Abstract

We present a maximum-likelihood approach to improve blind deconvolution of an image. Blind deconvolution is performed through the minimization of an error function by use of the conjugate gradient method, as suggested by Lane [ J. Opt. Soc. Am. A 9, 1508 ( 1992)]. We show how to implement strict constraints, such as image positivity, using a reparameterization. As an example, the point-spread function can be described by phase aberrations in the case of speckle imaging. The improvement brought by the use of strict rather than loose constraints is demonstrated on both simulated and real data. Different noise levels and object types are considered.

© 1995 Optical Society of America

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  1. L. B. Lucy, “An iterative technique for the rectification of observed distribution,” Astrophys. J. 79, 745–754 (1974).
  2. W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. 62, 55–59 (1972).
    [CrossRef]
  3. T. G. Stockham, T. M. Cannon, I. R. B. Ingebreston, “Blind deconvolution through digital signal processing,” Proc. IEEE 63, 678–692 (1975).
    [CrossRef]
  4. R. G. Lane, R. H. T. Bates, “Automatic multidimensional deconvolution,” J. Opt. Soc. Am. A 4, 180–188 (1987).
    [CrossRef]
  5. G. R. Ayers, J. C. Dainty, “Iterative blind deconvolution and its applications,” Opt. Lett. 13, 547–549 (1988).
    [CrossRef] [PubMed]
  6. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).
  7. 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]
  8. T. J. Holmes, “Blind deconvolution of speckle images quantum-limited incoherent imagery: maximum-likehood approach,” J. Opt. Soc. Am. A 9, 1052–1061 (1992).
    [CrossRef] [PubMed]
  9. T. J. Schulz, “Multiframe blind deconvolution of astronomical images,” J. Opt. Soc. Am. A 10, 1064–1073 (1993).
    [CrossRef]
  10. R. G. Lane, “Blind deconvolution of speckle images,” J. Opt. Soc. Am. A 9, 1508–1514 (1992).
    [CrossRef]
  11. A. Lannes, S. Roques, M. J. Casanove, “Resolution and robustness in image processing: a new regularization principle,” J. Opt. Soc. Am. 4, 189–199 (1987).
    [CrossRef]
  12. Y. Biraud, “A new approach for increasing the resolving power by data processing,” Astron. Astrophys. 1, 124–127 (1969).
  13. F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1981), Vol. 19, pp. 281–376.
    [CrossRef]
  14. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1990).
  15. J.-M. Conan, P.-Y. Madec, G. Rousset, “Image formation in adaptive optics partial correction,” in International Commission for Optics Conference on Active and Adaptive Optics, Garching, Germany, August 1993 (European Southern Observatory, Garching, Germany, 1993), pp. 181–186.
  16. G. Rousset, P. Y. Madec, D. Rabaud, “Adaptive optics partial correction simulation for two telescope interferometry,” in European Southern Observatory Symposium on High Resolution Imaging, Garching, Germany, October 1991, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1991), pp. 1095–1104.
  17. G. Rousset, J.-L. Beuzit, N. Hubin, E. Gendron, C. Boyer, P.-Y. Madec, P. Gigan, J.-C. Richard, M. Vittot, J.-P. Gaffard, F. Rigaut, P. Léna, “The COME-ON-PLUS adaptive optics system: results and performance,” in International Commission for Optics Conference on Active and Adaptive Optics, Garching, Germany, August 1993, F. Merkle, ed. (European Southern Observatory, Garching, Germany, 1993), pp. 64–70.
  18. R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
    [CrossRef]
  19. V. Michau, T. Marais, J. Laurent, J. Primot, J.-C. Fontanella, M. Tallon, J. Fuensalida, “High-resolution astronomical observations using deconvolution from wavefront sensing,” in Propagation Engineering IV, L. R. Bissonette, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1487, (1991), paper 24.
    [CrossRef]
  20. T. Marais, V. Michau, G. Fertin, J. Primot, J.-C. Fontanella, “Deconvolution from wave-front sensing on a 4 m telescope,” in European Southern Observatory Symposium on High Resolution Imaging, Garching, Germany, October 1991, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1991), pp. 589–597.
  21. E. Thiebaut, “Imagerie astrophysique à la limite de diffraction des grands télescopes. Application à l’observation des objets froids,” Ph.D. dissertation (Paris VII University, Paris, France, 1994).

1993 (1)

1992 (3)

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)

A. Lannes, S. Roques, M. J. Casanove, “Resolution and robustness in image processing: a new regularization principle,” J. Opt. Soc. Am. 4, 189–199 (1987).
[CrossRef]

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

1975 (1)

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

1974 (1)

L. B. Lucy, “An iterative technique for the rectification of observed distribution,” Astrophys. J. 79, 745–754 (1974).

1972 (2)

W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. 62, 55–59 (1972).
[CrossRef]

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

1969 (1)

Y. Biraud, “A new approach for increasing the resolving power by data processing,” Astron. Astrophys. 1, 124–127 (1969).

Ayers, G. R.

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, “Automatic multidimensional deconvolution,” J. Opt. Soc. Am. A 4, 180–188 (1987).
[CrossRef]

Beuzit, J.-L.

G. Rousset, J.-L. Beuzit, N. Hubin, E. Gendron, C. Boyer, P.-Y. Madec, P. Gigan, J.-C. Richard, M. Vittot, J.-P. Gaffard, F. Rigaut, P. Léna, “The COME-ON-PLUS adaptive optics system: results and performance,” in International Commission for Optics Conference on Active and Adaptive Optics, Garching, Germany, August 1993, F. Merkle, ed. (European Southern Observatory, Garching, Germany, 1993), pp. 64–70.

Biraud, Y.

Y. Biraud, “A new approach for increasing the resolving power by data processing,” Astron. Astrophys. 1, 124–127 (1969).

Boyer, C.

G. Rousset, J.-L. Beuzit, N. Hubin, E. Gendron, C. Boyer, P.-Y. Madec, P. Gigan, J.-C. Richard, M. Vittot, J.-P. Gaffard, F. Rigaut, P. Léna, “The COME-ON-PLUS adaptive optics system: results and performance,” in International Commission for Optics Conference on Active and Adaptive Optics, Garching, Germany, August 1993, F. Merkle, ed. (European Southern Observatory, Garching, Germany, 1993), pp. 64–70.

Cannon, T. M.

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

Casanove, M. J.

A. Lannes, S. Roques, M. J. Casanove, “Resolution and robustness in image processing: a new regularization principle,” J. Opt. Soc. Am. 4, 189–199 (1987).
[CrossRef]

Conan, J.-M.

J.-M. Conan, P.-Y. Madec, G. Rousset, “Image formation in adaptive optics partial correction,” in International Commission for Optics Conference on Active and Adaptive Optics, Garching, Germany, August 1993 (European Southern Observatory, Garching, Germany, 1993), pp. 181–186.

Dainty, J. C.

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

G. R. Ayers, J. C. Dainty, “Iterative blind deconvolution and its applications,” Opt. Lett. 13, 547–549 (1988).
[CrossRef] [PubMed]

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]

Fertin, G.

T. Marais, V. Michau, G. Fertin, J. Primot, J.-C. Fontanella, “Deconvolution from wave-front sensing on a 4 m telescope,” in European Southern Observatory Symposium on High Resolution Imaging, Garching, Germany, October 1991, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1991), pp. 589–597.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1990).

Fontanella, J.-C.

V. Michau, T. Marais, J. Laurent, J. Primot, J.-C. Fontanella, M. Tallon, J. Fuensalida, “High-resolution astronomical observations using deconvolution from wavefront sensing,” in Propagation Engineering IV, L. R. Bissonette, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1487, (1991), paper 24.
[CrossRef]

T. Marais, V. Michau, G. Fertin, J. Primot, J.-C. Fontanella, “Deconvolution from wave-front sensing on a 4 m telescope,” in European Southern Observatory Symposium on High Resolution Imaging, Garching, Germany, October 1991, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1991), pp. 589–597.

Fuensalida, J.

V. Michau, T. Marais, J. Laurent, J. Primot, J.-C. Fontanella, M. Tallon, J. Fuensalida, “High-resolution astronomical observations using deconvolution from wavefront sensing,” in Propagation Engineering IV, L. R. Bissonette, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1487, (1991), paper 24.
[CrossRef]

Gaffard, J.-P.

G. Rousset, J.-L. Beuzit, N. Hubin, E. Gendron, C. Boyer, P.-Y. Madec, P. Gigan, J.-C. Richard, M. Vittot, J.-P. Gaffard, F. Rigaut, P. Léna, “The COME-ON-PLUS adaptive optics system: results and performance,” in International Commission for Optics Conference on Active and Adaptive Optics, Garching, Germany, August 1993, F. Merkle, ed. (European Southern Observatory, Garching, Germany, 1993), pp. 64–70.

Gendron, E.

G. Rousset, J.-L. Beuzit, N. Hubin, E. Gendron, C. Boyer, P.-Y. Madec, P. Gigan, J.-C. Richard, M. Vittot, J.-P. Gaffard, F. Rigaut, P. Léna, “The COME-ON-PLUS adaptive optics system: results and performance,” in International Commission for Optics Conference on Active and Adaptive Optics, Garching, Germany, August 1993, F. Merkle, ed. (European Southern Observatory, Garching, Germany, 1993), pp. 64–70.

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Gigan, P.

G. Rousset, J.-L. Beuzit, N. Hubin, E. Gendron, C. Boyer, P.-Y. Madec, P. Gigan, J.-C. Richard, M. Vittot, J.-P. Gaffard, F. Rigaut, P. Léna, “The COME-ON-PLUS adaptive optics system: results and performance,” in International Commission for Optics Conference on Active and Adaptive Optics, Garching, Germany, August 1993, F. Merkle, ed. (European Southern Observatory, Garching, Germany, 1993), pp. 64–70.

Glindemann, A.

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Holmes, T. J.

Hubin, N.

G. Rousset, J.-L. Beuzit, N. Hubin, E. Gendron, C. Boyer, P.-Y. Madec, P. Gigan, J.-C. Richard, M. Vittot, J.-P. Gaffard, F. Rigaut, P. Léna, “The COME-ON-PLUS adaptive optics system: results and performance,” in International Commission for Optics Conference on Active and Adaptive Optics, Garching, Germany, August 1993, F. Merkle, ed. (European Southern Observatory, Garching, Germany, 1993), pp. 64–70.

Ingebreston, I. R. B.

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

Lane, R. G.

R. G. Lane, “Blind deconvolution of speckle images,” J. Opt. Soc. Am. A 9, 1508–1514 (1992).
[CrossRef]

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[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, “Automatic multidimensional deconvolution,” J. Opt. Soc. Am. A 4, 180–188 (1987).
[CrossRef]

Lannes, A.

A. Lannes, S. Roques, M. J. Casanove, “Resolution and robustness in image processing: a new regularization principle,” J. Opt. Soc. Am. 4, 189–199 (1987).
[CrossRef]

Laurent, J.

V. Michau, T. Marais, J. Laurent, J. Primot, J.-C. Fontanella, M. Tallon, J. Fuensalida, “High-resolution astronomical observations using deconvolution from wavefront sensing,” in Propagation Engineering IV, L. R. Bissonette, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1487, (1991), paper 24.
[CrossRef]

Léna, P.

G. Rousset, J.-L. Beuzit, N. Hubin, E. Gendron, C. Boyer, P.-Y. Madec, P. Gigan, J.-C. Richard, M. Vittot, J.-P. Gaffard, F. Rigaut, P. Léna, “The COME-ON-PLUS adaptive optics system: results and performance,” in International Commission for Optics Conference on Active and Adaptive Optics, Garching, Germany, August 1993, F. Merkle, ed. (European Southern Observatory, Garching, Germany, 1993), pp. 64–70.

Lucy, L. B.

L. B. Lucy, “An iterative technique for the rectification of observed distribution,” Astrophys. J. 79, 745–754 (1974).

Madec, P. Y.

G. Rousset, P. Y. Madec, D. Rabaud, “Adaptive optics partial correction simulation for two telescope interferometry,” in European Southern Observatory Symposium on High Resolution Imaging, Garching, Germany, October 1991, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1991), pp. 1095–1104.

Madec, P.-Y.

J.-M. Conan, P.-Y. Madec, G. Rousset, “Image formation in adaptive optics partial correction,” in International Commission for Optics Conference on Active and Adaptive Optics, Garching, Germany, August 1993 (European Southern Observatory, Garching, Germany, 1993), pp. 181–186.

G. Rousset, J.-L. Beuzit, N. Hubin, E. Gendron, C. Boyer, P.-Y. Madec, P. Gigan, J.-C. Richard, M. Vittot, J.-P. Gaffard, F. Rigaut, P. Léna, “The COME-ON-PLUS adaptive optics system: results and performance,” in International Commission for Optics Conference on Active and Adaptive Optics, Garching, Germany, August 1993, F. Merkle, ed. (European Southern Observatory, Garching, Germany, 1993), pp. 64–70.

Marais, T.

T. Marais, V. Michau, G. Fertin, J. Primot, J.-C. Fontanella, “Deconvolution from wave-front sensing on a 4 m telescope,” in European Southern Observatory Symposium on High Resolution Imaging, Garching, Germany, October 1991, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1991), pp. 589–597.

V. Michau, T. Marais, J. Laurent, J. Primot, J.-C. Fontanella, M. Tallon, J. Fuensalida, “High-resolution astronomical observations using deconvolution from wavefront sensing,” in Propagation Engineering IV, L. R. Bissonette, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1487, (1991), paper 24.
[CrossRef]

Michau, V.

T. Marais, V. Michau, G. Fertin, J. Primot, J.-C. Fontanella, “Deconvolution from wave-front sensing on a 4 m telescope,” in European Southern Observatory Symposium on High Resolution Imaging, Garching, Germany, October 1991, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1991), pp. 589–597.

V. Michau, T. Marais, J. Laurent, J. Primot, J.-C. Fontanella, M. Tallon, J. Fuensalida, “High-resolution astronomical observations using deconvolution from wavefront sensing,” in Propagation Engineering IV, L. R. Bissonette, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1487, (1991), paper 24.
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1990).

Primot, J.

V. Michau, T. Marais, J. Laurent, J. Primot, J.-C. Fontanella, M. Tallon, J. Fuensalida, “High-resolution astronomical observations using deconvolution from wavefront sensing,” in Propagation Engineering IV, L. R. Bissonette, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1487, (1991), paper 24.
[CrossRef]

T. Marais, V. Michau, G. Fertin, J. Primot, J.-C. Fontanella, “Deconvolution from wave-front sensing on a 4 m telescope,” in European Southern Observatory Symposium on High Resolution Imaging, Garching, Germany, October 1991, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1991), pp. 589–597.

Rabaud, D.

G. Rousset, P. Y. Madec, D. Rabaud, “Adaptive optics partial correction simulation for two telescope interferometry,” in European Southern Observatory Symposium on High Resolution Imaging, Garching, Germany, October 1991, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1991), pp. 1095–1104.

Richard, J.-C.

G. Rousset, J.-L. Beuzit, N. Hubin, E. Gendron, C. Boyer, P.-Y. Madec, P. Gigan, J.-C. Richard, M. Vittot, J.-P. Gaffard, F. Rigaut, P. Léna, “The COME-ON-PLUS adaptive optics system: results and performance,” in International Commission for Optics Conference on Active and Adaptive Optics, Garching, Germany, August 1993, F. Merkle, ed. (European Southern Observatory, Garching, Germany, 1993), pp. 64–70.

Richardson, W. H.

Rigaut, F.

G. Rousset, J.-L. Beuzit, N. Hubin, E. Gendron, C. Boyer, P.-Y. Madec, P. Gigan, J.-C. Richard, M. Vittot, J.-P. Gaffard, F. Rigaut, P. Léna, “The COME-ON-PLUS adaptive optics system: results and performance,” in International Commission for Optics Conference on Active and Adaptive Optics, Garching, Germany, August 1993, F. Merkle, ed. (European Southern Observatory, Garching, Germany, 1993), pp. 64–70.

Roddier, F.

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1981), Vol. 19, pp. 281–376.
[CrossRef]

Roques, S.

A. Lannes, S. Roques, M. J. Casanove, “Resolution and robustness in image processing: a new regularization principle,” J. Opt. Soc. Am. 4, 189–199 (1987).
[CrossRef]

Rousset, G.

G. Rousset, J.-L. Beuzit, N. Hubin, E. Gendron, C. Boyer, P.-Y. Madec, P. Gigan, J.-C. Richard, M. Vittot, J.-P. Gaffard, F. Rigaut, P. Léna, “The COME-ON-PLUS adaptive optics system: results and performance,” in International Commission for Optics Conference on Active and Adaptive Optics, Garching, Germany, August 1993, F. Merkle, ed. (European Southern Observatory, Garching, Germany, 1993), pp. 64–70.

J.-M. Conan, P.-Y. Madec, G. Rousset, “Image formation in adaptive optics partial correction,” in International Commission for Optics Conference on Active and Adaptive Optics, Garching, Germany, August 1993 (European Southern Observatory, Garching, Germany, 1993), pp. 181–186.

G. Rousset, P. Y. Madec, D. Rabaud, “Adaptive optics partial correction simulation for two telescope interferometry,” in European Southern Observatory Symposium on High Resolution Imaging, Garching, Germany, October 1991, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1991), pp. 1095–1104.

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Schulz, T. J.

Stockham, T. G.

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

Tallon, M.

V. Michau, T. Marais, J. Laurent, J. Primot, J.-C. Fontanella, M. Tallon, J. Fuensalida, “High-resolution astronomical observations using deconvolution from wavefront sensing,” in Propagation Engineering IV, L. R. Bissonette, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1487, (1991), paper 24.
[CrossRef]

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1990).

Thiebaut, E.

E. Thiebaut, “Imagerie astrophysique à la limite de diffraction des grands télescopes. Application à l’observation des objets froids,” Ph.D. dissertation (Paris VII University, Paris, France, 1994).

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1990).

Vittot, M.

G. Rousset, J.-L. Beuzit, N. Hubin, E. Gendron, C. Boyer, P.-Y. Madec, P. Gigan, J.-C. Richard, M. Vittot, J.-P. Gaffard, F. Rigaut, P. Léna, “The COME-ON-PLUS adaptive optics system: results and performance,” in International Commission for Optics Conference on Active and Adaptive Optics, Garching, Germany, August 1993, F. Merkle, ed. (European Southern Observatory, Garching, Germany, 1993), pp. 64–70.

Astron. Astrophys. (1)

Y. Biraud, “A new approach for increasing the resolving power by data processing,” Astron. Astrophys. 1, 124–127 (1969).

Astrophys. J. (1)

L. B. Lucy, “An iterative technique for the rectification of observed distribution,” Astrophys. J. 79, 745–754 (1974).

J. Opt. Soc. Am. (2)

A. Lannes, S. Roques, M. J. Casanove, “Resolution and robustness in image processing: a new regularization principle,” J. Opt. Soc. Am. 4, 189–199 (1987).
[CrossRef]

W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. 62, 55–59 (1972).
[CrossRef]

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

Opt. Commun. (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]

Opt. Lett. (1)

Optik (Stuttgart) (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Proc. IEEE (1)

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

Waves Random Media (1)

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Other (8)

V. Michau, T. Marais, J. Laurent, J. Primot, J.-C. Fontanella, M. Tallon, J. Fuensalida, “High-resolution astronomical observations using deconvolution from wavefront sensing,” in Propagation Engineering IV, L. R. Bissonette, W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1487, (1991), paper 24.
[CrossRef]

T. Marais, V. Michau, G. Fertin, J. Primot, J.-C. Fontanella, “Deconvolution from wave-front sensing on a 4 m telescope,” in European Southern Observatory Symposium on High Resolution Imaging, Garching, Germany, October 1991, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1991), pp. 589–597.

E. Thiebaut, “Imagerie astrophysique à la limite de diffraction des grands télescopes. Application à l’observation des objets froids,” Ph.D. dissertation (Paris VII University, Paris, France, 1994).

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1981), Vol. 19, pp. 281–376.
[CrossRef]

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1990).

J.-M. Conan, P.-Y. Madec, G. Rousset, “Image formation in adaptive optics partial correction,” in International Commission for Optics Conference on Active and Adaptive Optics, Garching, Germany, August 1993 (European Southern Observatory, Garching, Germany, 1993), pp. 181–186.

G. Rousset, P. Y. Madec, D. Rabaud, “Adaptive optics partial correction simulation for two telescope interferometry,” in European Southern Observatory Symposium on High Resolution Imaging, Garching, Germany, October 1991, J. M. Beckers, F. Merkle, eds. (European Southern Observatory, Garching, Germany, 1991), pp. 1095–1104.

G. Rousset, J.-L. Beuzit, N. Hubin, E. Gendron, C. Boyer, P.-Y. Madec, P. Gigan, J.-C. Richard, M. Vittot, J.-P. Gaffard, F. Rigaut, P. Léna, “The COME-ON-PLUS adaptive optics system: results and performance,” in International Commission for Optics Conference on Active and Adaptive Optics, Garching, Germany, August 1993, F. Merkle, ed. (European Southern Observatory, Garching, Germany, 1993), pp. 64–70.

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Figures (4)

Fig. 1
Fig. 1

Blind deconvolution of a partially corrected noise-free image: (a) original PSF (left) and object (right), (b) noise-free degraded image, (c) reconstructed PSF (left) and object (right) with strict positivity constraints, (d) reconstructed PSF (left) and object (right) with loose positivity constraints.

Fig. 2
Fig. 2

Blind deconvolution of a partially corrected image with photon noise. The original PSF and object are those shown in Fig. 1. (a) Photon-limited degraded image with 2 × 108 photons, (b) reconstructed PSF (left) and object (right) with strict positivity and loose band-limited constraints (uc was set to 1/3 of the telescope cutoff frequency), (c) photon-limited degraded image with 105 photons, (d) reconstructed PSF (left) and object (right) with the same constraints as those for (b) (with uc set to 1/6 of the telescope cutoff frequency).

Fig. 3
Fig. 3

Blind deconvolution of turbulence-degraded photon-limited data: (a) original PSF (left) and object brightness distribution (right), (b) noise-free degraded image, (c) photon-limited degraded image with 104 photons, (d) reconstructed PSF (left) and object (right) with strict positivity for the object and phase aberration description for the PSF.

Fig. 4
Fig. 4

Blind deconvolution of turbulence-degraded image of Capella: (a) observed short-exposure degraded image, (b) reconstructed turbulence-plus-telescope PSF (left) and object convolved with detector response (right) with strict positivity for the object and phase aberration description for the PSF, (c) reconstructed detector PSF (left) and Capella (right) with strict positivity for the object and for the detector PSF; a further loose band-limited constraint was used for the latter.

Equations (35)

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g ( x ) = h * f ( x ) FT G ( u ) = H ( u ) F ( u ) ,
Pr ( h * f g ) = Pr ( g h * f ) Pr ( f ) Pr ( h ) Pr ( g ) .
= - log [ Pr ( g h * f ) ] - log [ Pr ( f ) ] - log [ Pr ( h ) ] .
= g + f + h ,
g = - log Pr ( g h * f ) ] ,
f = - log Pr ( f ) ] ,
h = - log Pr ( h ) ] .
d f ( x i ) = f ( x i ) ,
D f ( u j ) = 1 N 2 { Re [ F ( u i ) ] + j Im [ F ( u i ) ] } ,
D f ( u j ) = H * ( u j ) D h * f ( u j ) ,
D h ( u j ) = F * ( u j ) D h * f ( u j ) .
g = i h * f ( x i ) - i g ( x i ) log [ h * f ( x i ) ] ,
g = 1 2 i [ h * f ( x i ) - g ( x i ) σ ( x i ) ] 2 ,
g = i [ h * f ( x i ) - g ( x i ) ] 2 .
g = N 2 j F ( u j ) H ( u j ) - G ( u j ) 2 .
D f g ( u j ) = 2 H * ( u j ) [ F ( u j ) H ( u j ) - G ( u j ) ] .
Pr ( f ) = { 0 if f violates the constraints 1 / Ω f otherwise ,
f = i ξ f ( x i ) f ( x i ) 2 ,
h = i ξ h ( x i ) h ( x i ) 2 ,
ξ f ( x i ) = { 0 if f ( x i ) violates the constraints α f otherwise ,
h = i ξ h ( x i ) h ( x i ) 2 + j ζ h ( u j ) H ( u j ) 2 ,
ζ h ( u i ) = { β h if u j > u c 0 otherwise ,
f ( x i ) = ψ f ( x i ) 2 .
d ψ f ( x i ) = 2 ψ f ( x i ) d f ( x i ) ,
h ( x i ) = ψ h ( x i ) 2 i ψ h ( x i ) 2 .
d ψ h ( x i ) = 2 ψ h ( x i ) [ 1 - h ( x i ) ] i ψ h ( x i ) 2 d h ( x i ) .
h ( x i ) = | j P ( u j ) exp { j [ 2 π u j x i N - ϕ ( u j ) ] } | 2 ,
h ( x i ) ϕ ( u j ) = 2 Im [ a * ( x i ) A ( u j ) exp ( j 2 π u j x i / N ) ] ,
d ϕ ( u j ) = - 2 Im [ A * ( u j ) i d h ( x i ) a ( x i ) × exp ( - j 2 π u j x i / N ) ] ,
f ( x ) = u = 0 N - 1 Re [ F ( u ) ] Re [ F ( u ) ] f ( x ) + Im [ F ( u ) ] Im [ F ( u ) ] f ( x ) ,
f ( x ) = u = 0 N - 1 F ( u ) exp ( j 2 π u x / N )
DFT F ( u ) = 1 N x = 0 N - 1 f ( x ) exp ( - j 2 π u x / N ) ;
f ( x ) = 1 N u = 0 N - 1 Re [ F ( u ) ] cos ( j 2 π u x N ) - Im [ F ( u ) ] sin ( j 2 π u x N ) ,
f ( x ) = Re ( u = 0 N - 1 { Re [ F ( u ) ] + j Im [ F ( u ) ] } × exp [ j 2 π ( u x / N ) N ) .
f ( x ) = 1 N u = 0 N - 1 { Re [ F ( u ) ] + j Im [ F ( u ) ] } × exp ( j 2 π u x N ) .

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