Abstract

A parallel-distributed blind deconvolution method based on a self-organizing neural network is introduced. A large degraded image is segmented into smaller subpatterns. Each subpattern can be used to get a blur function. Moreover, we propose a two-step unsupervised learning method in the self-organizing neural network. The two-step learning method includes parallel learning and series learning operations. The series learning operation is similar to a typical learning operation in the self-organizing neural network. The parallel learning operation is used as a positive perturbation to let the learning operation leave a local minimum. Several improved blur functions can be estimated from the different subpatterns, and the optimized blur function is evolved by use of a genetic algorithm. As the blur function is estimated, the source image of the large degraded image can be easily restored by use of a Wiener-type filter or other deconvolution methods. Computer simulations show that the proposed parallel-distributed blind deconvolution method gives good reconstruction and that the two-step learning method in the self-organizing neural network can promote learning. Since the main computational cost is dependent on the size of the subpattern, the proposed method is effective for the restoration of the large image.

© 1999 Optical Society of America

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  1. H. Stark, Image Recovery (Academic, San Diego, Calif., 1987).
  2. P. A. Jansson, Deconvolution of Image and Spectra (Academic, San Diego, Calif., 1996).
  3. T. G. Stockham, T. M. Cannon, R. B. Ingebretson, “Blind deconvolution through digital signal processing,” Proc. IEEE 63, 678–692 (1975).
    [CrossRef]
  4. J. Biemond, F. G. V. Putten, J. W. Woods, “Identification and restoration of images with symmetric noncausal blurs,” IEEE Trans. Circuits Syst. 23, 385–394 (1988).
    [CrossRef]
  5. A. K. Katsaggelos, “Iterative image restoration algorithms,” Opt. Eng. 28, 735–748 (1989).
    [CrossRef]
  6. G. R. Ayers, J. C. Dainty, “Iterative blind deconvolution method and its applications,” Opt. Lett. 13, 547–549 (1988).
    [CrossRef]
  7. B. C. McCallum, “Blind deconvolution by simulated annealing,” Opt. Commun. 75, 547–549 (1988).
  8. Y. W. Chen, Z. Nakao, K. Arakaki, S. Tamura, “Blind deconvolution based on genetic algorithms,” IEICE Trans. Electron. E80-A, 2603–2607 (1997).
  9. Y. T. Zhou, R. Chellappa, A. Vaid, B. K. Jenkins, “Image restoration using a neural network,” IEEE Trans. Acoust. Speech Signal Process. ASSP-36, 1141–1151 (1988).
    [CrossRef]
  10. K. Sivakumar, V. B. Desai, “Image Restoration using a multilayer perception with a multilevel sigmoidal function,” IEEE Trans. Acoust. Speech Signal Process. 41, 2018–2022 (1993).
    [CrossRef]
  11. W. Tai, R. Lin, C. Liou, “Blind deconvolution by self-organizing,” in Proceedings of the International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 1568–1573.
  12. S. Haykin, Neural Networks: a Comprehensive Foundation (Prentice-Hall, Englewood Cliffs, N.J., 1999).
  13. Y.-W. Chen, Z. Nakao, K. Arakaki, X. Fang, S. Tamura, “Restoration of gray images based on a genetic algorithm with Laplacian constraint,” Fuzzy Sets Syst. 103, 285–293 (1999).
    [CrossRef]
  14. R. Klette, P. Zamperon, Handbook of Image Processing Operators (Wiley, Chichester, UK, 1996).
  15. B. Gordon, R. Bender, G. T. Herman, “Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography,” J. Theor. Biol. 29, 471–481 (1970).
    [CrossRef] [PubMed]
  16. G. T. Herman, “Two direct methods for reconstructing pictures from their projections: a comparative study,” CVGIP Graph Models Image Process. 1, 123–144 (1972).
    [CrossRef]
  17. T. Kohonen, “The self-organizing map,” Proc. IEEE 78, 1464–1480 (1990).
    [CrossRef]
  18. Z. Michalewics, Genetic Algorithms + Data Structures = Evolution Programs (Springer-Verlag, Berlin, 1992).
    [CrossRef]

1999 (1)

Y.-W. Chen, Z. Nakao, K. Arakaki, X. Fang, S. Tamura, “Restoration of gray images based on a genetic algorithm with Laplacian constraint,” Fuzzy Sets Syst. 103, 285–293 (1999).
[CrossRef]

1997 (1)

Y. W. Chen, Z. Nakao, K. Arakaki, S. Tamura, “Blind deconvolution based on genetic algorithms,” IEICE Trans. Electron. E80-A, 2603–2607 (1997).

1993 (1)

K. Sivakumar, V. B. Desai, “Image Restoration using a multilayer perception with a multilevel sigmoidal function,” IEEE Trans. Acoust. Speech Signal Process. 41, 2018–2022 (1993).
[CrossRef]

1990 (1)

T. Kohonen, “The self-organizing map,” Proc. IEEE 78, 1464–1480 (1990).
[CrossRef]

1989 (1)

A. K. Katsaggelos, “Iterative image restoration algorithms,” Opt. Eng. 28, 735–748 (1989).
[CrossRef]

1988 (4)

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

B. C. McCallum, “Blind deconvolution by simulated annealing,” Opt. Commun. 75, 547–549 (1988).

J. Biemond, F. G. V. Putten, J. W. Woods, “Identification and restoration of images with symmetric noncausal blurs,” IEEE Trans. Circuits Syst. 23, 385–394 (1988).
[CrossRef]

Y. T. Zhou, R. Chellappa, A. Vaid, B. K. Jenkins, “Image restoration using a neural network,” IEEE Trans. Acoust. Speech Signal Process. ASSP-36, 1141–1151 (1988).
[CrossRef]

1975 (1)

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

1972 (1)

G. T. Herman, “Two direct methods for reconstructing pictures from their projections: a comparative study,” CVGIP Graph Models Image Process. 1, 123–144 (1972).
[CrossRef]

1970 (1)

B. Gordon, R. Bender, G. T. Herman, “Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography,” J. Theor. Biol. 29, 471–481 (1970).
[CrossRef] [PubMed]

Arakaki, K.

Y.-W. Chen, Z. Nakao, K. Arakaki, X. Fang, S. Tamura, “Restoration of gray images based on a genetic algorithm with Laplacian constraint,” Fuzzy Sets Syst. 103, 285–293 (1999).
[CrossRef]

Y. W. Chen, Z. Nakao, K. Arakaki, S. Tamura, “Blind deconvolution based on genetic algorithms,” IEICE Trans. Electron. E80-A, 2603–2607 (1997).

Ayers, G. R.

Bender, R.

B. Gordon, R. Bender, G. T. Herman, “Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography,” J. Theor. Biol. 29, 471–481 (1970).
[CrossRef] [PubMed]

Biemond, J.

J. Biemond, F. G. V. Putten, J. W. Woods, “Identification and restoration of images with symmetric noncausal blurs,” IEEE Trans. Circuits Syst. 23, 385–394 (1988).
[CrossRef]

Cannon, T. M.

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

Chellappa, R.

Y. T. Zhou, R. Chellappa, A. Vaid, B. K. Jenkins, “Image restoration using a neural network,” IEEE Trans. Acoust. Speech Signal Process. ASSP-36, 1141–1151 (1988).
[CrossRef]

Chen, Y. W.

Y. W. Chen, Z. Nakao, K. Arakaki, S. Tamura, “Blind deconvolution based on genetic algorithms,” IEICE Trans. Electron. E80-A, 2603–2607 (1997).

Chen, Y.-W.

Y.-W. Chen, Z. Nakao, K. Arakaki, X. Fang, S. Tamura, “Restoration of gray images based on a genetic algorithm with Laplacian constraint,” Fuzzy Sets Syst. 103, 285–293 (1999).
[CrossRef]

Dainty, J. C.

Desai, V. B.

K. Sivakumar, V. B. Desai, “Image Restoration using a multilayer perception with a multilevel sigmoidal function,” IEEE Trans. Acoust. Speech Signal Process. 41, 2018–2022 (1993).
[CrossRef]

Fang, X.

Y.-W. Chen, Z. Nakao, K. Arakaki, X. Fang, S. Tamura, “Restoration of gray images based on a genetic algorithm with Laplacian constraint,” Fuzzy Sets Syst. 103, 285–293 (1999).
[CrossRef]

Gordon, B.

B. Gordon, R. Bender, G. T. Herman, “Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography,” J. Theor. Biol. 29, 471–481 (1970).
[CrossRef] [PubMed]

Haykin, S.

S. Haykin, Neural Networks: a Comprehensive Foundation (Prentice-Hall, Englewood Cliffs, N.J., 1999).

Herman, G. T.

G. T. Herman, “Two direct methods for reconstructing pictures from their projections: a comparative study,” CVGIP Graph Models Image Process. 1, 123–144 (1972).
[CrossRef]

B. Gordon, R. Bender, G. T. Herman, “Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography,” J. Theor. Biol. 29, 471–481 (1970).
[CrossRef] [PubMed]

Ingebretson, R. B.

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

Jansson, P. A.

P. A. Jansson, Deconvolution of Image and Spectra (Academic, San Diego, Calif., 1996).

Jenkins, B. K.

Y. T. Zhou, R. Chellappa, A. Vaid, B. K. Jenkins, “Image restoration using a neural network,” IEEE Trans. Acoust. Speech Signal Process. ASSP-36, 1141–1151 (1988).
[CrossRef]

Katsaggelos, A. K.

A. K. Katsaggelos, “Iterative image restoration algorithms,” Opt. Eng. 28, 735–748 (1989).
[CrossRef]

Klette, R.

R. Klette, P. Zamperon, Handbook of Image Processing Operators (Wiley, Chichester, UK, 1996).

Kohonen, T.

T. Kohonen, “The self-organizing map,” Proc. IEEE 78, 1464–1480 (1990).
[CrossRef]

Lin, R.

W. Tai, R. Lin, C. Liou, “Blind deconvolution by self-organizing,” in Proceedings of the International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 1568–1573.

Liou, C.

W. Tai, R. Lin, C. Liou, “Blind deconvolution by self-organizing,” in Proceedings of the International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 1568–1573.

McCallum, B. C.

B. C. McCallum, “Blind deconvolution by simulated annealing,” Opt. Commun. 75, 547–549 (1988).

Michalewics, Z.

Z. Michalewics, Genetic Algorithms + Data Structures = Evolution Programs (Springer-Verlag, Berlin, 1992).
[CrossRef]

Nakao, Z.

Y.-W. Chen, Z. Nakao, K. Arakaki, X. Fang, S. Tamura, “Restoration of gray images based on a genetic algorithm with Laplacian constraint,” Fuzzy Sets Syst. 103, 285–293 (1999).
[CrossRef]

Y. W. Chen, Z. Nakao, K. Arakaki, S. Tamura, “Blind deconvolution based on genetic algorithms,” IEICE Trans. Electron. E80-A, 2603–2607 (1997).

Putten, F. G. V.

J. Biemond, F. G. V. Putten, J. W. Woods, “Identification and restoration of images with symmetric noncausal blurs,” IEEE Trans. Circuits Syst. 23, 385–394 (1988).
[CrossRef]

Sivakumar, K.

K. Sivakumar, V. B. Desai, “Image Restoration using a multilayer perception with a multilevel sigmoidal function,” IEEE Trans. Acoust. Speech Signal Process. 41, 2018–2022 (1993).
[CrossRef]

Stark, H.

H. Stark, Image Recovery (Academic, San Diego, Calif., 1987).

Stockham, T. G.

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

Tai, W.

W. Tai, R. Lin, C. Liou, “Blind deconvolution by self-organizing,” in Proceedings of the International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 1568–1573.

Tamura, S.

Y.-W. Chen, Z. Nakao, K. Arakaki, X. Fang, S. Tamura, “Restoration of gray images based on a genetic algorithm with Laplacian constraint,” Fuzzy Sets Syst. 103, 285–293 (1999).
[CrossRef]

Y. W. Chen, Z. Nakao, K. Arakaki, S. Tamura, “Blind deconvolution based on genetic algorithms,” IEICE Trans. Electron. E80-A, 2603–2607 (1997).

Vaid, A.

Y. T. Zhou, R. Chellappa, A. Vaid, B. K. Jenkins, “Image restoration using a neural network,” IEEE Trans. Acoust. Speech Signal Process. ASSP-36, 1141–1151 (1988).
[CrossRef]

Woods, J. W.

J. Biemond, F. G. V. Putten, J. W. Woods, “Identification and restoration of images with symmetric noncausal blurs,” IEEE Trans. Circuits Syst. 23, 385–394 (1988).
[CrossRef]

Zamperon, P.

R. Klette, P. Zamperon, Handbook of Image Processing Operators (Wiley, Chichester, UK, 1996).

Zhou, Y. T.

Y. T. Zhou, R. Chellappa, A. Vaid, B. K. Jenkins, “Image restoration using a neural network,” IEEE Trans. Acoust. Speech Signal Process. ASSP-36, 1141–1151 (1988).
[CrossRef]

CVGIP Graph Models Image Process. (1)

G. T. Herman, “Two direct methods for reconstructing pictures from their projections: a comparative study,” CVGIP Graph Models Image Process. 1, 123–144 (1972).
[CrossRef]

Fuzzy Sets Syst. (1)

Y.-W. Chen, Z. Nakao, K. Arakaki, X. Fang, S. Tamura, “Restoration of gray images based on a genetic algorithm with Laplacian constraint,” Fuzzy Sets Syst. 103, 285–293 (1999).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process. (2)

Y. T. Zhou, R. Chellappa, A. Vaid, B. K. Jenkins, “Image restoration using a neural network,” IEEE Trans. Acoust. Speech Signal Process. ASSP-36, 1141–1151 (1988).
[CrossRef]

K. Sivakumar, V. B. Desai, “Image Restoration using a multilayer perception with a multilevel sigmoidal function,” IEEE Trans. Acoust. Speech Signal Process. 41, 2018–2022 (1993).
[CrossRef]

IEEE Trans. Circuits Syst. (1)

J. Biemond, F. G. V. Putten, J. W. Woods, “Identification and restoration of images with symmetric noncausal blurs,” IEEE Trans. Circuits Syst. 23, 385–394 (1988).
[CrossRef]

IEICE Trans. Electron. (1)

Y. W. Chen, Z. Nakao, K. Arakaki, S. Tamura, “Blind deconvolution based on genetic algorithms,” IEICE Trans. Electron. E80-A, 2603–2607 (1997).

J. Theor. Biol. (1)

B. Gordon, R. Bender, G. T. Herman, “Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography,” J. Theor. Biol. 29, 471–481 (1970).
[CrossRef] [PubMed]

Opt. Commun. (1)

B. C. McCallum, “Blind deconvolution by simulated annealing,” Opt. Commun. 75, 547–549 (1988).

Opt. Eng. (1)

A. K. Katsaggelos, “Iterative image restoration algorithms,” Opt. Eng. 28, 735–748 (1989).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (2)

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

T. Kohonen, “The self-organizing map,” Proc. IEEE 78, 1464–1480 (1990).
[CrossRef]

Other (6)

Z. Michalewics, Genetic Algorithms + Data Structures = Evolution Programs (Springer-Verlag, Berlin, 1992).
[CrossRef]

R. Klette, P. Zamperon, Handbook of Image Processing Operators (Wiley, Chichester, UK, 1996).

H. Stark, Image Recovery (Academic, San Diego, Calif., 1987).

P. A. Jansson, Deconvolution of Image and Spectra (Academic, San Diego, Calif., 1996).

W. Tai, R. Lin, C. Liou, “Blind deconvolution by self-organizing,” in Proceedings of the International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 1568–1573.

S. Haykin, Neural Networks: a Comprehensive Foundation (Prentice-Hall, Englewood Cliffs, N.J., 1999).

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Figures (5)

Fig. 1
Fig. 1

Parallel-distributed blind deconvolution algorithm.

Fig. 2
Fig. 2

(a) Source image (unknown); (b) its degraded image with random noise (noise-to-signal radio at 2%), which is used as an input image.

Fig. 3
Fig. 3

Simulation results by means of the self-organizing neural network with the proposed two-step learning method. (a) Error distribution, (b) estimated blur function, (c) reconstructed source image.

Fig. 4
Fig. 4

Simulation results by means of the self-organizing neural network with only the series learning operation, which corresponds to conventional learning operations. (a) Error distribution, (b) estimated blur function, (c) reconstructed source image.

Fig. 5
Fig. 5

Reconstructed source image by means of the genetic-algorithm-based optimized blur function.

Equations (16)

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

gi, j=p,qS hp, qfi-p, j-q+ni, j, fori, j  R,
i,jS hi, j=1.
hˆi, j=FT-1Hu, v=FT-1Gu, vF*u, v|Fu, v|2+α|Fu, v|2,
fˆi, j=FT-1Fu, v=FT-1Gu, vH*u, v|Hu, v|2+α|Hu, v|2,
errorg0, gˆs=i,jRR |g0i, j-gˆsi, j|2=i,jRR |g0i, j-hˆi, j  fˆsi, j|2,
errorg0, gˆs=i,jRR |g0i, j-hˆi, j  fˆsi, j|2+ρ i,jRR |2gˆsi, j|2,
2gˆsi, j=gˆsi+1, j+gˆsi-1, j+gˆsi, j+1+gˆsi, j-1-4gˆsi, j,
c1, c2=arg mink, lerrorg0, gˆs.
g1i, j=mini,jRg0i, j,gai, j=maxi,jRg0i, j,fˆ0i, j=g1i, j,if g0i, jgai, j+g1i, j2gai, jotherwise.
fˆc1,c2newi, j=fˆc1,c2oldi, j+δJg0i, jhˆc1,c2old  fˆpi, j fˆpi, j,i, j  R;hˆc1,c2newi, j=hˆc1,c2oldi, j+Jhˆhˆp-hˆc1,c2oldi, j,i, j  S;if hˆc1,c2newi, j<0,  then hˆc1,c2newi, j=0,
fˆc1,c2newi, j=fˆc1,c2oldi, j+βJLg0i, jhˆc1,c2  fˆqi, j fqi, j,i, j  R,
hˆc1,c2newi, j=hˆc1,c2oldi, j+γ/JLhˆq-hˆc1,c2oldi, j,i, j  S,if hˆc1,c2newi, j<0,  hˆc1,c2newi, j=0,
errorg0, hˆc1,c2new  fˆc1,c2new-error×g0, hˆc1,c2old  fˆc1,c2oldτ/J,
hˆk,lnewi, j=hˆk,loldi, j+ηΦc1,c2,k,lhˆc1,c2-hˆk,loldi, j,Φc1,c2,k,l=exp-1Ni,j|hˆc1,c2-hˆk,loldi, j|2, fork, l  Nc,  k, lc1, c2,Nc=k, l, c1, c2, if1Ni,j |hˆc1,c2-hˆk,loldi, j|2<λJ2,
El=i,jK |g-hˆc1,c2l  fˆ|2i, j,
hˆc1,c20=arg minlEl,

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