Phase retrieval from coded diffraction patterns

Applied and Computational Harmonic Analysis

Volumn 39, Issue 2, 2015, Pages 277-299

  Candès, Emmanuel J ^a   Li, Xiaodong ^b   Soltanolkotabi, Mahdi ^c  

^a STANFORD UNIVERSITY   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

^c Stanford University   (United States)

Author keywords

Convex optimization; Diffraction; Fourier transform; Phase retrieval; Random matrix theory

Indexed keywords

CONVEX OPTIMIZATION; DIFFRACTION; DIFFRACTION PATTERNS; FOURIER TRANSFORMS; INTERFEROMETRY; MODULATION; RANDOM VARIABLES;

NUMERICAL EXPERIMENTS; PHASE INFORMATION; PHASE RETRIEVAL; POLYLOGARITHMIC; PROGRAMMING TECHNIQUE; RANDOM MATRIX THEORY; RANDOM MODULATION; SIGNAL OF INTERESTS;

X RAY CRYSTALLOGRAPHY;

EID: 84920061457     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1016/j.acha.2014.09.004     Document Type: Article

References (55)

1. www.stanford.edu/~mahdisol/PhaseRetrieval-CDP.html
2. D.G. Mixon blog: Saving phase: Injectivity and stability for phase retrieval.
3. D.G. Mixon blog: AIM workshop: frame theory intersects geometry.
4. A. Ahmed, B. Recht, and J. Romberg Blind deconvolution using convex programming arXiv preprint arXiv:1211.5608 2012
5. B. Alexeev, A.S. Bandeira, M. Fickus, and D.G. Mixon Phase retrieval with polarization arXiv preprint arXiv:1210.7752 2012
6. A. Auslender, and M. Teboulle Interior gradient and proximal methods for convex and conic optimization SIAM J. Optim. 16 3 2006 697 725
7. R. Balan A nonlinear reconstruction algorithm from absolute value of frame coefficients for low redundancy frames International Conference on Sampling Theory and Applications SAMPTA 2009
8. R. Balan On signal reconstruction from its spectrogram 44th Annual Conference on Information Sciences and Systems CISS 2010 1 4
9. R. Balan Reconstruction of signals from magnitudes of redundant representations arXiv preprint arXiv:1207.1134 2012
10. R. Balan Stability of phase retrievable frames arXiv preprint arXiv:1308.5465 2013
11. R. Balan, B.G. Bodmann, P.G. Casazza, and D. Edidin Painless reconstruction from magnitudes of frame coefficients J. Fourier Anal. Appl. 15 4 2009 488 501
12. R. Balan, P. Casazza, and D. Edidin On signal reconstruction without phase Appl. Comput. Harmon. Anal. 20 3 2006 345 356
13. R. Balan, P. Casazza, and D. Edidin Equivalence of reconstruction from the absolute value of the frame coefficients to a sparse representation problem IEEE Signal Process. Lett. 14 5 2007 341 343
14. R. Balan, and Y. Wang Invertibility and robustness of phaseless reconstruction arXiv preprint arXiv:1308.4718 2013
15. A.S. Bandeira, J. Cahill, D.G. Mixon, and A.A. Nelson Saving phase: injectivity and stability for phase retrieval arXiv preprint arXiv:1302.4618 2013
16. A.S. Bandeira, Y. Chen, and D.G. Mixon Phase retrieval from power spectra of masked signals arXiv preprint arXiv:1303.4458 2013
17. S.R. Becker, E.J. Candes, and M.C. Grant Templates for convex cone problems with applications to sparse signal recovery Math. Program. Comput. 3 3 2011 165 218
18. O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D.K. Satapathy, and J.F. Veen Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels Acta Crystallogr. Sect. A 63 4 2007 306 314
19. J. Cahill, P. Casazza, J. Peterson, and L. Woodland Phase retrieval by projections arXiv preprint arXiv:1305.6226 2013
20. E.J. Candes, Y.C. Eldar, T. Strohmer, and V. Voroninski Phase retrieval via matrix completion SIAM J. Imaging Sci. 6 1 2013 199 225
21. E.J. Candes, and X. Li Solving quadratic equations via phaselift when there are about as many equations as unknowns Found. Comput. Math. 2012 1 10
22. E.J. Candes, X. Li, Y. Ma, and J. Wright Robust principal component analysis? J. ACM 58 3 2011 11
23. E.J. Candes, T. Strohmer, and V. Voroninski Phaselift: exact and stable signal recovery from magnitude measurements via convex programming Comm. Pure Appl. Math. 2012
24. A. Chai, M. Moscoso, and G. Papanicolaou Array imaging using intensity-only measurements Inverse Problems 27 1 2011
25. J.V. Corbett The Pauli problem, state reconstruction and quantum-real numbers Rep. Math. Phys. 57 1 2006 53 68
26. J.C. Dainty, and J.R. Fienup Phase retrieval and image reconstruction for astronomy H. Stark, Image Recovery: Theory and Application 1987 Academic Press San Diego 231 275
27. L. Demanet, and P. Hand Stable optimizationless recovery from phaseless linear measurements arXiv preprint arXiv:1208.1803 2012
28. L. Demanet, and V. Jugnon Convex recovery from interferometric measurements arXiv preprint arXiv:1307.6864 2013
29. Y.C. Eldar, and S. Mendelson Phase retrieval: stability and recovery guarantees arXiv preprint arXiv:1211.0872 2012
30. M.X. Goemans, and D.P. Williamson Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming J. ACM 42 6 1995 1115 1145
31. D. Gross Recovering low-rank matrices from few coefficients in any basis IEEE Trans. Inform. Theory 57 3 2011 1548 1566
32. D. Gross, F. Krahmer, and R. Kueng A partial derandomization of phaselift using spherical designs arXiv:1310.2267 2013
33. R.W. Harrison Phase problem in crystallography J. Opt. Soc. Amer. A 10 5 1993 1046 1055
34. T. Heinosaari, L. Mazzarella, and M.M. Wolf Quantum tomography under prior information Comm. Math. Phys. 318 2 2013 355 374
35. K. Jaganathan, S. Oymak, and B. Hassibi On robust phase retrieval for sparse signals 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton) 2012 794 799
36. X. Li, and V. Voroninski Sparse signal recovery from quadratic measurements via convex programming SIAM J. Math. Anal. 45 5 2013 3019 3033
37. E.G. Loewen, and E. Popov Diffraction Gratings and Applications 1997 CRC Press
38. J. Miao, T. Ishikawa, Q. Shen, and T. Earnest Extending x-ray crystallography to allow the imaging of noncrystalline materials, cells, and single protein complexes Annu. Rev. Phys. Chem. 59 2008 387 410
39. R.P. Millane Phase retrieval in crystallography and optics J. Opt. Soc. Amer. A 7 3 1990 394 411
40. D. Mondragon, and V. Voroninski Determination of all pure quantum states from a minimal number of observables arXiv preprint arXiv:1306.1214 2013
41. A. Nemirovski, Lectures on modern convex optimization, in: Society for Industrial and Applied Mathematics (SIAM), Citeseer, 2001.
42. P. Netrapalli, P. Jain, and S. Sanghavi Phase retrieval using alternating minimization arXiv preprint arXiv:1306.0160 2013
43. H. Ohlsson, A.Y. Yang, R. Dong, and S.S. Sastry Compressive phase retrieval from squared output measurements via semidefinite programming arXiv preprint arXiv:1111.6323 2011
44. S. Oymak, A. Jalali, M. Fazel, Y.C. Eldar, and B. Hassibi Simultaneously structured models with application to sparse and low-rank matrices arXiv preprint arXiv:1212.3753 2012
45. J. Ranieri, A. Chebira, Y.M. Lu, and M. Vetterli Phase retrieval for sparse signals: uniqueness conditions arXiv preprint arXiv:1308.3058 2013
46. O. Raz, N. Dudovich, and B. Nadler Vectorial phase retrieval of 1-d signals IEEE Trans. Signal Process. 61 7 2013 1632 1643
47. H. Reichenbach Philosophic Foundations of Quantum Mechanics 1965 University of California, Pr
48. J.M. Rodenburg Ptychography and related diffractive imaging methods Adv. Imaging Electron Phys. 150 2008 87 184
49. 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 19 16 2011 14807 14822
50. P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer Probe retrieval in ptychographic coherent diffractive imaging Ultramicroscopy 109 4 2009 338 343
51. J.A. Tropp User-friendly tail bounds for sums of random matrices Found. Comput. Math. 12 4 2012 389 434
52. Z. Uo, W. Ma, A.C. So, Y. Ye, and S. Zhang Semidefinite relaxation of quadratic optimization problems IEEE Signal Process. Mag. 27 3 2010 20 34
53. I. Waldspurger, A. d'Aspremont, and S. Mallat Phase recovery, maxcut and complex semidefinite programming arXiv preprint arXiv:1206.0102 2012
54. A. Walther The question of phase retrieval in optics J. Modern Opt. 10 1 1963 41 49
55. J.D. Watson, and F.H.C. Crick A structure for deoxyribose nucleic acid Nature 171 1953