Abstract

A technique for deconvolving an image from both a single convolution and an ensemble of differently blurred images is presented. The method is more robust than the earlier blind deconvolution algorithms proposed by Ayers and Dainty [ Opt. Lett.13, 547 ( 1988)] and Davey et al. [ Opt. Commun.69, 353 ( 1989)]. The performance of the algorithm in the presence of noise is evaluated. It is also demonstrated how the algorithm can be modified to utilize the much greater amount of information contained in an ensemble of differently blurred pictures of an image. Reconstructions using both computer simulations and infrared astronomical speckle data are presented. The speckle reconstructions are compared with those obtained by both Fourier phase retrieval and bispectral estimation.

© 1992 Optical Society of America

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  1. T. G. Stockham, T. M. Cannon, R. B. Ingebretson, “Blind deconvolution through signal processing,” Proc. IEEE 63, 678–692 (1975).
    [CrossRef]
  2. R. H. T. Bates, D. Mnyama, “The status of practical Fourier phase retrieval,” in Advances in Electronics and Electron Physics, P. W. Hawkes, ed. (Academic, London, 1986), pp. 1–64.
  3. R. G. Lane, R. H. T. Bates, “Automatic multidimensional deconvolution,” J. Opt. Soc. Am. A 4, 180–188 (1987).
    [CrossRef]
  4. G. Ayers, J. C. Dainty, “Iterative blind deconvolution method and its applications,” Opt. Lett. 13, 547–549 (1988).
    [CrossRef] [PubMed]
  5. 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]
  6. B. C. MacCallum, “Blind deconvolution by simulated annealing,” Opt. Commun. 75, 101–105 (1990).
    [CrossRef]
  7. R. G. Lane, R. H. T. Bates, “Relevance for blind deconvolution of recovering Fourier magnitude,” Opt. Commun. 63, 11–14 (1987).
    [CrossRef]
  8. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [CrossRef] [PubMed]
  9. 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, 72–81 (1990).
  10. A. Levi, H. Stark, “Image restoration by generalized projections with application to restoration from magnitude,” J. Opt. Soc. Am. A 1, 932–943 (1984).
    [CrossRef]
  11. R. Fletcher, Practical Methods of Optimization (Wiley, New York, 1987).
  12. Numerical Algorithms Group, NAG fortran Library Manual (NAG Inc., Downers Grove, Ill., 1990).
  13. R. G. Lane, “Phase retrieval using conjugate gradients,” J. Mod. Opt. 38, 1797–1813 (1991).
    [CrossRef]
  14. P. E. Gill, W. Murray, eds., Numerical Methods for Constrained Optimisation (Academic, London, 1974).
  15. J. H. Seldin, J. R. Fienup, “Numerical investigation of the uniqueness of phase retrieval,” J. Opt. Soc. Am. A 7, 412–427 (1990).
    [CrossRef]
  16. M. Nieto-Vesperinas, “A study of the performance of nonlinear least square optimization methods in the problem of phase retrieval,” Opt. Acta 33, 713–722 (1986).
    [CrossRef]
  17. A. Labeyrie, “Attainment of diffraction-limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).
  18. J. C. Christou, D. W. McCarthy, M. L. Cobb, “Image selection and binning for improved atmospheric calibration of infrared speckle data,” Astron. J. 94, 516–522 (1987).
    [CrossRef]
  19. J. C. Christou, J. D. Freeman, F. Roddier, D. W. McCarthy, M. L. Cobb, S. B. Shaklan, “Application of bispectrum analysis to infrared speckle data,” in Digital Image Recovery and Synthesis, P. S. Idell, ed., Proc. Soc. Photo-Opt. Instrum. Eng.828, 32–39 (1987).
  20. M. H. Hayes, “The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform,”IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 140–154 (1982).
    [CrossRef]
  21. C. A. Haniff, “Least-squares Fourier phase estimation from the modulus 2πbispectrum phase,” J. Opt. Soc. Am. A 8, 134–140 (1991).
    [CrossRef]
  22. C. A. Haniff, D. A. Buscher, J. C. Christou, S. T. Ridgeway, “Diffraction limited imaging at IR wavelengths using aperture masks and fully filled apertures,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1237, 259–271 (1990).

1991 (2)

1990 (2)

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 (3)

R. G. Lane, R. H. T. Bates, “Automatic multidimensional deconvolution,” J. Opt. Soc. Am. A 4, 180–188 (1987).
[CrossRef]

J. C. Christou, D. W. McCarthy, M. L. Cobb, “Image selection and binning for improved atmospheric calibration of infrared speckle data,” Astron. J. 94, 516–522 (1987).
[CrossRef]

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

1986 (1)

M. Nieto-Vesperinas, “A study of the performance of nonlinear least square optimization methods in the problem of phase retrieval,” Opt. Acta 33, 713–722 (1986).
[CrossRef]

1984 (1)

1982 (2)

M. H. Hayes, “The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform,”IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 140–154 (1982).
[CrossRef]

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[CrossRef] [PubMed]

1975 (1)

T. G. Stockham, T. M. Cannon, R. B. Ingebretson, “Blind deconvolution through signal processing,” Proc. IEEE 63, 678–692 (1975).
[CrossRef]

1970 (1)

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

Ayers, G.

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]

R. G. Lane, R. H. T. Bates, “Automatic multidimensional deconvolution,” J. Opt. Soc. Am. A 4, 180–188 (1987).
[CrossRef]

R. H. T. Bates, D. Mnyama, “The status of practical Fourier phase retrieval,” in Advances in Electronics and Electron Physics, P. W. Hawkes, ed. (Academic, London, 1986), pp. 1–64.

Buscher, D. A.

C. A. Haniff, D. A. Buscher, J. C. Christou, S. T. Ridgeway, “Diffraction limited imaging at IR wavelengths using aperture masks and fully filled apertures,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1237, 259–271 (1990).

Cannon, T. M.

T. G. Stockham, T. M. Cannon, R. B. Ingebretson, “Blind deconvolution through signal processing,” Proc. IEEE 63, 678–692 (1975).
[CrossRef]

Christou, J. C.

J. C. Christou, D. W. McCarthy, M. L. Cobb, “Image selection and binning for improved atmospheric calibration of infrared speckle data,” Astron. J. 94, 516–522 (1987).
[CrossRef]

J. C. Christou, J. D. Freeman, F. Roddier, D. W. McCarthy, M. L. Cobb, S. B. Shaklan, “Application of bispectrum analysis to infrared speckle data,” in Digital Image Recovery and Synthesis, P. S. Idell, ed., Proc. Soc. Photo-Opt. Instrum. Eng.828, 32–39 (1987).

C. A. Haniff, D. A. Buscher, J. C. Christou, S. T. Ridgeway, “Diffraction limited imaging at IR wavelengths using aperture masks and fully filled apertures,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1237, 259–271 (1990).

Cobb, M. L.

J. C. Christou, D. W. McCarthy, M. L. Cobb, “Image selection and binning for improved atmospheric calibration of infrared speckle data,” Astron. J. 94, 516–522 (1987).
[CrossRef]

J. C. Christou, J. D. Freeman, F. Roddier, D. W. McCarthy, M. L. Cobb, S. B. Shaklan, “Application of bispectrum analysis to infrared speckle data,” in Digital Image Recovery and Synthesis, P. S. Idell, ed., Proc. Soc. Photo-Opt. Instrum. Eng.828, 32–39 (1987).

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, 72–81 (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]

Fienup, J. R.

Fletcher, R.

R. Fletcher, Practical Methods of Optimization (Wiley, New York, 1987).

Freeman, J. D.

J. C. Christou, J. D. Freeman, F. Roddier, D. W. McCarthy, M. L. Cobb, S. B. Shaklan, “Application of bispectrum analysis to infrared speckle data,” in Digital Image Recovery and Synthesis, P. S. Idell, ed., Proc. Soc. Photo-Opt. Instrum. Eng.828, 32–39 (1987).

Haniff, C. A.

C. A. Haniff, “Least-squares Fourier phase estimation from the modulus 2πbispectrum phase,” J. Opt. Soc. Am. A 8, 134–140 (1991).
[CrossRef]

C. A. Haniff, D. A. Buscher, J. C. Christou, S. T. Ridgeway, “Diffraction limited imaging at IR wavelengths using aperture masks and fully filled apertures,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1237, 259–271 (1990).

Hayes, M. H.

M. H. Hayes, “The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform,”IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 140–154 (1982).
[CrossRef]

Ingebretson, R. B.

T. G. Stockham, T. M. Cannon, R. B. Ingebretson, “Blind deconvolution through signal processing,” Proc. IEEE 63, 678–692 (1975).
[CrossRef]

Labeyrie, A.

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

Lane, R. G.

R. G. Lane, “Phase retrieval using conjugate gradients,” J. Mod. Opt. 38, 1797–1813 (1991).
[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]

R. G. Lane, R. H. T. Bates, “Automatic multidimensional deconvolution,” J. Opt. Soc. Am. A 4, 180–188 (1987).
[CrossRef]

Levi, A.

MacCallum, B. C.

B. C. MacCallum, “Blind deconvolution by simulated annealing,” Opt. Commun. 75, 101–105 (1990).
[CrossRef]

McCarthy, D. W.

J. C. Christou, D. W. McCarthy, M. L. Cobb, “Image selection and binning for improved atmospheric calibration of infrared speckle data,” Astron. J. 94, 516–522 (1987).
[CrossRef]

J. C. Christou, J. D. Freeman, F. Roddier, D. W. McCarthy, M. L. Cobb, S. B. Shaklan, “Application of bispectrum analysis to infrared speckle data,” in Digital Image Recovery and Synthesis, P. S. Idell, ed., Proc. Soc. Photo-Opt. Instrum. Eng.828, 32–39 (1987).

Mnyama, D.

R. H. T. Bates, D. Mnyama, “The status of practical Fourier phase retrieval,” in Advances in Electronics and Electron Physics, P. W. Hawkes, ed. (Academic, London, 1986), pp. 1–64.

Nieto-Vesperinas, M.

M. Nieto-Vesperinas, “A study of the performance of nonlinear least square optimization methods in the problem of phase retrieval,” Opt. Acta 33, 713–722 (1986).
[CrossRef]

Ridgeway, S. T.

C. A. Haniff, D. A. Buscher, J. C. Christou, S. T. Ridgeway, “Diffraction limited imaging at IR wavelengths using aperture masks and fully filled apertures,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1237, 259–271 (1990).

Roddier, F.

J. C. Christou, J. D. Freeman, F. Roddier, D. W. McCarthy, M. L. Cobb, S. B. Shaklan, “Application of bispectrum analysis to infrared speckle data,” in Digital Image Recovery and Synthesis, P. S. Idell, ed., Proc. Soc. Photo-Opt. Instrum. Eng.828, 32–39 (1987).

Seldin, J. H.

Shaklan, S. B.

J. C. Christou, J. D. Freeman, F. Roddier, D. W. McCarthy, M. L. Cobb, S. B. Shaklan, “Application of bispectrum analysis to infrared speckle data,” in Digital Image Recovery and Synthesis, P. S. Idell, ed., Proc. Soc. Photo-Opt. Instrum. Eng.828, 32–39 (1987).

Stark, H.

Stockham, T. G.

T. G. Stockham, T. M. Cannon, R. B. Ingebretson, “Blind deconvolution through signal processing,” Proc. IEEE 63, 678–692 (1975).
[CrossRef]

Appl. Opt. (1)

Astron. Astrophys. (1)

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

Astron. J. (1)

J. C. Christou, D. W. McCarthy, M. L. Cobb, “Image selection and binning for improved atmospheric calibration of infrared speckle data,” Astron. J. 94, 516–522 (1987).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process. (1)

M. H. Hayes, “The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform,”IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 140–154 (1982).
[CrossRef]

J. Mod. Opt. (1)

R. G. Lane, “Phase retrieval using conjugate gradients,” J. Mod. Opt. 38, 1797–1813 (1991).
[CrossRef]

J. Opt. Soc. Am. A (4)

Opt. Acta (1)

M. Nieto-Vesperinas, “A study of the performance of nonlinear least square optimization methods in the problem of phase retrieval,” Opt. Acta 33, 713–722 (1986).
[CrossRef]

Opt. Commun. (3)

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]

B. C. MacCallum, “Blind deconvolution by simulated annealing,” Opt. Commun. 75, 101–105 (1990).
[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)

Proc. IEEE (1)

T. G. Stockham, T. M. Cannon, R. B. Ingebretson, “Blind deconvolution through signal processing,” Proc. IEEE 63, 678–692 (1975).
[CrossRef]

Other (7)

R. H. T. Bates, D. Mnyama, “The status of practical Fourier phase retrieval,” in Advances in Electronics and Electron Physics, P. W. Hawkes, ed. (Academic, London, 1986), pp. 1–64.

P. E. Gill, W. Murray, eds., Numerical Methods for Constrained Optimisation (Academic, London, 1974).

R. Fletcher, Practical Methods of Optimization (Wiley, New York, 1987).

Numerical Algorithms Group, NAG fortran Library Manual (NAG Inc., Downers Grove, Ill., 1990).

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, 72–81 (1990).

C. A. Haniff, D. A. Buscher, J. C. Christou, S. T. Ridgeway, “Diffraction limited imaging at IR wavelengths using aperture masks and fully filled apertures,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1237, 259–271 (1990).

J. C. Christou, J. D. Freeman, F. Roddier, D. W. McCarthy, M. L. Cobb, S. B. Shaklan, “Application of bispectrum analysis to infrared speckle data,” in Digital Image Recovery and Synthesis, P. S. Idell, ed., Proc. Soc. Photo-Opt. Instrum. Eng.828, 32–39 (1987).

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