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In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted.
A. L. Patterson, “A direct method for the determination of the components of interatomic distances in crystals,” Zeitschrift für Kristallographie , vol. 90, 1935
1935
Earlier work this paper cites.
S. Piccard, Sur les ensembles de distances des ensembles de points d’un espace euclidien . Paris: Librairie Gauthier-Villars, Aug. 1939
1939
Earlier work this paper cites.
F. Bauer, “Ein direktes iterationsverfahren zur hurwitz-zerlegung eines polynoms,” Arch. Elektr. Uebertragung , vol. 9, pp. 285–290, 1955
1955
Earlier work this paper cites.
M. M. Woolfson, “Direct methods in crystallography,” Rep. Prog. Phys , vol. 34, no. 2, p. 369, 1971
1971
Earlier work this paper cites.
R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik , vol. 35, p. 237, 1972
1972
Earlier work this paper cites.
G. S. Bloom, “A counterexample to a theorem of S. Piccard,” J. Comb. Theory A , vol. 22, no. 3, pp. 378–379, Nov. 1975
1975
Earlier work this paper cites.
J. Y. Wang and J. K. Markey, “Modal compensation of atmospheric turbulence phase distortion,” J. Opt. Soc. Am. , vol. 68, no. 1, pp. 78–87, 1978
1978
Earlier work this paper cites.
M. H. Hayes, M. H. Hayes, J. S. Lim, J. S. Lim, A. V. Oppenheim, and A. V. Oppenheim, “Signal reconstruction from phase or magnitude,” IEEE Trans. Acoust. Speech Signal Process. , vol. 28, pp. 672–680, Dec. 1980
1980
Earlier work this paper cites.
J. R. Fienup, “Phase retrieval algorithms: a comparison,” Applied Optics , 1982
1982
Earlier work this paper cites.
M. H. Hayes, “The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform,” IEEE Trans. Acoust. Speech Signal Process. , vol. 30, no. 2, pp. 140–154, 1982
1982
Earlier work this paper cites.
P. Van Hove, M. H. Hayes, J. S. Lim, and A. V. Oppenheim, “Signal reconstruction from signed Fourier transform magnitude,” IEEE Trans. Acoust. Speech Signal Process. , vol. 31, no. 5, pp. 1286–1293, 1983
1983
Earlier work this paper cites.
R. P. Millane, “Phase retrieval in crystallography and optics,” J. Opt. Soc. Am. A , vol. 7, no. 3, pp. 394–411, Mar. 1990
1990
Earlier work this paper cites.
S. S. Skiena, W. D. Smith, and P. Lemke, “Reconstructing sets from interpoint distances,” in SoCG . ACM, 1990, pp. 332–339
1990
Earlier work this paper cites.
Z. Zhang, “An exponential example for a partial digest mapping algorithm,” J. Comp. Biol. , vol. 1, no. 3, pp. 235–239, 1994
1994
Cited alongside, same era.
S. S. Skiena and G. Sundaram, “A partial digest approach to restriction site mapping,” B. Math. Biol. , vol. 56, no. 2, pp. 275–294, 1994
1994
Cited alongside, same era.
M. X. Goemans and D. P. Williamson, “Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming,” J. ACM , vol. 42, no. 6, pp. 1115–1145, 1995
1995
Cited alongside, same era.
I. Kang, M. P. Fitz, and S. B. Gelfand, “Blind estimation of multipath channel parameters: a modal analysis approach,” IEEE Trans. Commun. , vol. 47, no. 8, pp. 1140–1150, 1999
1999
Cited alongside, same era.
R. van Nee and R. Prasad, OFDM for wireless multimedia communications , 1st ed. Norwood, MA, USA: Artech House, Inc., 2000
A. Bekir and S. W. Golomb, “There are no further counterexamples to S. Piccard’s theorem,” IEEE Trans. Inf. Theory , vol. 53, no. 8, pp. 2864–2867, 2007
2007
Later among the works it cites.
——, “The charge flipping algorithm,” Acta Crystallogr., Sect. A: Found. Crystallogr. , vol. 64, no. 1, pp. 123–134, 2007
2007
Later among the works it cites.
R. M. Balan, B. G. Bodmann, P. G. Casazza, and D. Edidin, “Fast algorithms for signal reconstruction without phase,” SPIE Optical Engineering+Applications , pp. 67 011L–67 011L–9, 2007
2007
Later among the works it cites.
R. M. Balan, P. G. Casazza, and D. Edidin, “Equivalence of reconstruction from the absolute value of the frame coefficients to a sparse representation problem,” IEEE Signal Process. Lett. , vol. 14, no. 5, pp. 341–343, 2007
2007
Later among the works it cites.
M. Senechal, “A point set puzzle revisited,” European J. Combin. , vol. 29, no. 8, pp. 1933–1944, Oct. 2008
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2000
Cited alongside, same era.
A. H. Sayed and T. Kailath, “A survey of spectral factorization methods,” Numer. Linear Algebr. , vol. 8, pp. 467–496, 2001
2001
Cited alongside, same era.
T. F. Cox and M. A. A. Cox, Multidimensional scaling , 2nd ed. Chapman and Hall/CRC, 2001
2001
Cited alongside, same era.
M. Vetterli, P. Marziliano, and T. Blu, “Sampling signals with finite rate of innovation,” IEEE Trans. Signal Process. , vol. 50, no. 6, pp. 1417–1428, 2002
2002
Cited alongside, same era.
D. Sayre, “X-ray crystallography: the past and present of the phase problem,” J. Struct. Chem. , vol. 13, pp. 81–96, 2002
2002
Cited alongside, same era.
M. Cieliebak, S. Eidenbenz, and P. Penna, “Noisy data make the partial digest problem NP-hard,” WABI , pp. 111–123, 2003
2003
Cited alongside, same era.
G. Oszlanyi and A. Suto, “Ab initio structure solution by charge flipping,” Acta Crystallogr., Sect. A: Found. Crystallogr. , vol. 60, no. 2, pp. 134–141, Mar. 2004
2004
Cited alongside, same era.
——, “On signal reconstruction from absolute value of frame coefficients,” Proc. SPIE, Wavelets XI , 2005
2005
Cited alongside, same era.
2008
Later among the works it cites.
A. Chebira, M. Fickus, and M. Vetterli, “Frame domain signal processing: framework and applications,” in IEEE ICASSP , Dallas, 2010
2010
Later among the works it cites.
M. Hirsch, S. Harmeling, S. Sra, and B. Schölkopf, “Online multi-frame blind deconvolution with super-resolution and saturation correction,” Astron. Astrophys. , vol. 531, p. A9, May 2011
2011
Later among the works it cites.
Y. M. Lu and M. Vetterli, “Sparse spectral factorization: unicity and reconstruction algorithms,” in IEEE ICASSP , Prague, Feb. 2011, pp. 1–4
2011
Later among the works it cites.
E. J. Candès, Y. C. Eldar, T. Strohmer, and V. Voroninski, “Phase retrieval via matrix completion,” arXiv , Sep. 2011
2011
Later among the works it cites.
Y. Barbotin and M. Vetterli, “Fast and robust parametric estimation of jointly sparse channels,” IEEE J. Emerg. Sel. Topics Circuits Syst. , vol. PP, no. 3, pp. 1–11, 2012
2012
Later among the works it cites.
E. J. Candès, T. Strohmer, and V. Voroninski, “PhaseLift: Exact and stable signal recovery from magnitude measurements via convex programming,” Comm. Pure Appl. Math. , 2012
2012
Later among the works it cites.
K. Jaganathan, S. Oymak, and B. Hassibi, “Recovery of sparse 1-D signals from the magnitudes of their Fourier transform,” ISIT , pp. 1473–1477, 2012
2012
Later among the works it cites.
I. Waldspurger, A. d’Aspremont, and S. Mallat, “Phase recovery, MaxCut and complex semidefinite programming,” arXiv , Jun. 2012
2012
Later among the works it cites.