Reconstruction of an object from its Fourier modulus: Development of the combination algorithm composed of the hybrid input–output algorithm and its converging part

Applied Optics

Volumn 41, Issue 29, 2002, Pages 6143-6153

  Takajo, Hiroaki ^a   Takahashi, Tohru ^b   Itoh, Katsuhiko ^a   Fujisaki, Toshiro ^a  

^a KYUSHU INSTITUTE OF TECHNOLOGY   (Japan)

^b OITA NATIONAL COLLEGE OF TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; ELECTRON MICROSCOPY; FOURIER OPTICS; FOURIER TRANSFORMS; IMAGE RETRIEVAL;

PHASE RETRIEVAL;

IMAGE RECONSTRUCTION;

EID: 0037057776     PISSN: 1559128X     EISSN: 21553165     Source Type: Journal    
DOI: 10.1364/AO.41.006143     Document Type: Article

References (17)

1. J. R. Fienup, “Phase retrieval algorithms: A comparison,” Appl. Opt. 21, 2758-2769 (1982).
2. J. C. Dainty and J. R. Fienup, “Phase retrieval and image reconstruction for astronomy,” in Image Recovery: Theory and Application, H. Stark, ed. (Academic, San Diego, Calif., 1987), Chap. 7, pp. 231-275.
3. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237-246 (1972).
4. R. G. Lane, “Recovery of complex images from Fourier magnitude,” Opt. Commun. 63, 6-10 (1987).
5. C. R. Parker and P. J. Bones, “Convergence of iterative phase retrieval improved by utilizing zero sheets,” Opt. Commun. 92, 209 -214 (1992).
6. J. R. Fienup and C. C. Wackerman, “Phase-retrieval stagnation problems and solutions,” J. Opt. Soc. Am. A 3, 1897-1907 (1986).
7. J. H. Seldin and J. R. Fienup, “Numerical investigation of the uniqueness of phase retrieval,” J. Opt. Soc. Am. A 7, 412-427 (1990).
8. H. Takajo, T. Takahashi, H. Kawanami, and R. Ueda, “Numerical investigation of the iterative phase-retrieval stagnation problem: territories of convergence objects and holes in their boundaries,” J. Opt. Soc. Am. A 14, 3175-3187 (1997).
9. H. Takajo, T. Takahashi, R. Ueda, and M. Taninaka, “Study on the convergence property of the hybrid input-output algorithm used for phase retrieval,” J. Opt. Soc. Am. A 15, 2849-2861 (1998).
10. H. Takajo, T. Takahashi, and T. Shizuma, “Further study on the convergence property of the hybrid input-output algorithm used for phase retrieval,” J. Opt. Soc. Am. A 16, 2163-2168 (1999).
11. We use this simplification throughout this paper. That is, the term “the support” always means “the support imposed as the object-domain constraint.”
12. R. G. Lane, “Phase retrieval using conjugate gradient minimization,” J. Modern Opt. 38, 1797-1813 (1991).
13. H. Takajo, T. Shizuma, T. Takahashi, and S. Takahata, “Reconstruction of an object from its noisy Fourier modulus: Ideal estimate of the object to be reconstructed and a method that attempts to find that estimate,” Appl. Opt. 38, 5568-5576(1999).
14. 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).
15. A. Levi and H. Stark, “Restoration from phase and magnitude by generalized projections,” in Image Recovery: Theory and Application, H. Stark, ed. (Academic, San Diego, Calif., 1987), Chap. 8, pp. 277-320.
16. Y. M. Bruck and L. G. Sodin, “On the ambiguity of the image reconstruction problem,” Opt. Commun. 30, 304-308 (1979).
17. M. H. Hayes, “The reconstruction of a multidimensional sequence from the phase of its Fourier transform,” IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 140-154 (1982).