Built on

S. Pawar and K. Ramchandran, “A hybrid dft-ldpc framework for fast, efficient and robust compressive sensing,” in 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton) , 2012, pp. 1943–1950
1950
Earlier work this paper cites.
R. Tarjan, “Depth first search and linear graph algorithms,” SIAM Journal on Computing , 1972
1972
Earlier work this paper cites.
J. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. , vol. 21, pp. 2758–2769, 1982
1982
Earlier work this paper cites.
J. Dainty and J. Fienup, “Phase retrieval and image reconstruction for astronomy,” In: H. Stark, ed., Image Recovery: Theory and Application, Academic Press, New York , pp. 231–275, 1987
1987
Earlier work this paper cites.
C. McDiarmid, “On the method of bounded differences,” Surveys in combinatorics , vol. 141, no. 1, pp. 148–188, 1989
Original
1989
Earlier work this paper cites.
R. Millane, “Phase retrieval in crystallography and optics,” J. Opt. Soc. Am. A , vol. 7, pp. 394–411, 1990
1990
Earlier work this paper cites.
R. Motwani and P. Raghavan, “Randomized algorithms,” Cambridge University Press , 1995
1995
Earlier work this paper cites.
B. Bollobas, “Random graphs,” Cambridge University Press , 2001
2001
Earlier work this paper cites.
E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Transactions on Information Theory , vol. 52, no. 2, pp. 489–509, 2006
2006
Earlier work this paper cites.

Similar

H. Ohlsson, A. Yang, R. Dong, and S. Sastry, “Compressive phase retrieval from squared output measurements via semidenite programming,” e-prints, arXiv:1111.6323v3 [math.ST] , 2011
Original
2011
Cited alongside, same era.
E. Candès and B. Recht, “Exact matrix completion via convex optimization,” Commun. ACM , vol. 55, no. 6, pp. 111–119, Jun. 2012
2012
Cited alongside, same era.
B. Alexeev, A. S. Bandeira, M. Fickus, and D. G. Mixon, “Phase retrieval with polarization,” e-prints, arXiv:1210.7752[cs.IT] , 2012
Original
2012
Cited alongside, same era.
X. Li and V. Voroninski, “Sparse signal recovery from quadratic measurements via convex programming,” e-prints, arXiv:1209.4785[cs.IT] , 2012
Original
2012
Cited alongside, same era.

Then

I. Waldspurger, A. d’Aspremont, and S. Mallat, “Phase recovery, maxcut and complex semidefinite programming,” Mathematical Programming , pp. 1–35, 2013
2013
Later among the works it cites.
E. Candès and X. Li, “Solving quadratic equations via phaselift when there are about as many equations as unknowns,” Foundations of Computational Mathematics , pp. 1–10, 2013
2013
Later among the works it cites.
P. Netrapalli, P. Jain, and S. Sanghavi, “Phase retrieval using alternating minimization,” e-prints, arXiv:1306.0160v1 [stat.ML] , 2013
Original
2013
Later among the works it cites.
H. Ohlsson and Y. C. Eldar, “On conditions for uniqueness in sparse phase retrieval,” e-prints, arXiv:1308.5447[cs.IT] , 2013
Original
2013
Later among the works it cites.
M. Akçakaya and V. Tarokh, “New conditions for sparse phase retrieval,” e-prints, arXiv:1310.1351[cs.IT] , 2013

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Reading the bibliography…

2014

SUPER: Sparse signals with Unknown Phases Efficiently Recovered

Cai, Sheng, Bakshi, Mayank, Jaggi, Sidharth et al.

Understand

Suppose ${\bf x}$ is any exactly $k$-sparse vector in $\mathbb{C}^{n}$.

We present a class of phase measurement matrix $A$ in $\mathbb{C}^{m\times n}$, and a corresponding algorithm, called SUPER, that can resolve ${\bf x}$ up to a global phase from intensity measurements $|A{\bf x}|$ with high probability over $A$.
Here $|A{\bf x}|$ is a vector of component-wise magnitudes of $A{\bf x}$.
The SUPER algorithm is the first to simultaneously have the following properties: (a) it requires only ${\cal O}(k)$ (order-optimal) measurements, (b) the computational complexity of decoding is ${\cal O}(k\log k)$ (near order-optimal) arithmetic operations.

Built on

S. Pawar and K. Ramchandran, “A hybrid dft-ldpc framework for fast, efficient and robust compressive sensing,” in 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton) , 2012, pp. 1943–1950
1950
Earlier work this paper cites.
R. Tarjan, “Depth first search and linear graph algorithms,” SIAM Journal on Computing , 1972
1972
Earlier work this paper cites.
J. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. , vol. 21, pp. 2758–2769, 1982
1982
Earlier work this paper cites.
J. Dainty and J. Fienup, “Phase retrieval and image reconstruction for astronomy,” In: H. Stark, ed., Image Recovery: Theory and Application, Academic Press, New York , pp. 231–275, 1987
1987
Earlier work this paper cites.
C. McDiarmid, “On the method of bounded differences,” Surveys in combinatorics , vol. 141, no. 1, pp. 148–188, 1989
Original
1989
Earlier work this paper cites.
R. Millane, “Phase retrieval in crystallography and optics,” J. Opt. Soc. Am. A , vol. 7, pp. 394–411, 1990
1990
Earlier work this paper cites.
R. Motwani and P. Raghavan, “Randomized algorithms,” Cambridge University Press , 1995
1995
Earlier work this paper cites.
B. Bollobas, “Random graphs,” Cambridge University Press , 2001
2001
Earlier work this paper cites.
E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Transactions on Information Theory , vol. 52, no. 2, pp. 489–509, 2006
2006
Earlier work this paper cites.

Similar

H. Ohlsson, A. Yang, R. Dong, and S. Sastry, “Compressive phase retrieval from squared output measurements via semidenite programming,” e-prints, arXiv:1111.6323v3 [math.ST] , 2011
Original
2011
Cited alongside, same era.
E. Candès and B. Recht, “Exact matrix completion via convex optimization,” Commun. ACM , vol. 55, no. 6, pp. 111–119, Jun. 2012
2012
Cited alongside, same era.
B. Alexeev, A. S. Bandeira, M. Fickus, and D. G. Mixon, “Phase retrieval with polarization,” e-prints, arXiv:1210.7752[cs.IT] , 2012
Original
2012
Cited alongside, same era.
X. Li and V. Voroninski, “Sparse signal recovery from quadratic measurements via convex programming,” e-prints, arXiv:1209.4785[cs.IT] , 2012
Original
2012
Cited alongside, same era.

Then

I. Waldspurger, A. d’Aspremont, and S. Mallat, “Phase recovery, maxcut and complex semidefinite programming,” Mathematical Programming , pp. 1–35, 2013
2013
Later among the works it cites.
E. Candès and X. Li, “Solving quadratic equations via phaselift when there are about as many equations as unknowns,” Foundations of Computational Mathematics , pp. 1–10, 2013
2013
Later among the works it cites.
P. Netrapalli, P. Jain, and S. Sanghavi, “Phase retrieval using alternating minimization,” e-prints, arXiv:1306.0160v1 [stat.ML] , 2013
Original
2013
Later among the works it cites.
H. Ohlsson and Y. C. Eldar, “On conditions for uniqueness in sparse phase retrieval,” e-prints, arXiv:1308.5447[cs.IT] , 2013
Original
2013
Later among the works it cites.
M. Akçakaya and V. Tarokh, “New conditions for sparse phase retrieval,” e-prints, arXiv:1310.1351[cs.IT] , 2013

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

K. Jaganathan, S. Oymak, and B. Hassibi, “Recovery of sparse 1-d signals from the magnitudes of their fourier transform,” in 2012 IEEE International Symposium on Information Theory Proceedings (ISIT) , 2012, pp. 1473–1477

2012

Cited alongside, same era.

——, “Phase retrieval for sparse signals using rank minimization,” in 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) , 2012, pp. 3449–3452

2012

Cited alongside, same era.

M. Bakshi, S. Jaggi, S. Cai, and M. Chen, “Sho-fa: Robust compressive sensing with order-optimal complexity, measurements, and bits,” in 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton) , 2012, pp. 786–793

2012

Cited alongside, same era.

——, “Phase retrieval algorithms: a personal tour [invited],” Appl. Opt. , vol. 52, pp. 45–56, 2013

2013

Cited alongside, same era.

E. Candès, 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

Cited alongside, same era.

Original

2013

Later among the works it cites.

Y. Shechtman, A. Beck, and Y. C. Eldar, “Gespar: Effcient phase retrieval of sparse signals,” e-prints, arXiv:1301.1018[cs.IT] , 2013

Original

2013

Later among the works it cites.

——, “Sparse phase retrieval: Convex algorithms and limitations,” in 2013 IEEE International Symposium on Information Theory Proceedings (ISIT) , 2013, pp. 1022–1026

2013

Later among the works it cites.

S. Oymak, A. Jalali, M. Fazel, Y. C. Eldar, and B. Hassibi, “Simultaneously structured models with application to sparse and low-rank matrices,” e-prints, arXiv:1212.3753[cs.IT] , 2013

Original

2013

Later among the works it cites.