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This paper deals with finding an $n$-dimensional solution $x$ to a system of quadratic equations of the form $y_i=|\langle{a}_i,x\rangle|^2$ for $1\le i \le m$, which is also known as phase retrieval and is NP-hard in general.
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E. J. Candès and X. Li, “Solving quadratic equations via PhaseLift when there are about as many equations as unknowns,” Found. Comput. Math. , vol. 14, no. 5, pp. 1017–1026, 2014
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G. Wang and G. B. Giannakis, “Solving random systems of quadratic equations via truncated generalized gradient flow,” in Adv. Neural Inf. Process. Syst. , Barcelona, Spain, 2016, pp. 568–576
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2015
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P. Netrapalli, P. Jain, and S. Sanghavi, “Phase retrieval using alternating minimization,” IEEE Trans. Signal Process. , vol. 63, no. 18, pp. 4814–4826, Sept. 2015
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Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase retrieval with application to optical imaging: A contemporary overview,” IEEE Signal Process. Mag. , vol. 32, no. 3, pp. 87–109, May 2015
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I. Waldspurger, A. d’Aspremont, and S. Mallat, “Phase recovery, maxcut and complex semidefinite programming,” Math. Program. , vol. 149, no. 1, pp. 47–81, 2015
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2016
Cited alongside, same era.
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2017
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Y. Chen and E. J. Candès, “Solving random quadratic systems of equations is nearly as easy as solving linear systems,” Comm. Pure Appl. Math. , vol. 70, no. 5, pp. 822–883, Dec. 2017
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R. Kueng, H. Rauhut, and U. Terstiege, “Low rank matrix recovery from rank one measurements,” Appl. Comput. Harmon. Anal. , vol. 42, no. 1, pp. 88–116, Jan. 2017
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G. Wang, G. B. Giannakis, and J. Chen, “Scalable solvers of random quadratic equations via stochastic truncated amplitude flow,” IEEE Trans. Signal Process. , vol. 65, no. 8, pp. 1961–1974, Apr. 2017
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