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The problem of recovering a one-dimensional signal from its Fourier transform magnitude, called Fourier phase retrieval, is ill-posed in most cases.
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2012
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E. Candes, T. Strohmer, and V. Voroninski, “Phaselift: Exact and stable signal recovery from magnitude measurements via convex programming,” Communications on Pure and Applied Mathematics , vol. 66, no. 8, pp. 1241–1274, 2013
2013
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K. Jaganathan, S. Oymak, and B. Hassibi, “Sparse phase retrieval: Convex algorithms and limitations,” in Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on . IEEE, 2013, pp. 1022–1026
2013
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I. Bojarovska and A. Flinth, “Phase retrieval from gabor measurements,” Journal of Fourier Analysis and Applications , vol. 22, no. 3, pp. 542–567, 2016
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N. Boumal, “Nonconvex phase synchronization,” SIAM Journal on Optimization , vol. 26, no. 4, pp. 2355–2377, 2016
2016
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K. Huang, Y. C. Eldar, and N. D. Sidiropoulos, “Phase retrieval from 1d fourier measurements: Convexity, uniqueness, and algorithms,” IEEE Transactions on Signal Processing , vol. 64, no. 23, pp. 6105–6117, 2016
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2013
Cited alongside, same era.
N. Boumal, B. Mishra, P.-A. Absil, and R. Sepulchre, “Manopt, a Matlab toolbox for optimization on manifolds,” Journal of Machine Learning Research , vol. 15, pp. 1455–1459, 2014. [Online]. Available: http://www.manopt.org
2014
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E. Candès and X. Li, “Solving quadratic equations via Phaselift when there are about as many equations as unknowns,” Foundations of Computational Mathematics , vol. 14, no. 5, pp. 1017–1026, 2014
2014
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E. J. Candès and C. Fernandez-Granda, “Towards a mathematical theory of super-resolution,” Communications on Pure and Applied Mathematics , vol. 67, no. 6, pp. 906–956, 2014
2014
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Y. C. Eldar and S. Mendelson, “Phase retrieval: Stability and recovery guarantees,” Applied and Computational Harmonic Analysis , vol. 36, no. 3, pp. 473–494, 2014
2014
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Y. Shechtman, A. Beck, and Y. C. Eldar, “GESPAR: Efficient phase retrieval of sparse signals,” Signal Processing, IEEE Transactions on , vol. 62, no. 4, pp. 928–938, 2014
2014
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Y. Wang and Z. Xu, “Phase retrieval for sparse signals,” Applied and Computational Harmonic Analysis , vol. 37, no. 3, pp. 531–544, 2014
2014
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2015
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M. A. Iwen, A. Viswanathan, and Y. Wang, “Fast phase retrieval from local correlation measurements,” SIAM Journal on Imaging Sciences , vol. 9, no. 4, pp. 1655–1688, 2016
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——, “STFT phase retrieval: Uniqueness guarantees and recovery algorithms,” IEEE Journal of Selected Topics in Signal Processing , vol. 10, no. 4, pp. 770–781, 2016
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S. Sanghavi, R. Ward, and C. D. White, “The local convexity of solving systems of quadratic equations,” Results in Mathematics , pp. 1–40, 2016
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T. Bendory, P. Sidorenko, and Y. C. Eldar, “On the uniqueness of FROG methods,” IEEE Signal Processing Letters , vol. 24, no. 5, pp. 722–726, 2017
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T. Bendory, “Robust recovery of positive stream of pulses,” IEEE Transactions on Signal Processing , vol. 65, no. 8, pp. 2114–2122, 2017
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Y. Chen and E. J. Candes, “Solving random quadratic systems of equations is nearly as easy as solving linear systems,” Communications on Pure and Applied Mathematics , vol. 70, no. 5, pp. 822–883, 2017
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