Abstract

An algorithm for stellar object reconstruction without a reference star is described. The algorithm is based on parallel application of the iterative blind deconvolution method to several speckle frames, and it permits reconstruction of an object that satisfies the convolution relation in all the frames used. Computer simulations with noisy speckle images are carried out to demonstrate performances of the algorithm. The algorithm is applied to observational data of binary stars, and high-resolution images are clearly reconstructed. Binary parameters extracted from the images show good consistency with those obtained both with the power spectrum analysis and with the shift-and-add method.

© 1993 Optical Society of America

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References

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  1. G. R. Ayers, J. C. Dainty, “Iterative blind deconvolution method and its application,” Opt. Lett. 13, 547–549 (1988).
    [CrossRef] [PubMed]
  2. B. L. K. Davey, R. G. Lane, R. H. T. Bates, “Blind deconvolution of noisy complex-valued image,” Opt. Commun. 69, 353–356 (1989).
    [CrossRef]
  3. J. H. Seldin, J. R. Fienup, “Iterative blind deconvolution algorithm applied to phase retrieval,” J. Opt. Soc. Am. A 7, 428–433 (1990).
    [CrossRef]
  4. P. Nisenson, “Single speckle frame imaging using Ayers–Dainty blind deconvolution,” in Proceedings of the ESO Conference on High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1993), pp. 299–308.
  5. A. M. Darling, “Blind deconvolution for referenceless speckle imaging,” in Digital Image Synthesis and Inverse Optics, A. F. Gmitro, P. S. Idell, I. J. LaHaie, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1351, 590–599 (1990).
  6. N. Miura, N. Baba, S. Isobe, M. Noguchi, Y. Norimoto, “Binary star reconstruction with use of the blind deconvolution method,” J. Mod. Opt. 39, 1137–1146 (1992).
    [CrossRef]
  7. N. Miura, N. Baba, S. Isobe, M. Noguchi, “Speckle imaging with sequential use of the iterative blind deconvolution method: application to binary star data,” in Proceedings of the ESO Conference on High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1993), pp. 345–352.
  8. A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle pattern in star images,” Astron. Astrophys. 6, 85–87 (1970).
  9. R. G. Lane, R. H. T. Bates, “Relevance for blind deconvolution of recovering Fourier magnitude,” Opt. Commun. 63, 11–14 (1987).
    [CrossRef]
  10. N. Nakajima, “Blind deconvolution of a Hermitian and a non-Hermitian function,” J. Opt. Soc. Am. A 8, 808–813 (1991).
    [CrossRef]
  11. N. Miura, N. Baba, “Extended-object reconstruction with sequential use of the iterative blind deconvolution method,” Opt. Commun. 89, 375–379 (1992).
    [CrossRef]
  12. R. H. T. Bates, F. M. Cady, “Towards true imaging by wideband speckle interferometry,” Opt. Commun. 32, 365–369(1980).
    [CrossRef]
  13. A. M. Sinton, B. L. K. Davey, R. H. T. Bates, “Augmenting shift-and-add with zero-and-add,” J. Opt. Soc. Am. A 3, 1010–1017 (1986).
    [CrossRef]
  14. N. Baba, S. Isobe, M. Noguchi, Y. Norimoto, N. Miura, “Data reduction for stellar speckle interferograms of binary stars based on the shift-and-add method,” Appl. Opt. 26, 2306–2310 (1987).
    [CrossRef] [PubMed]
  15. S. Kuwamura, N. Baba, N. Miura, N. Noguchi, Y. Norimoto, S. Isobe, “Preliminary observational results of wideband speckle spectroscopy,” in Proceedings of the ESO Conference on High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1993), pp. 461–469.
  16. B. L. McGlamery, “Computer simulation studies of compensation of turbulence degraded images,” in Image Processing, J. C. Urbach, ed., Proc. Soc. Photo-Opt. Instrum. Eng.74, 225–233 (1976).
  17. S. Isobe, Y. Norimoto, M. Noguchi, J. Ohtsubo, N. Baba, N. Miura, H. Yanaka, T. Tanaka, “Speckle observation of visual and spectroscopic binaries. I,” Publ. Natl. Astron. Obs. Jpn. 1, 217–225 (1990).
  18. N. Miura, N. Baba, M. Ni-ino, J. Ohtsubo, M. Noguchi, S. Isobe, “Speckle observation of visual and spectroscopic binaries. IV,” Publ. Natl. Astron. Obs. Jpn. 2, 561–571 (1992).

1992 (3)

N. Miura, N. Baba, S. Isobe, M. Noguchi, Y. Norimoto, “Binary star reconstruction with use of the blind deconvolution method,” J. Mod. Opt. 39, 1137–1146 (1992).
[CrossRef]

N. Miura, N. Baba, “Extended-object reconstruction with sequential use of the iterative blind deconvolution method,” Opt. Commun. 89, 375–379 (1992).
[CrossRef]

N. Miura, N. Baba, M. Ni-ino, J. Ohtsubo, M. Noguchi, S. Isobe, “Speckle observation of visual and spectroscopic binaries. IV,” Publ. Natl. Astron. Obs. Jpn. 2, 561–571 (1992).

1991 (1)

1990 (2)

S. Isobe, Y. Norimoto, M. Noguchi, J. Ohtsubo, N. Baba, N. Miura, H. Yanaka, T. Tanaka, “Speckle observation of visual and spectroscopic binaries. I,” Publ. Natl. Astron. Obs. Jpn. 1, 217–225 (1990).

J. H. Seldin, J. R. Fienup, “Iterative blind deconvolution algorithm applied to phase retrieval,” J. Opt. Soc. Am. A 7, 428–433 (1990).
[CrossRef]

1989 (1)

B. L. K. Davey, R. G. Lane, R. H. T. Bates, “Blind deconvolution of noisy complex-valued image,” Opt. Commun. 69, 353–356 (1989).
[CrossRef]

1988 (1)

1987 (2)

1986 (1)

1980 (1)

R. H. T. Bates, F. M. Cady, “Towards true imaging by wideband speckle interferometry,” Opt. Commun. 32, 365–369(1980).
[CrossRef]

1970 (1)

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle pattern in star images,” Astron. Astrophys. 6, 85–87 (1970).

Ayers, G. R.

Baba, N.

N. Miura, N. Baba, M. Ni-ino, J. Ohtsubo, M. Noguchi, S. Isobe, “Speckle observation of visual and spectroscopic binaries. IV,” Publ. Natl. Astron. Obs. Jpn. 2, 561–571 (1992).

N. Miura, N. Baba, S. Isobe, M. Noguchi, Y. Norimoto, “Binary star reconstruction with use of the blind deconvolution method,” J. Mod. Opt. 39, 1137–1146 (1992).
[CrossRef]

N. Miura, N. Baba, “Extended-object reconstruction with sequential use of the iterative blind deconvolution method,” Opt. Commun. 89, 375–379 (1992).
[CrossRef]

S. Isobe, Y. Norimoto, M. Noguchi, J. Ohtsubo, N. Baba, N. Miura, H. Yanaka, T. Tanaka, “Speckle observation of visual and spectroscopic binaries. I,” Publ. Natl. Astron. Obs. Jpn. 1, 217–225 (1990).

N. Baba, S. Isobe, M. Noguchi, Y. Norimoto, N. Miura, “Data reduction for stellar speckle interferograms of binary stars based on the shift-and-add method,” Appl. Opt. 26, 2306–2310 (1987).
[CrossRef] [PubMed]

S. Kuwamura, N. Baba, N. Miura, N. Noguchi, Y. Norimoto, S. Isobe, “Preliminary observational results of wideband speckle spectroscopy,” in Proceedings of the ESO Conference on High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1993), pp. 461–469.

N. Miura, N. Baba, S. Isobe, M. Noguchi, “Speckle imaging with sequential use of the iterative blind deconvolution method: application to binary star data,” in Proceedings of the ESO Conference on High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1993), pp. 345–352.

Bates, R. H. T.

B. L. K. Davey, R. G. Lane, R. H. T. Bates, “Blind deconvolution of noisy complex-valued image,” Opt. Commun. 69, 353–356 (1989).
[CrossRef]

R. G. Lane, R. H. T. Bates, “Relevance for blind deconvolution of recovering Fourier magnitude,” Opt. Commun. 63, 11–14 (1987).
[CrossRef]

A. M. Sinton, B. L. K. Davey, R. H. T. Bates, “Augmenting shift-and-add with zero-and-add,” J. Opt. Soc. Am. A 3, 1010–1017 (1986).
[CrossRef]

R. H. T. Bates, F. M. Cady, “Towards true imaging by wideband speckle interferometry,” Opt. Commun. 32, 365–369(1980).
[CrossRef]

Cady, F. M.

R. H. T. Bates, F. M. Cady, “Towards true imaging by wideband speckle interferometry,” Opt. Commun. 32, 365–369(1980).
[CrossRef]

Dainty, J. C.

Darling, A. M.

A. M. Darling, “Blind deconvolution for referenceless speckle imaging,” in Digital Image Synthesis and Inverse Optics, A. F. Gmitro, P. S. Idell, I. J. LaHaie, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1351, 590–599 (1990).

Davey, B. L. K.

B. L. K. Davey, R. G. Lane, R. H. T. Bates, “Blind deconvolution of noisy complex-valued image,” Opt. Commun. 69, 353–356 (1989).
[CrossRef]

A. M. Sinton, B. L. K. Davey, R. H. T. Bates, “Augmenting shift-and-add with zero-and-add,” J. Opt. Soc. Am. A 3, 1010–1017 (1986).
[CrossRef]

Fienup, J. R.

Isobe, S.

N. Miura, N. Baba, M. Ni-ino, J. Ohtsubo, M. Noguchi, S. Isobe, “Speckle observation of visual and spectroscopic binaries. IV,” Publ. Natl. Astron. Obs. Jpn. 2, 561–571 (1992).

N. Miura, N. Baba, S. Isobe, M. Noguchi, Y. Norimoto, “Binary star reconstruction with use of the blind deconvolution method,” J. Mod. Opt. 39, 1137–1146 (1992).
[CrossRef]

S. Isobe, Y. Norimoto, M. Noguchi, J. Ohtsubo, N. Baba, N. Miura, H. Yanaka, T. Tanaka, “Speckle observation of visual and spectroscopic binaries. I,” Publ. Natl. Astron. Obs. Jpn. 1, 217–225 (1990).

N. Baba, S. Isobe, M. Noguchi, Y. Norimoto, N. Miura, “Data reduction for stellar speckle interferograms of binary stars based on the shift-and-add method,” Appl. Opt. 26, 2306–2310 (1987).
[CrossRef] [PubMed]

S. Kuwamura, N. Baba, N. Miura, N. Noguchi, Y. Norimoto, S. Isobe, “Preliminary observational results of wideband speckle spectroscopy,” in Proceedings of the ESO Conference on High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1993), pp. 461–469.

N. Miura, N. Baba, S. Isobe, M. Noguchi, “Speckle imaging with sequential use of the iterative blind deconvolution method: application to binary star data,” in Proceedings of the ESO Conference on High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1993), pp. 345–352.

Kuwamura, S.

S. Kuwamura, N. Baba, N. Miura, N. Noguchi, Y. Norimoto, S. Isobe, “Preliminary observational results of wideband speckle spectroscopy,” in Proceedings of the ESO Conference on High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1993), pp. 461–469.

Labeyrie, A.

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle pattern in star images,” Astron. Astrophys. 6, 85–87 (1970).

Lane, R. G.

B. L. K. Davey, R. G. Lane, R. H. T. Bates, “Blind deconvolution of noisy complex-valued image,” Opt. Commun. 69, 353–356 (1989).
[CrossRef]

R. G. Lane, R. H. T. Bates, “Relevance for blind deconvolution of recovering Fourier magnitude,” Opt. Commun. 63, 11–14 (1987).
[CrossRef]

McGlamery, B. L.

B. L. McGlamery, “Computer simulation studies of compensation of turbulence degraded images,” in Image Processing, J. C. Urbach, ed., Proc. Soc. Photo-Opt. Instrum. Eng.74, 225–233 (1976).

Miura, N.

N. Miura, N. Baba, “Extended-object reconstruction with sequential use of the iterative blind deconvolution method,” Opt. Commun. 89, 375–379 (1992).
[CrossRef]

N. Miura, N. Baba, M. Ni-ino, J. Ohtsubo, M. Noguchi, S. Isobe, “Speckle observation of visual and spectroscopic binaries. IV,” Publ. Natl. Astron. Obs. Jpn. 2, 561–571 (1992).

N. Miura, N. Baba, S. Isobe, M. Noguchi, Y. Norimoto, “Binary star reconstruction with use of the blind deconvolution method,” J. Mod. Opt. 39, 1137–1146 (1992).
[CrossRef]

S. Isobe, Y. Norimoto, M. Noguchi, J. Ohtsubo, N. Baba, N. Miura, H. Yanaka, T. Tanaka, “Speckle observation of visual and spectroscopic binaries. I,” Publ. Natl. Astron. Obs. Jpn. 1, 217–225 (1990).

N. Baba, S. Isobe, M. Noguchi, Y. Norimoto, N. Miura, “Data reduction for stellar speckle interferograms of binary stars based on the shift-and-add method,” Appl. Opt. 26, 2306–2310 (1987).
[CrossRef] [PubMed]

S. Kuwamura, N. Baba, N. Miura, N. Noguchi, Y. Norimoto, S. Isobe, “Preliminary observational results of wideband speckle spectroscopy,” in Proceedings of the ESO Conference on High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1993), pp. 461–469.

N. Miura, N. Baba, S. Isobe, M. Noguchi, “Speckle imaging with sequential use of the iterative blind deconvolution method: application to binary star data,” in Proceedings of the ESO Conference on High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1993), pp. 345–352.

Nakajima, N.

Ni-ino, M.

N. Miura, N. Baba, M. Ni-ino, J. Ohtsubo, M. Noguchi, S. Isobe, “Speckle observation of visual and spectroscopic binaries. IV,” Publ. Natl. Astron. Obs. Jpn. 2, 561–571 (1992).

Nisenson, P.

P. Nisenson, “Single speckle frame imaging using Ayers–Dainty blind deconvolution,” in Proceedings of the ESO Conference on High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1993), pp. 299–308.

Noguchi, M.

N. Miura, N. Baba, S. Isobe, M. Noguchi, Y. Norimoto, “Binary star reconstruction with use of the blind deconvolution method,” J. Mod. Opt. 39, 1137–1146 (1992).
[CrossRef]

N. Miura, N. Baba, M. Ni-ino, J. Ohtsubo, M. Noguchi, S. Isobe, “Speckle observation of visual and spectroscopic binaries. IV,” Publ. Natl. Astron. Obs. Jpn. 2, 561–571 (1992).

S. Isobe, Y. Norimoto, M. Noguchi, J. Ohtsubo, N. Baba, N. Miura, H. Yanaka, T. Tanaka, “Speckle observation of visual and spectroscopic binaries. I,” Publ. Natl. Astron. Obs. Jpn. 1, 217–225 (1990).

N. Baba, S. Isobe, M. Noguchi, Y. Norimoto, N. Miura, “Data reduction for stellar speckle interferograms of binary stars based on the shift-and-add method,” Appl. Opt. 26, 2306–2310 (1987).
[CrossRef] [PubMed]

N. Miura, N. Baba, S. Isobe, M. Noguchi, “Speckle imaging with sequential use of the iterative blind deconvolution method: application to binary star data,” in Proceedings of the ESO Conference on High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1993), pp. 345–352.

Noguchi, N.

S. Kuwamura, N. Baba, N. Miura, N. Noguchi, Y. Norimoto, S. Isobe, “Preliminary observational results of wideband speckle spectroscopy,” in Proceedings of the ESO Conference on High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1993), pp. 461–469.

Norimoto, Y.

N. Miura, N. Baba, S. Isobe, M. Noguchi, Y. Norimoto, “Binary star reconstruction with use of the blind deconvolution method,” J. Mod. Opt. 39, 1137–1146 (1992).
[CrossRef]

S. Isobe, Y. Norimoto, M. Noguchi, J. Ohtsubo, N. Baba, N. Miura, H. Yanaka, T. Tanaka, “Speckle observation of visual and spectroscopic binaries. I,” Publ. Natl. Astron. Obs. Jpn. 1, 217–225 (1990).

N. Baba, S. Isobe, M. Noguchi, Y. Norimoto, N. Miura, “Data reduction for stellar speckle interferograms of binary stars based on the shift-and-add method,” Appl. Opt. 26, 2306–2310 (1987).
[CrossRef] [PubMed]

S. Kuwamura, N. Baba, N. Miura, N. Noguchi, Y. Norimoto, S. Isobe, “Preliminary observational results of wideband speckle spectroscopy,” in Proceedings of the ESO Conference on High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1993), pp. 461–469.

Ohtsubo, J.

N. Miura, N. Baba, M. Ni-ino, J. Ohtsubo, M. Noguchi, S. Isobe, “Speckle observation of visual and spectroscopic binaries. IV,” Publ. Natl. Astron. Obs. Jpn. 2, 561–571 (1992).

S. Isobe, Y. Norimoto, M. Noguchi, J. Ohtsubo, N. Baba, N. Miura, H. Yanaka, T. Tanaka, “Speckle observation of visual and spectroscopic binaries. I,” Publ. Natl. Astron. Obs. Jpn. 1, 217–225 (1990).

Seldin, J. H.

Sinton, A. M.

Tanaka, T.

S. Isobe, Y. Norimoto, M. Noguchi, J. Ohtsubo, N. Baba, N. Miura, H. Yanaka, T. Tanaka, “Speckle observation of visual and spectroscopic binaries. I,” Publ. Natl. Astron. Obs. Jpn. 1, 217–225 (1990).

Yanaka, H.

S. Isobe, Y. Norimoto, M. Noguchi, J. Ohtsubo, N. Baba, N. Miura, H. Yanaka, T. Tanaka, “Speckle observation of visual and spectroscopic binaries. I,” Publ. Natl. Astron. Obs. Jpn. 1, 217–225 (1990).

Appl. Opt. (1)

Astron. Astrophys. (1)

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle pattern in star images,” Astron. Astrophys. 6, 85–87 (1970).

J. Mod. Opt. (1)

N. Miura, N. Baba, S. Isobe, M. Noguchi, Y. Norimoto, “Binary star reconstruction with use of the blind deconvolution method,” J. Mod. Opt. 39, 1137–1146 (1992).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Commun. (4)

N. Miura, N. Baba, “Extended-object reconstruction with sequential use of the iterative blind deconvolution method,” Opt. Commun. 89, 375–379 (1992).
[CrossRef]

R. H. T. Bates, F. M. Cady, “Towards true imaging by wideband speckle interferometry,” Opt. Commun. 32, 365–369(1980).
[CrossRef]

B. L. K. Davey, R. G. Lane, R. H. T. Bates, “Blind deconvolution of noisy complex-valued image,” Opt. Commun. 69, 353–356 (1989).
[CrossRef]

R. G. Lane, R. H. T. Bates, “Relevance for blind deconvolution of recovering Fourier magnitude,” Opt. Commun. 63, 11–14 (1987).
[CrossRef]

Opt. Lett. (1)

Publ. Natl. Astron. Obs. Jpn. (2)

S. Isobe, Y. Norimoto, M. Noguchi, J. Ohtsubo, N. Baba, N. Miura, H. Yanaka, T. Tanaka, “Speckle observation of visual and spectroscopic binaries. I,” Publ. Natl. Astron. Obs. Jpn. 1, 217–225 (1990).

N. Miura, N. Baba, M. Ni-ino, J. Ohtsubo, M. Noguchi, S. Isobe, “Speckle observation of visual and spectroscopic binaries. IV,” Publ. Natl. Astron. Obs. Jpn. 2, 561–571 (1992).

Other (5)

S. Kuwamura, N. Baba, N. Miura, N. Noguchi, Y. Norimoto, S. Isobe, “Preliminary observational results of wideband speckle spectroscopy,” in Proceedings of the ESO Conference on High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1993), pp. 461–469.

B. L. McGlamery, “Computer simulation studies of compensation of turbulence degraded images,” in Image Processing, J. C. Urbach, ed., Proc. Soc. Photo-Opt. Instrum. Eng.74, 225–233 (1976).

P. Nisenson, “Single speckle frame imaging using Ayers–Dainty blind deconvolution,” in Proceedings of the ESO Conference on High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1993), pp. 299–308.

A. M. Darling, “Blind deconvolution for referenceless speckle imaging,” in Digital Image Synthesis and Inverse Optics, A. F. Gmitro, P. S. Idell, I. J. LaHaie, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1351, 590–599 (1990).

N. Miura, N. Baba, S. Isobe, M. Noguchi, “Speckle imaging with sequential use of the iterative blind deconvolution method: application to binary star data,” in Proceedings of the ESO Conference on High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1993), pp. 345–352.

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Figures (5)

Fig. 1
Fig. 1

Flow chart of the present algorithm: (a) parallel scheme of the BD, (b) BD process with the nth frame. F.T.’s, Fourier transforms; I.F.T.’s, inverse Fourier transforms.

Fig. 2
Fig. 2

Simulation on image reconstruction: (a) object, (b) diffraction-limited image of (a), (c) one of the speckle images. Reconstructed images: (d) N = 1, MSE = 0.119, EV = 0.994; (e) N = 2, MSE = 0.047, EV = 0.994; (f) N = 5, MSE = 0.041, EV = 0.991; (g) N = 10, MSE = 0.041, EV = 0.988; (h) N = 20, MSE = 0.023, EV = 0.980. The speckle image in (c) is displayed with 64 × 64 pixels, and other images are displayed with the central 32 × 32 pixels. The contour maps are drawn in ten levels between the maximum and the minimum values in each image.

Fig. 3
Fig. 3

Behaviors of an evaluation function (solid curves) and an MSE function (dashed curves) with J = 200 for (a) N = 1, (b) N = 5, and (c) N = 20.

Fig. 4
Fig. 4

Reconstructed images: (a) ADS15281, EV = 0.905; (b) HD185936, EV = 0.917; and (c) HD207330, EV = 0.919. All figures are with north down and east to the right. The contour maps are drawn in ten levels between the maximum and the minimum values in each image.

Fig. 5
Fig. 5

Reconstructed image of HD185936 by the SAA method. The figure is with north down and east to the right. The contour map is drawn in ten levels between the maximum and the minimum values.

Tables (2)

Tables Icon

Table 1 Results of Simulation

Tables Icon

Table 2 Resultant Binary Parameters

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

i n ( x , y ) = o ( x , y ) * p n ( x , y ) ,
Q ( j ) = MIN [ C 0 ( j ) , , C n ( j ) , , C N ( j ) ] ,
P ¯ n ( j ) ( u , v ) = [ O n ( j - 1 ) ( u , v ) ] * I n ( u , v ) O n ( j - 1 ) ( u , v ) 2 + [ σ 2 P n ( j - 1 ) ( u , v ) 2 ] ,
O ¯ n ( j ) ( u , v ) = [ P n ( j ) ( u , v ) ] * I n ( u , v ) P n ( j ) ( u , v ) 2 + [ σ 2 O n ( j - 1 ) ( u , v ) 2 ] ,
o n ( 0 ) ( x , y ) = o ( 0 ) ( x , y ) ,
p n ( 0 ) ( x , y ) = i ( x , y ) o ( 0 ) ( x , y ) d x d y ,
o n ( j ) ( x , y ) = { 1 N n = 1 N o n ( j ) ( x , y ) j N 1 j SUM ( j ) [ o 1 ( j ) ( x , y ) , , o N ( j ) ( x , y ) ] 1 j < N ,
M ( j ) = x y [ o s ( j ) ( x , y ) - o D ( x , y ) ] 2 x y [ o D ( x , y ) ] 2 ,
F s = E s S s ,
E s = x y i ( x , y ) 2 ,
S s = 2.25 π { x y [ ( x - x c ) 2 + ( y - y c ) 2 ] 1 / 2 i ( x , y ) x y i ( x , y ) } 2 ,

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