Vectorial phase retrieval of 1-d signals

IEEE Transactions on Signal Processing

Volumn 61, Issue 7, 2013, Pages 1632-1643

  Raz, Oren ^a   Dudovich, Nirit ^a   Nadler, Boaz ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

1 D phase retrieval; Convex relaxation; signal recovery from modulus Fourier measurements; statistical model selection

Indexed keywords

COMPACTLY SUPPORTED; COMPUTATIONAL CHALLENGES; COMPUTATIONALLY EFFICIENT; CONVEX RELAXATION; FOURIER; PHASE RETRIEVAL; SPECTRAL INTENSITY; SPECTRAL INTENSITY MEASUREMENTS;

ALGORITHMS; RELAXATION PROCESSES;

PHASE SHIFTERS;

EID: 84874987241     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2013.2239994     Document Type: Article

References (42)

1. D. R. Luke, J. Burke, and R. Lyon, "Optical wavefront reconstruction: Theory and numerical methods," SIAM Rev., vol. 44, pp. 169-224, 2002 (Pubitemid 34792617)
2. S. Marchesini, "A unified evaluation of iterative projection algorithms for phase retrieval," Rev. Sci. Instrum., vol. 78, pp. 011301-011301, 2007.
3. R. P. Millane, "Phase retrieval in crystallography and optics," J. Opt. Soc. Amer. A, vol. 7, pp. 394-411, 1990.
4. P. McDonald and A. Lonergana, "Two-dimensional Fourier transform NMR imaging of solids using multiple pulse line narrowing," Physica B, vol. 176, no. 3, pp. 173-179, 1992.
5. J. C. Dainty and J. R. Fienup, Image Recovery - Theory and Application. London: Academic, ch. 7, pp. 1987-1987.
6. H. N. Chapman et al., "Femtosecond diffractive imaging with a soft-X-ray free-electron laser," Nature Phys., vol. 2, no. 12, pp. 839-843, 2006. (Pubitemid 44853581)
7. H. Quiney, A. Peele, Z. Cai, D. Paterson, and K. Nugent, "Diffractive imaging of highly focused X-ray fields," Nature Phys., vol. 2, no. 2, pp. 101-104, 2006. (Pubitemid 43731379)
8. K. J. Gaffney and H. N. Chapman, "Imaging atomic structure and dynamics with ultrafast x-ray scattering," Sci., vol. 316, 2007.
9. 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, andM. Segev, "Sparsity- based single-shot subwavelength coherent diffractive imaging," Nature Mater., vol. 11, pp. 455-459, 2012.
10. H. Chapman andK. Nugent, "Coherent lensless x-ray imaging," Nature Photon., vol. 4, pp. 833-839, 2010.
11. H. Jiang, C. Song, C.-C. Chen, R. Xu, K. Raines, B. Fahimian, C.-H. Lu, T.-K. Lee, A. Nakashima, J. Urano, T. Ishikawa, F. Tamanoi, and J. Miao, "Quantitative 3d imaging of whole, unstained cells by using x-ray diffraction microscopy," Proc. Nat. Acad. Sci., vol. 107, no. 25, pp. 11 234-11 239, 2010.
12. P. Jaming, "Phase retrieval techniques for radar ambiguity problems," J. Fourier Anal. Appl., vol. 5, pp. 309-329, 1999.
13. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum., vol. 68, no. 9, pp. 3277-3295, 1997. (Pubitemid 127665658)
14. I. A. Walmsley and C. Dorrer, "Characterization of ultrashort electromagnetic pulses," Adv. Opt. Photon., vol. 1, pp. 308-437, 2009.
15. Y. Bruck and L. Sodin, "On the ambiguity of the image reconstruction problem," Opt. Commun., vol. 30, no. 3, pp. 304-308, 1979.
16. R. Gerchberg and W. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik, vol. 35, pp. 235-246, 1972.
17. J. R. Fienup, "Phase retrieval algorithms: A comparison," App. Opt., vol. 21, no. 15, pp. 2758-2769, 1982.
18. H. Bauschke, P. Combettes, and D. R. Luke, "Phase retrieval, error reduction algorithm, and Fienup variants: A view from convex optimization," J. Opt. Soc. Amer. A., vol. 19, pp. 1334-45, 2002.
19. J. N. Cederquist and C. C.Wackerman, "Phase-retrieval error: A lower bound," J. Opt. Soc. Am. A, vol. 4, pp. 1788-1792, 1987.
20. J. Sanz, "Mathematical considerations for the problem of Fourier transform phase retrieval from magnitude," SIAM J. Appl. Math., vol. 45, pp. 651-664, 1985. (Pubitemid 15529929)
21. M. Klibanov, P. E. Sacks, and A. V. Tikhonravov, "The phase retrieval problem," Inverse Problems, vol. 11, pp. 1-28, 1995.
22. O. Raz, O. Schwartz, D. Austin, A. S.Wyatt, A. Schiavi, O. Smirnova, B. Nadler, I. A.Walmsley, D. Oron, and N. Dudovich, "Vectorial phase retrieval for linear characterization of attosecond pulses," Phys. Rev. Lett., vol. 107, p. 133902, 2011.
23. D. R. Austin, T. Witting, C. A. Arrell, F. Frank, A. S. Wyatt, J. P. Marangos, J. W. Tisch, and I. A. Walmsley, "Lateral shearing interferometry of high-harmonic wavefronts," Opt. Lett., vol. 36, no. 10, pp. 1746-1748, 2011.
24. J. Walker, "The phase retrieval problem, a solution based on zero location by exponential apodization," Optica Acta, vol. 28, pp. 735-738, 1981.
25. J.W.Wood, M. A. Fiddy, and R. E. Burge, "Phase retrieval using two intensity measurements in the complex plane," Opt. Lett., vol. 6, pp. 514-516, 1981.
26. L. J. Allen and M. P. Oxley, "Phase retrieval from series of images obtained by defocus variation," Opt. Commun., vol. 199, pp. 65-75, 2001. (Pubitemid 33039449)
27. T. E. Gureyev, A. Roberts, and K. A. Nugent, "Phase retrieval with the transport-of-intensity equation:Matrix solution with use of zernike polynomials," J. Opt. Soc. Amer. A, vol. 12, pp. 1932-1941, 1995.
28. E. Osherovich, M. Zibulevsky, and I. Yavneh, Phase Retrieval Combined With Digital Holography 2012 [Online]. Available: http://arxiv. org/pdf/1203.0853v1.pdf
29. E. J. Candes, Y. Eldar, T. Strohmer, and V.Voroninski, "Phase retrieval via matrix completion," SIAM J. Imag. Sci., 2012.
30. H. Faulkner and J. M. Rodenburg, "Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm," Phys. Rev. Lett., vol. 93, no. 2, p. 023903, 2004.
31. H. Ohlsson, A. Y. Yang, R. Dong, and S. Sastry, "Compressive phase retrieval from squared output measurements via semidefinite programming," in Proc. 16th IFAC Symp. Syst. Identif., 2012.
32. E. J. Candes, T. Strohmer, and V. Voroninski, "Phaselift: Exact and stable signal recovery from magnitude measurements via convex programming," Commun. Pure Appl. Math., 2012.
33. L. Demanet and P. Hand, "Stable optimizationless recovery from phaseless linear measurements," 2012 [Online]. Available: http://arxiv.org/abs/1208.1803
34. I. Waldspurger, A. D'Aspremont, and S. Mallat, "Phase recovery, maxcut and complex semidefinite programming," 2012 [Online]. Available: http://arxiv.org/abs/1206.0102
35. R. Balan, B. Bodmann, P. Casazza, and D. Edidin, "Painless reconstruction from magnitudes of frame coefficients," J. Fourier Anal. Appl., vol. 15, pp. 488-501, 2009.
36. D. W. Kammler, A First Course in Fourier Analysis. : Cambridge University press, 2008.
37. A. Yagle, "1-d and 2-d minimum and non-minimum phase retrieval by solving linear systems of equations," in IEEE Int. Conf. Acoust., Speech, Signal Process., 1996.
38. G. Thakur, "Reconstruction of bandlimited functions from unsigned samples," J. Fourier Anal. Appl, vol. 17, pp. 720-732, 2011.
39. M. Chu and J. Watterson, "On a multivariate eigenvalue problem: I. Algebraic theory and power method," SIAM J. Sci. Comput., vol. 14, pp. 1089-1106, 1993.
40. L.-H. Zhang, "Riemannian newton method for the multivariate eigenvalue problem," SIAM J. Matrix Anal. Appl., vol. 31, no. 5, pp. 2972-2996, 2010.
41. L.-H. Zhang and L.-Z. Liao, "An alternating variable method for the maximal correlation problem," J. Glob. Optim., vol. 54, pp. 199-218, 2012.
42. A. Singer, "Angular synchronization by eigenvectors and semidefinite programming," Appl. Computat. Harmon. Anal., vol. 30, pp. 20-36, 2011.