Abstract

A new algorithm has been developed for performing blind deconvolution on degraded images. The algorithm naturally preserves the nonnegative constraint on the iterative solutions of blind deconvolution and can produce a restored image of high resolution. Furthermore, benefiting from the multiplicative form, the algorithm is free from the instability of numerical computation. Results of applying the algorithm to simulated and real degraded images are reported.

© 2008 Optical Society of America

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References

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  1. A. V. Oppenheim, R. W. Schafer, and T. G. Stockham, Proc. IEEE 56, 1264 (1968).
    [CrossRef]
  2. T. G. Stockham, T. M. Cannon, and R. B. Ingebretsen, Proc. IEEE 63, 678 (1975).
    [CrossRef]
  3. G. R. Ayers and J. C. Dainty, Opt. Lett. 13, 547 (1988).
    [CrossRef] [PubMed]
  4. D. G. Sheppard, B. R. Hunt, and M. W. Marcellin, J. Opt. Soc. Am. A 15, 978 (1998).
    [CrossRef]
  5. E. Y. Lam and J. W. Goodman, J. Opt. Soc. Am. A 17, 1177 (2000).
    [CrossRef]
  6. D. A. Fish, A. M. Brinicombe, and E. R. Pike, J. Opt. Soc. Am. A 12, 58 (1995).
    [CrossRef]
  7. N. F. Law and R. G. Lane, Opt. Commun. 128, 341 (1996).
    [CrossRef]
  8. R. Vio, J. Bardsley, and W. Wamsteker, Astron. Astrophys. 436, 741 (2005).
    [CrossRef]
  9. H. Lantéri, R. Soummer, and C. Aime, Astrophys. J. Suppl. Ser. 140, 235 (1999).
    [CrossRef]
  10. C. Xu, I. Assaoui, and S. Jacquery, J. Opt. Soc. Am. A 11, 2804 (1994).
    [CrossRef]
  11. E. Thiébaut and J.-M. Conan, J. Opt. Soc. Am. A 12, 485 (1995).
    [CrossRef]
  12. V. I. Isträtescu, Fixed Point Theory: An Introduction (Reidel, 1981).
  13. http://sse.jpl.nasa.gov/multimedia/display. cfm?IMlowbarID=131.
  14. M. C. Roggemann and B. Welsh, Imaging through Turbulence (CRC Press, 1996).
  15. P. Ré, "Image restoration," http://www.astrosurf.com/re/resto.html.

2005 (1)

R. Vio, J. Bardsley, and W. Wamsteker, Astron. Astrophys. 436, 741 (2005).
[CrossRef]

2000 (1)

1999 (1)

H. Lantéri, R. Soummer, and C. Aime, Astrophys. J. Suppl. Ser. 140, 235 (1999).
[CrossRef]

1998 (1)

1996 (1)

N. F. Law and R. G. Lane, Opt. Commun. 128, 341 (1996).
[CrossRef]

1995 (2)

1994 (1)

1988 (1)

1975 (1)

T. G. Stockham, T. M. Cannon, and R. B. Ingebretsen, Proc. IEEE 63, 678 (1975).
[CrossRef]

1968 (1)

A. V. Oppenheim, R. W. Schafer, and T. G. Stockham, Proc. IEEE 56, 1264 (1968).
[CrossRef]

Astron. Astrophys. (1)

R. Vio, J. Bardsley, and W. Wamsteker, Astron. Astrophys. 436, 741 (2005).
[CrossRef]

Astrophys. J. Suppl. Ser. (1)

H. Lantéri, R. Soummer, and C. Aime, Astrophys. J. Suppl. Ser. 140, 235 (1999).
[CrossRef]

J. Opt. Soc. Am. A (5)

Opt. Commun. (1)

N. F. Law and R. G. Lane, Opt. Commun. 128, 341 (1996).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (2)

A. V. Oppenheim, R. W. Schafer, and T. G. Stockham, Proc. IEEE 56, 1264 (1968).
[CrossRef]

T. G. Stockham, T. M. Cannon, and R. B. Ingebretsen, Proc. IEEE 63, 678 (1975).
[CrossRef]

Other (4)

V. I. Isträtescu, Fixed Point Theory: An Introduction (Reidel, 1981).

http://sse.jpl.nasa.gov/multimedia/display. cfm?IMlowbarID=131.

M. C. Roggemann and B. Welsh, Imaging through Turbulence (CRC Press, 1996).

P. Ré, "Image restoration," http://www.astrosurf.com/re/resto.html.

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Figures (3)

Fig. 1
Fig. 1

Restoration of a simulated degraded image. a, Original image [13]; b, simulated degraded image; c, image of b, restored by the MIA with λ = 2.2 × 10 4 after 300 iterations; d–f, central parts ( 150 × 80 ) of the spectra of images a–c.

Fig. 2
Fig. 2

NMSE versus iteration number of the three methods (MIA, RLA, and ISRA).

Fig. 3
Fig. 3

Restoration of a real degraded image. a, Real degraded image [15]; b, image restored in [15] by maximum entropy deconvolution; c, image from; b, restored by the MIA with λ = 2.5 × 10 4 after 100 iterations; d–f, central parts of a–c at 0.85 × their original scale.

Tables (1)

Tables Icon

Table 1 NMSE of Blurred Image and Images Restored by Different Algorithms

Equations (14)

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g ( x ) = h ( x ) o ( x ) + n ( x ) ,
P ( g o , h ) = x 1 2 π σ exp { [ g ( x ) h ( x ) o ( x ) ] 2 2 σ 2 } ,
J ( o , h ) σ 2 log [ P ( g o , h ) ] = x [ g ( x ) h ( x ) o ( x ) ] 2 2 + C ,
J ( o , h ) o = h c ( x ) [ g ( x ) h ( x ) o ( x ) ] ,
J ( o , h ) h = o c ( x ) [ g ( x ) h ( x ) o ( x ) ] ,
h c ( x ) [ g ( x ) h ( x ) o ( x ) ] = 0 ,
o c ( x ) [ g ( x ) h ( x ) o ( x ) ] = 0 .
exp { λ h c ( x ) [ g ( x ) h ( x ) o ( x ) ] } = 1 ,
exp { λ o c ( x ) [ g ( x ) h ( x ) o ( x ) ] } = 1 .
o k + 1 ( x ) = o k ( x ) exp [ λ J ( o k , h k ) o k ] = o k ( x ) exp { λ h k c ( x ) [ g ( x ) h k ( x ) o k ( x ) ] } ,
o k + 1 ( x ) = o k + 1 ( x ) [ x o k + 1 ( x ) ] , λ > 0 ,
h k + 1 ( x ) = h k ( x ) exp [ λ J ( o k + 1 , h k ) h k ] = h k ( x ) exp { λ o k + 1 c ( x ) [ g ( x ) h k ( x ) o k + 1 ( x ) ] } ,
h k + 1 ( x ) = h k + 1 ( x ) [ x h k + 1 ( x ) ] , λ > 0 ,
NMSE = x [ g ( x ) o ( x ) ] 2 x [ o ( x ) ] 2 .

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