2013

GESPAR: Efficient Phase Retrieval of Sparse Signals

Shechtman, Yoav, Beck, Amir, Eldar, Yonina C.

Understand

We consider the problem of phase retrieval, namely, recovery of a signal from the magnitude of its Fourier transform, or of any other linear transform.

Due to the loss of the Fourier phase information, this problem is ill-posed.
Therefore, prior information on the signal is needed in order to enable its recovery.
In this work we consider the case in which the signal is known to be sparse, i.e., it consists of a small number of nonzero elements in an appropriate basis.

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Similar

D. Bertsekas, “Nonlinear programming,” 1999
1999
Cited alongside, same era.
N. Hurt, Phase Retrieval and Zero Crossings: Mathematical Methods in Image Reconstruction . Springer, 2001, vol. 52
2001
Cited alongside, same era.
H. Bauschke, P. Combettes, and D. Luke, “Phase retrieval, error reduction algorithm, and fienup variants: a view from convex optimization,” JOSA A , vol. 19, no. 7, pp. 1334–1345, 2002
2002
Cited alongside, same era.
E. Candes, Y. Eldar, T. Strohmer, and V. Voroninski, “Phase retrieval via matrix completion,” arXiv preprint arXiv:1109.0573 , 2011
Original
2011
Cited alongside, same era.
Y. Shechtman, Y. Eldar, A. Szameit, and M. Segev, “Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing,” Optics Express , vol. 19, no. 16, pp. 14 807–14 822, 2011
2011
Cited alongside, same era.

Then

H. Ohlsson, A. Yang, R. Dong, and S. Sastry, “Compressive phase retrieval from squared output measurements via semidefinite programming,” arXiv preprint arXiv:1111.6323 , 2011
Original
2011
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,” CoRR , vol. abs/1206.1405, 2012
Original
2012
Later among the works it cites.
I. Waldspurger, A. d’Aspremont, and S. Mallat, “Phase recovery, maxcut and complex semidefinite programming,” arXiv preprint arXiv:1206.0102 , 2012
Original
2012
Later among the works it cites.
S. Mukherjee and C. Seelamantula, “An iterative algorithm for phase retrieval with sparsity constraints: application to frequency domain optical coherence tomography,” in Acoustics, Speech and Signal Processing (ICASSP), 2012 IEEE International Conference on . IEEE, 2012, pp. 553–556
2012
Later among the works it cites.
A. Beck and Y. Eldar, “Sparsity constrained nonlinear optimization: Optimality conditions and algorithms,” arXiv preprint arXiv:1203.4580 , 2012
Original
2012
Later among the works it cites.

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