Hybrid projection-reflection method for phase retrieval

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 20, Issue 6, 2003, Pages 1025-1034

  Bauschke, Heinz H ^a   Combettes, Patrick L ^b   Luke, D Russell ^c  

^a UNIVERSITY OF GUELPH   (Canada)

^b UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^c SIMON FRASER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; ERROR ANALYSIS; FOURIER TRANSFORMS; LIGHT REFLECTION; PROJECTION SYSTEMS;

PHASE RETRIEVAL;

OPTICAL PHASE CONJUGATION;

EID: 0041573292     PISSN: 10847529     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAA.20.001025     Document Type: Article

References (22)

1. R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Stuttgart) 35, 237-246 (1972).
2. J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758-2769 (1982).
3. A. Levi and H. Stark, "Image restoration by the method of generalized projections with application to restoration from magnitude," J. Opt. Soc. Am. A 1, 932-943 (1984).
4. A. Levi and H. Stark, "Restoration from phase and magnitude by generalized projections," in Image Recovery: Theory and Application, H. Stark, ed. (Academic, Orlando, Fla., 1987), pp. 277-320.
5. P. L. Combettes, "The foundations of set theoretic estimation, " Proc. IEEE 81, 182-208 (1993).
6. D. C. Youla and H. Webb, "Image restoration by the method of convex projections: Part I - theory," IEEE Trans. Med. Imaging MI-1, 81-94 (1982).
7. J. P. Boyle and R. L. Dykstra, "A method for finding projections onto the intersection of convex sets in Hubert spaces," Lect. Notes Stat. 37, 28-47 (1986).
8. P.-L. Lions and B. Mercier, "Splitting algorithms for the sum of two nonlinear operators," SIAM J. Numer. Anal. 16, 964-979 (1979).
9. H. H. Bauschke, P. L. Combettes, and D. R. Luke, "Phase retrieval, error reduction algorithm, and Fienup variants: a view from convex optimization," J. Opt. Soc. Am. A 19, 1334-1345 (2002).
10. R. P. Millane, "Phase retrieval in crystallography and optics, " J. Opt. Soc. Am. A 7, 394-411 (1990).
11. In general, the object-domain space need not be restricted to real-valued signals. For a review of a phase-retrieval application in which the iterates are complex valued, see Ref. 12.
12. D. R. Luke, J. V. Burke, and R. Lyon, "Optical wavefront reconstruction: theory and numerical methods," SIAM Rev. 44, 169-224 (2002).
13. H. Stark, ed., Image Recovery: Theory and Application (Academic, Orlando, Fla. 1987).
14. Topically, 0.5 ≤ β ≤ 1.
15. n) outside of D are negligible, Eq. (31) reduces to Eq. (14). In digital computing, this assumption is justified by the fact that the probability of obtaining zero numbers is virtually zero.
16. If m = 0, then x = 0 is the unique solution of the corresponding phase-retrieval problem.
17. For the BIO algorithm, this was already pointed out in Remark 5.6 of Ref. 9.
18. n) is an indicator of the quality of the stagnation point.
19. H. H. Bauschke and J. M. Borwein, "On the convergence of von Neumann's alternating projection algorithm for two sets," Set-Valued Anal. 1, 185-212 (1993).
20. J. C. Dainty and J. R. Fienup, "Phase retrieval and image reconstruction for astronomy," in Image Recovery: Theory and Application, H. Stark, ed. (Academic, Orlando, Fla., 1987), pp. 231-275.
21. T. R. Crimmins, J. R. Fienup, and B. J. Thelen, "Improved bound on object support from autocorrelation support and application to phase retrival," J. Opt. Soc. Am. A 7, 3-13 (1990).
22. J. R. Fienup and C. C. Wackerman, "Phase-retrieval stagnation problems and solutions," J. Opt. Soc. Am. A 3, 1897-1907 (1986).