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2014

Phase Retrieval from 4N-4 Measurements

Philipp, Friedrich

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We prove by means of elementary methods that phase retrieval of complex polynomials p of degree less than N is possible with 4N-4 phaseless Fourier measurements of p and p'.

In addition, we provide an associated algorithm and prove that it recovers p up to global phase.

Phase Retrieval from 4N-4 Measurements · Around

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J.R. Fienup, Phase retrieval algorithms: a comparison, Applied Optics 21
1982
Earlier work this paper cites.
R.P. Millane, Phase retrieval in crystallography and optics, J. Opt. Soc. Am. A. 7
1990
Earlier work this paper cites.
M.W. Farn, New iterative algorithm for the design of phase-only gratings, Proc. SPIE 1555, SPIE, Bellingham, WA, 1991, pp. 3442
1991
Earlier work this paper cites.

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R. Balan, P.G. Casazza, and D. Edidin, On signal reconstruction without phase, Appl. Comp. Harmon. Anal. 20
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9 A. Conca, D. Edidin, M. Hering, C. Vinzant, An algebraic characterization of injectivity in phase retrieval, Preprint, arXiv:1312.0158
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Then

J.V. Corbett, The Pauli problem, state reconstruction and quantum-real numbers, Rep. Math. Phys. 57
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A.I. Lvovsky and M.G. Raymer, Continuous-variable optical quantum state tomography, Reviews of Modern Physics 81
2009
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T. Heinosaari, L. Mazzarella, M.M. Wolf, Quantum tomography under prior information, Commun. Math. Phys. 318
2013
Later among the works it cites.

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