Fetching the paper…

Reading the bibliography…

2013

Phase retrieval from power spectra of masked signals

Bandeira, Afonso S., Chen, Yutong, Mixon, Dustin G.

Original
PDF
Post on X

Understand

In diffraction imaging, one is tasked with reconstructing a signal from its power spectrum.

To resolve the ambiguity in this inverse problem, one might invoke prior knowledge about the signal, but phase retrieval algorithms in this vein have found limited success.
One alternative is to create redundancy in the measurement process by illuminating the signal multiple times, distorting the signal each time with a different mask.
Despite several recent advances in phase retrieval, the community has yet to construct an ensemble of masks which uniquely determines all signals and admits an efficient reconstruction algorithm.

Phase retrieval from power spectra of masked signals · Around

Built on

J. D. Watson, F. H. C. Crick, A structure for deoxyribose nucleic acid, Nature 171 (1953) 737–738
1953
Earlier work this paper cites.
J. Cheeger, A lower bound for the smallest eigenvalue of the Laplacian, In: Problems in analysis (Papers dedicated to Salomon Bochner, 1969), Princeton Univ. Press, Princeton, 1970, 195–199
1970
Earlier work this paper cites.
R. W. Gerchberg, W. O. Saxton, A practical algorithm for the determination of the phase from image and diffraction plane pictures, Optik 35 (1972) 237–246
1972
Earlier work this paper cites.
N. Alon, V. D. Milman, λ 1 \lambda_{1} , isoperimetric inequalities for graphs, and superconcentrators, J. Comb. Theory B 38 (1985) 73–88
1985
Earlier work this paper cites.

Similar

N. Alon, Eigenvalues and expanders, Combinatorica 6 (1986) 83–96
1986
Cited alongside, same era.
T. Hagerup, C. Rüb, A guided tour of Chernoff bounds, Inform. Process. Lett. 33 (1990) 305–308
1990
Cited alongside, same era.
M. Püschel, J. Kovačević, Real, tight frames with maximal robustness to erasures, Proc. Data Compr. Conf. (2005) 63–72
2005
Cited alongside, same era.
T. Tao, V. H. Vu, Additive combinatorics, Cambridge University Press, 2006
2006
Cited alongside, same era.
B. Alexeev, A. S. Bandeira, M. Fickus, D. G. Mixon, Phase retrieval with polarization, Available online: arXiv:1210.7752
Original
Cited in the paper.
A. S. Bandeira, J. Cahill, D. G. Mixon, A. A. Nelson. Saving phase: Injectivity and stability for phase retrieval, Available online: arXiv:1302.4618
Original
Cited in the paper.
A. S. Bandeira, A. Singer, D. A. Spielman, A Cheeger inequality for the graph connection Laplacian, Available online: arXiv:1204.3873
Original
Cited in the paper.
E. J. Candès, Y. Eldar, T. Strohmer, V. Voroninski, Phase retrieval via matrix completion, Available online: arXiv:1109.0573
Original
Cited in the paper.
E. J. Candès, X. Li, Solving quadratic equations via PhaseLift when there are about as many equations as unknowns, Available online: arXiv:1208.6247
Original
Cited in the paper.
E. J. Candès, T. Strohmer, V. Voroninski, PhaseLift: Exact and stable signal recovery from magnitude measurements via convex programming, Available online: arXiv:1109.4499
Original
Cited in the paper.
L. Demanet, P. Hand, Stable optimizationless recovery from phaseless linear measurements, Available online: arXiv:1208.1803
Original
Cited in the paper.
P. Harsha, A. Barth, Lecture 5: Derandomization (Part II), http://www.tcs.tifr.res.in/~prahladh/teaching/05spring/lectures/lec5.pdf
Cited in the paper.

Then

S. Marchesini, A unified evaluation of iterative projection algorithms for phase retrieval, Rev. Sci. Inst. 78 (2007) 011301
2007
Later among the works it cites.
A. Singer, Angular synchronization by eigenvectors and semidefinite programming, Appl. Comput. Harmon. Anal. 30 (2011) 20–36
2011
Later among the works it cites.
B. Alexeev, J. Cahill, D. G. Mixon, Full spark frames, J. Fourier Anal. Appl. 18 (2012) 1167–1194
2012
Later among the works it cites.
A. Fannjiang, Absolute uniqueness of phase retrieval with random illumination, Inverse Probl. 28 (2012) 075008
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…