Built on

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik , vol. 35, pp. 237–246, 1972
1972
Earlier work this paper cites.
G. S. Bloom, “A counterexample to a theorem of S. Piccard,” Journal of Combinatorial Theory, Series A , vol. 22, no. 3, pp. 378–379, 1977
1977
Earlier work this paper cites.
J. Fienup, “Phase retrieval algorithms: a comparison,” Applied Optics , vol. 21, no. 15, pp. 2758–2769, 1982
1982
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.
R. W. Harrison, “Phase problem in crystallography,” J. Opt. Soc. Am. A , vol. 10, no. 5, pp. 1046–1055, May 1993
1993
Earlier work this paper cites.
R. Balan, P. Casazza, and D. Edidin, “On signal reconstruction without phase,” Applied and Computational Harmonic Analysis , vol. 20, pp. 345–356, 2006
2006
Earlier work this paper cites.
D. Donoho, “Compressed sensing,” IEEE Transactions on Information Theory , vol. 52, no. 4, pp. 1289–1306, Apr. 2006
2006
Earlier work this paper cites.

Similar

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Transactions on Information Theory , vol. 52, pp. 489–509, Feb. 2006
Original
2006
Cited alongside, same era.
M. Moravec, J. Romberg, and R. Baraniuk, “Compressive phase retrieval,” in SPIE International Symposium on Optical Science and Technology , 2007
2007
Cited alongside, same era.
E. Candès, Y. C. Eldar, T. Strohmer, and V. Voroninski, “Phase retrieval via matrix completion,” Stanford University, Tech. Rep. arXiv:1109.0573, Sep. 2011
Original
2011
Cited alongside, same era.
E. Candès, T. Strohmer, and V. Voroninski, “PhaseLift: Exact and stable signal recovery from magnitude measurements via convex programming,” Stanford University, Tech. Rep. arXiv:1109.4499, Sep. 2011
Original
2011
Cited alongside, same era.

Then

A. Beck and Y. C. Eldar, “Sparsity constrained nonlinear optimization: Optimality conditions and algorithms,” Tech. Rep. arXiv:1203.4580, 2012
Original
2012
Later among the works it cites.
A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nature Materials , vol. 11, no. 5, pp. 455–459, May 2012
2012
Later among the works it cites.
X. Li and V. Voroninski, “Sparse signal recovery from quadratic measurements via convex programming,” CoRR , vol. abs/1209.4785, 2012
Original
2012
Later among the works it cites.
Y. C. Eldar and G. Kutyniok, Compresed Sensing: Theory and Applications . Cambridge University Press, 2012
2012
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

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2013

On Conditions for Uniqueness in Sparse Phase Retrieval

Ohlsson, Henrik, Eldar, Yonina C.

Understand

The phase retrieval problem has a long history and is an important problem in many areas of optics.

Theoretical understanding of phase retrieval is still limited and fundamental questions such as uniqueness and stability of the recovered solution are not yet fully understood.
This paper provides several additions to the theoretical understanding of sparse phase retrieval.
In particular we show that if the measurement ensemble can be chosen freely, as few as 4k-1 phaseless measurements suffice to guarantee uniqueness of a k-sparse M-dimensional real solution.

Built on

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik , vol. 35, pp. 237–246, 1972
1972
Earlier work this paper cites.
G. S. Bloom, “A counterexample to a theorem of S. Piccard,” Journal of Combinatorial Theory, Series A , vol. 22, no. 3, pp. 378–379, 1977
1977
Earlier work this paper cites.
J. Fienup, “Phase retrieval algorithms: a comparison,” Applied Optics , vol. 21, no. 15, pp. 2758–2769, 1982
1982
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.
R. W. Harrison, “Phase problem in crystallography,” J. Opt. Soc. Am. A , vol. 10, no. 5, pp. 1046–1055, May 1993
1993
Earlier work this paper cites.
R. Balan, P. Casazza, and D. Edidin, “On signal reconstruction without phase,” Applied and Computational Harmonic Analysis , vol. 20, pp. 345–356, 2006
2006
Earlier work this paper cites.
D. Donoho, “Compressed sensing,” IEEE Transactions on Information Theory , vol. 52, no. 4, pp. 1289–1306, Apr. 2006
2006
Earlier work this paper cites.

Similar

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Transactions on Information Theory , vol. 52, pp. 489–509, Feb. 2006
Original
2006
Cited alongside, same era.
M. Moravec, J. Romberg, and R. Baraniuk, “Compressive phase retrieval,” in SPIE International Symposium on Optical Science and Technology , 2007
2007
Cited alongside, same era.
E. Candès, Y. C. Eldar, T. Strohmer, and V. Voroninski, “Phase retrieval via matrix completion,” Stanford University, Tech. Rep. arXiv:1109.0573, Sep. 2011
Original
2011
Cited alongside, same era.
E. Candès, T. Strohmer, and V. Voroninski, “PhaseLift: Exact and stable signal recovery from magnitude measurements via convex programming,” Stanford University, Tech. Rep. arXiv:1109.4499, Sep. 2011
Original
2011
Cited alongside, same era.

Then

A. Beck and Y. C. Eldar, “Sparsity constrained nonlinear optimization: Optimality conditions and algorithms,” Tech. Rep. arXiv:1203.4580, 2012
Original
2012
Later among the works it cites.
A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nature Materials , vol. 11, no. 5, pp. 455–459, May 2012
2012
Later among the works it cites.
X. Li and V. Voroninski, “Sparse signal recovery from quadratic measurements via convex programming,” CoRR , vol. abs/1209.4785, 2012
Original
2012
Later among the works it cites.
Y. C. Eldar and G. Kutyniok, Compresed Sensing: Theory and Applications . Cambridge University Press, 2012
2012
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Y. Shechtman, Y. C. Eldar, A. Szameit, and M. Segev, “Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing,” Opt. Express , vol. 19, no. 16, pp. 14 807–14 822, Aug 2011

2011

Cited alongside, same era.

H. Ohlsson, A. Y. Yang, R. Dong, and S. S. Sastry, “Compressive Phase Retrieval From Squared Output Measurements Via Semidefinite Programming,” University of California, Berkeley, Tech. Rep. arXiv:1111.6323, Nov. 2011

Original

2011

Cited alongside, same era.

Y. C. Eldar and S. Mendelson, “Phase retrieval: Stability and recovery guarantees,” CoRR , vol. abs/1211.0872, 2012

Original

2012

Cited alongside, same era.

Y. Shechtman, A. Beck, and Y. C. Eldar, “GESPAR: efficient phase retrieval of sparse signals,” CoRR , vol. abs/1301.1018, 2013

Original