Abstract

We propose a maximum a posteriori blind deconvolution approach using a Huber–Markov random-field model. Compared with the conventional maximum-likelihood method, our algorithm not only suppresses noise effectively but also significantly alleviates the artifacts produced by the deconvolution process. The performance of this method is demonstrated by computer simulations.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. H. Seldin and J. R. Fienup, J. Opt. Soc. Am. A 7, 428 (1990).
    [CrossRef]
  2. E. Y. Lam and J. W. Goodman, J. Opt. Soc. Am. A 17, 1177 (2000).
    [CrossRef]
  3. E. Y. Lam, IEEE Trans. Circuits Syst. II 54, 52 (2007).
    [CrossRef]
  4. A. S. Carasso, SIAM J. Appl. Math. 61, 1980 (2001).
    [CrossRef]
  5. J. N. Caron, N. M. Namazi, and C. J. Rollins, Appl. Opt. 41, 6884 (2002).
    [CrossRef] [PubMed]
  6. D. Kundur and D. Hatzinakos, IEEE Signal Process. Mag. 13, 43 (1996).
    [CrossRef]
  7. W. H. Richardson, J. Opt. Soc. Am. 62, 55 (1972).
    [CrossRef]
  8. L. B. Lucy, Astron. J. 79, 745 (1974).
    [CrossRef]
  9. D. A. Fish, A. M. Brinicombe, E. R. Pike, and J. G. Walker, J. Opt. Soc. Am. A 12, 58 (1995).
    [CrossRef]
  10. T. P. O'Rourke and R. L. Stevenson, IEEE Trans. Circuits Syst. Video Technol. 5, 490 (1995).
    [CrossRef]
  11. F. Šroubek, J. Flusser, and G. Cristóbal, in Blind Image Deconvolution: Theory and Application, P.Campisi and K.Egiazarian, eds. (CRC Press, 2007), pp. 317-348.
  12. R. Pan and S. J. Reeves, IEEE Trans. Image Process. 15, 3728 (2006).
    [CrossRef]
  13. H. He and L. P. Kondi, in Proceedings of 2003 International Conference on Image Processing (2003), Vol. 2, p. 933.
  14. N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
    [CrossRef] [PubMed]

2007 (1)

E. Y. Lam, IEEE Trans. Circuits Syst. II 54, 52 (2007).
[CrossRef]

2006 (2)

R. Pan and S. J. Reeves, IEEE Trans. Image Process. 15, 3728 (2006).
[CrossRef]

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef] [PubMed]

2002 (1)

2001 (1)

A. S. Carasso, SIAM J. Appl. Math. 61, 1980 (2001).
[CrossRef]

2000 (1)

1996 (1)

D. Kundur and D. Hatzinakos, IEEE Signal Process. Mag. 13, 43 (1996).
[CrossRef]

1995 (2)

T. P. O'Rourke and R. L. Stevenson, IEEE Trans. Circuits Syst. Video Technol. 5, 490 (1995).
[CrossRef]

D. A. Fish, A. M. Brinicombe, E. R. Pike, and J. G. Walker, J. Opt. Soc. Am. A 12, 58 (1995).
[CrossRef]

1990 (1)

1974 (1)

L. B. Lucy, Astron. J. 79, 745 (1974).
[CrossRef]

1972 (1)

Blanc-Feraud, L.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef] [PubMed]

Brinicombe, A. M.

Carasso, A. S.

A. S. Carasso, SIAM J. Appl. Math. 61, 1980 (2001).
[CrossRef]

Caron, J. N.

Cristóbal, G.

F. Šroubek, J. Flusser, and G. Cristóbal, in Blind Image Deconvolution: Theory and Application, P.Campisi and K.Egiazarian, eds. (CRC Press, 2007), pp. 317-348.

Dey, N.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef] [PubMed]

Fienup, J. R.

Fish, D. A.

Flusser, J.

F. Šroubek, J. Flusser, and G. Cristóbal, in Blind Image Deconvolution: Theory and Application, P.Campisi and K.Egiazarian, eds. (CRC Press, 2007), pp. 317-348.

Goodman, J. W.

Hatzinakos, D.

D. Kundur and D. Hatzinakos, IEEE Signal Process. Mag. 13, 43 (1996).
[CrossRef]

He, H.

H. He and L. P. Kondi, in Proceedings of 2003 International Conference on Image Processing (2003), Vol. 2, p. 933.

Kam, Z.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef] [PubMed]

Kondi, L. P.

H. He and L. P. Kondi, in Proceedings of 2003 International Conference on Image Processing (2003), Vol. 2, p. 933.

Kundur, D.

D. Kundur and D. Hatzinakos, IEEE Signal Process. Mag. 13, 43 (1996).
[CrossRef]

Lam, E. Y.

Lucy, L. B.

L. B. Lucy, Astron. J. 79, 745 (1974).
[CrossRef]

Namazi, N. M.

Olivo-Marin, J.-C.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef] [PubMed]

O'Rourke, T. P.

T. P. O'Rourke and R. L. Stevenson, IEEE Trans. Circuits Syst. Video Technol. 5, 490 (1995).
[CrossRef]

Pan, R.

R. Pan and S. J. Reeves, IEEE Trans. Image Process. 15, 3728 (2006).
[CrossRef]

Pike, E. R.

Reeves, S. J.

R. Pan and S. J. Reeves, IEEE Trans. Image Process. 15, 3728 (2006).
[CrossRef]

Richardson, W. H.

Rollins, C. J.

Roux, P.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef] [PubMed]

Seldin, J. H.

Šroubek, F.

F. Šroubek, J. Flusser, and G. Cristóbal, in Blind Image Deconvolution: Theory and Application, P.Campisi and K.Egiazarian, eds. (CRC Press, 2007), pp. 317-348.

Stevenson, R. L.

T. P. O'Rourke and R. L. Stevenson, IEEE Trans. Circuits Syst. Video Technol. 5, 490 (1995).
[CrossRef]

Walker, J. G.

Zerubia, J.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef] [PubMed]

Zimmer, C.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef] [PubMed]

Appl. Opt. (1)

Astron. J. (1)

L. B. Lucy, Astron. J. 79, 745 (1974).
[CrossRef]

IEEE Signal Process. Mag. (1)

D. Kundur and D. Hatzinakos, IEEE Signal Process. Mag. 13, 43 (1996).
[CrossRef]

IEEE Trans. Circuits Syst. II (1)

E. Y. Lam, IEEE Trans. Circuits Syst. II 54, 52 (2007).
[CrossRef]

IEEE Trans. Circuits Syst. Video Technol. (1)

T. P. O'Rourke and R. L. Stevenson, IEEE Trans. Circuits Syst. Video Technol. 5, 490 (1995).
[CrossRef]

IEEE Trans. Image Process. (1)

R. Pan and S. J. Reeves, IEEE Trans. Image Process. 15, 3728 (2006).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Microsc. Res. Tech. (1)

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J.-C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef] [PubMed]

SIAM J. Appl. Math. (1)

A. S. Carasso, SIAM J. Appl. Math. 61, 1980 (2001).
[CrossRef]

Other (2)

F. Šroubek, J. Flusser, and G. Cristóbal, in Blind Image Deconvolution: Theory and Application, P.Campisi and K.Egiazarian, eds. (CRC Press, 2007), pp. 317-348.

H. He and L. P. Kondi, in Proceedings of 2003 International Conference on Image Processing (2003), Vol. 2, p. 933.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Restorations of a simulated astronomy image: (a) original image, (b) blurred and noisy image, (c) image restored with RLA, and (d) image restored with our approach.

Fig. 2
Fig. 2

NMSE of RLA and our approach.

Fig. 3
Fig. 3

Restorations of a synthetic phantom image: (a) original image, (b) blurred and noisy image, (c) image restored with RLA, and (d) image restored with our approach.

Equations (13)

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

i ( x ) = h ( x ) o ( x ) ,
θ ̂ = arg max θ [ p ( i θ ) p ( θ ) ]
= arg max θ [ log p ( i θ ) + log p ( θ ) ] , θ = { o , h } ,
p ( i o , h ) = x [ h ( x ) * o ( x ) ] i ( x ) i ( x ) ! exp { [ h ( x ) o ( x ) ] } .
p ( o ) = 1 Z exp [ λ c C ρ ( a c T o ) ] ,
ρ ( u ) = { u 2 , ξ 2 + 2 ξ ( u ξ ) , } u ξ u > ξ .
J ( θ ) = x { { [ h ( x ) o ( x ) ] i ( x ) } + i ( x ) log i ( x ) h ( x ) o ( x ) + λ c C ρ [ a c T o ( x ) ] } .
h t ( k + 1 ) ( x ) = h ̂ ( k ) ( x ) { o ̂ ( k ) ( x ) [ i ( x ) h ̂ ( k ) ( x ) o ̂ ( k ) ( x ) ] } ,
h ̂ ( k + 1 ) ( x ) = h t ( k + 1 ) ( x ) [ x h t ( k + 1 ) ( x ) ] ,
o ̂ ( k + 1 ) ( x ) = o ̂ ( k ) ( x ) { h ̂ ( k + 1 ) ( x ) [ i ( x ) h ̂ ( k + 1 ) ( x ) o ̂ ( k ) ( x ) ] } × 1 { 1 + λ c C ( a c ρ [ a c T o ̂ ( k ) ( x ) ] ) } ,
ρ ( u ) = { 2 u , u ξ 2 ξ u u , u > ξ } .
a c = [ 1 2 1 1 2 1 6 1 1 2 1 1 2 ] .
NMSE = x [ o ̂ ( x ) o ( x ) ] 2 x [ o ( x ) ] 2 .

Metrics