8 (2013): 1241-1274
2013
Closest in time.
P. Netrapalli, P. Jain and S. Sanghavi, “Phase Retrieval using Alternating Minimization,” In Advances in Neural Information Processing Systems, pp. 2796-2804, 2013
2013
Closest in time.
X. Li and V. Voroninski, “Sparse Signal Recovery from Quadratic Measurements via Convex Programming,” SIAM Journal on Mathematical Analysis 45, no. 5 (2013): 3019-3033
2013
Closest in time.
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Y. M. Lu and M. Vetterli, “Sparse spectral factorization: Unicity and reconstruction algorithms,” Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on, pp. 5976-5979, 2011
2011
Cited alongside, same era.
Y. Shechtman, Y. C. Eldar, A. Szameit and M. Segev, “Sparsity Based Sub-Wavelength Imaging with Partially Incoherent Light Via Quadratic Compressed Sensing,” Optics Express, vol. 19, Issue 16, pp. 14807-14822, Aug. 2011
2011
Cited alongside, same era.
2011
Cited alongside, same era.
S. Mukherjee and C. Seelamantula, “An iterative algorithm for phase retrieval with sparsity constraints: Application to frequency domain optical coherence tomography,” Acoustics, Speech and Signal Processing (ICASSP), 2012 IEEE International Conference on, 2012, pp. 553Ð556
2012
Cited alongside, same era.
K. Jaganathan, S. Oymak and B. Hassibi, “Recovery of Sparse 1-D Signals from the Magnitudes of their Fourier Transform,” Information Theory Proceedings (ISIT), 2012 IEEE International Symposium On, pp. 1473-1477. IEEE, 2012
2012
Cited alongside, same era.
P. Schniter and S. Rangan, “Compressive phase retrieval via generalized approximate message passing,” Annual Allerton Conference on Communication, Control, and Computing, 2012
2012
Cited alongside, same era.
K. Jaganathan, S. Oymak and B. Hassibi, “On Robust Phase Retrieval for Sparse Signals,” Communication, Control, and Computing (Allerton), Annual Conference on, 2012
2012
Cited alongside, same era.
2013
Closest in time.
K. Jaganathan, S. Oymak and B. Hassibi, “Sparse Phase Retrieval: Convex Algorithms and Limitations,” Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on (pp. 1022-1026)
2013
Closest in time.
Y. Shechtman, A. Beck and Y. C. Eldar, “GESPAR: Efficient Phase Retrieval of Sparse Signals,” Signal Processing, IEEE Transactions on 62, no. 4 (2014): 928-938
2014
Closest in time.
A. S. Bandeira, Y. Chen and D. G. Mixon, “Phase retrieval from power spectra of masked signals,” Information and Inference (2014)
2014
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E. J. Candes, X. Li, and M. Soltanolkotabi, “Phase retrieval from coded diffraction patterns,” Applied and Computational Harmonic Analysis (2014)
2014
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Y. C. Eldar and S. Mendelson, “Phase retrieval: Stability and recovery guarantees,” Applied and Computational Harmonic Analysis 36, no. 3 (2014): 473-494
2014
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H. Ohlsson, A. Yang, R. Dong, M. Verhaegen and S. Sastry, “Quadratic Basis Pursuit,” Regularization, Optimization, Kernels, and Support Vector Machines (2014): 195
2014
Closest in time.