Abstract

Single-frame multichannel blind deconvolution is formulated by applying a bank of Gabor filters to a blurred image. The key observation is that spatially oriented Gabor filters produce sparse images and that a multichannel version of the observed image can be represented as a product of an unknown nonnegative sparse mixing vector and an unknown nonnegative source image. Therefore a blind-deconvolution problem is formulated as a nonnegative matrix factorization problem with a sparseness constraint. No a priori knowledge about the blurring kernel or the original image is required. The good experimental results demonstrate the viability of the proposed concept.

© 2005 Optical Society of America

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References

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  1. M. R. Banham and A. K. Katsaggelos, IEEE Signal Process. Mag. 14(3), 24 (1997).
    [CrossRef]
  2. D. Kundur and D. Hatzinakos, IEEE Signal Process. Mag. 13(5), 43 (1996).
    [CrossRef]
  3. M. M. Bronstein, A. Bronstein, M. Zibulevsky, and Y. Y. Zeevi, IEEE Trans. Image Process. 14, 726 (2005).
    [CrossRef] [PubMed]
  4. A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis (Wiley, 2001).
    [CrossRef]
  5. I. Kopriva, Q. Du, H. Szu, and W. Wasylkiwskyj, Opt. Commun. 233, 7 (2004).
    [CrossRef]
  6. S. Umeyama, Electron Commun. Jpn. Part 3 84, 1 (2001).
  7. J. G. Daugman, IEEE Trans. Acoust., Speech, Signal Process. 36, 1169 (1988).
    [CrossRef]
  8. M. Numata and N. Hamada, presented at the 2004 Research Institute on Signal Processing (RISP) International Workshop on Nonlinear Circuit and Signal Processing, Honolulu, HI, March 5–7, 2004.
  9. P. O. Hoyer, J. Mach. Learn. Res. 5, 1457 (2004).

2005 (1)

M. M. Bronstein, A. Bronstein, M. Zibulevsky, and Y. Y. Zeevi, IEEE Trans. Image Process. 14, 726 (2005).
[CrossRef] [PubMed]

2004 (2)

I. Kopriva, Q. Du, H. Szu, and W. Wasylkiwskyj, Opt. Commun. 233, 7 (2004).
[CrossRef]

P. O. Hoyer, J. Mach. Learn. Res. 5, 1457 (2004).

2001 (1)

S. Umeyama, Electron Commun. Jpn. Part 3 84, 1 (2001).

1997 (1)

M. R. Banham and A. K. Katsaggelos, IEEE Signal Process. Mag. 14(3), 24 (1997).
[CrossRef]

1996 (1)

D. Kundur and D. Hatzinakos, IEEE Signal Process. Mag. 13(5), 43 (1996).
[CrossRef]

1988 (1)

J. G. Daugman, IEEE Trans. Acoust., Speech, Signal Process. 36, 1169 (1988).
[CrossRef]

Banham, M. R.

M. R. Banham and A. K. Katsaggelos, IEEE Signal Process. Mag. 14(3), 24 (1997).
[CrossRef]

Bronstein, A.

M. M. Bronstein, A. Bronstein, M. Zibulevsky, and Y. Y. Zeevi, IEEE Trans. Image Process. 14, 726 (2005).
[CrossRef] [PubMed]

Bronstein, M. M.

M. M. Bronstein, A. Bronstein, M. Zibulevsky, and Y. Y. Zeevi, IEEE Trans. Image Process. 14, 726 (2005).
[CrossRef] [PubMed]

Daugman, J. G.

J. G. Daugman, IEEE Trans. Acoust., Speech, Signal Process. 36, 1169 (1988).
[CrossRef]

Du, Q.

I. Kopriva, Q. Du, H. Szu, and W. Wasylkiwskyj, Opt. Commun. 233, 7 (2004).
[CrossRef]

Hamada, N.

M. Numata and N. Hamada, presented at the 2004 Research Institute on Signal Processing (RISP) International Workshop on Nonlinear Circuit and Signal Processing, Honolulu, HI, March 5–7, 2004.

Hatzinakos, D.

D. Kundur and D. Hatzinakos, IEEE Signal Process. Mag. 13(5), 43 (1996).
[CrossRef]

Hoyer, P. O.

P. O. Hoyer, J. Mach. Learn. Res. 5, 1457 (2004).

Hyvärinen, A.

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis (Wiley, 2001).
[CrossRef]

Karhunen, J.

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis (Wiley, 2001).
[CrossRef]

Katsaggelos, A. K.

M. R. Banham and A. K. Katsaggelos, IEEE Signal Process. Mag. 14(3), 24 (1997).
[CrossRef]

Kopriva, I.

I. Kopriva, Q. Du, H. Szu, and W. Wasylkiwskyj, Opt. Commun. 233, 7 (2004).
[CrossRef]

Kundur, D.

D. Kundur and D. Hatzinakos, IEEE Signal Process. Mag. 13(5), 43 (1996).
[CrossRef]

Numata, M.

M. Numata and N. Hamada, presented at the 2004 Research Institute on Signal Processing (RISP) International Workshop on Nonlinear Circuit and Signal Processing, Honolulu, HI, March 5–7, 2004.

Oja, E.

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis (Wiley, 2001).
[CrossRef]

Szu, H.

I. Kopriva, Q. Du, H. Szu, and W. Wasylkiwskyj, Opt. Commun. 233, 7 (2004).
[CrossRef]

Umeyama, S.

S. Umeyama, Electron Commun. Jpn. Part 3 84, 1 (2001).

Wasylkiwskyj, W.

I. Kopriva, Q. Du, H. Szu, and W. Wasylkiwskyj, Opt. Commun. 233, 7 (2004).
[CrossRef]

Zeevi, Y. Y.

M. M. Bronstein, A. Bronstein, M. Zibulevsky, and Y. Y. Zeevi, IEEE Trans. Image Process. 14, 726 (2005).
[CrossRef] [PubMed]

Zibulevsky, M.

M. M. Bronstein, A. Bronstein, M. Zibulevsky, and Y. Y. Zeevi, IEEE Trans. Image Process. 14, 726 (2005).
[CrossRef] [PubMed]

Electron Commun. Jpn. Part 3 (1)

S. Umeyama, Electron Commun. Jpn. Part 3 84, 1 (2001).

IEEE Signal Process. Mag. (2)

M. R. Banham and A. K. Katsaggelos, IEEE Signal Process. Mag. 14(3), 24 (1997).
[CrossRef]

D. Kundur and D. Hatzinakos, IEEE Signal Process. Mag. 13(5), 43 (1996).
[CrossRef]

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

J. G. Daugman, IEEE Trans. Acoust., Speech, Signal Process. 36, 1169 (1988).
[CrossRef]

IEEE Trans. Image Process. (1)

M. M. Bronstein, A. Bronstein, M. Zibulevsky, and Y. Y. Zeevi, IEEE Trans. Image Process. 14, 726 (2005).
[CrossRef] [PubMed]

J. Mach. Learn. Res. (1)

P. O. Hoyer, J. Mach. Learn. Res. 5, 1457 (2004).

Opt. Commun. (1)

I. Kopriva, Q. Du, H. Szu, and W. Wasylkiwskyj, Opt. Commun. 233, 7 (2004).
[CrossRef]

Other (2)

M. Numata and N. Hamada, presented at the 2004 Research Institute on Signal Processing (RISP) International Workshop on Nonlinear Circuit and Signal Processing, Honolulu, HI, March 5–7, 2004.

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis (Wiley, 2001).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Image restoration by nonnegative matrix factorization and 2-D Gabor filters.

Fig. 2
Fig. 2

Gabor filters for two spatial frequencies and four orientations. The top two rows show real and imaginary parts of 2-D Gabor filters for one spatial frequency; the bottom two rows, for another spatial frequency. Each column shows one of the four orientations.

Fig. 3
Fig. 3

Kurtosis of the blurred and Gabor-filtered images.

Fig. 4
Fig. 4

Defocused image.

Fig. 5
Fig. 5

Reconstructed image.

Equations (8)

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g ( x , y ) = s = M M t = M M h ( s , t ) f ( x + s , y + t ) ,
g ( x , y ) = a 1 f ( x , y ) + a 2 f x ( x , y ) + a 3 f y ( x , y ) + ,
g l ( x , y ) = a l 1 f ( x , y ) + a l 2 f x ( x , y ) + a l 3 f y ( x , y ) + ,
G = [ g T g 1 T g L T ] [ a 1 a 2 a 3 a 11 a 12 a 13 a L 1 a L 2 a L 3 ] [ f T f x T f y T ] = A F ,
f x ( x , y ) = [ s = N N t = N N h x ( s , t ) ] f ( x , y ) + [ s = N N t = N N s h x ( s , t ) ] f x ( x , y ) + [ s = N N t = N N t h x ( s , t ) ] f y ( x , y ) + ,
f y ( x , y ) = [ s = N N t = N N h y ( s , t ) ] f ( x , y ) + [ s = N N t = N N s h y ( s , t ) ] f x ( x , y ) + [ s = N N t = N N t h y ( s , t ) ] f y ( x , y ) + .
G = [ g T g 1 T g L T ] [ a ̃ 1 a ̃ 21 a ̃ L 1 ] [ f T ] = a ̃ f T ,
( a ̃ ̂ , f ̂ ) = min i , j [ G i j ( a ̃ ̂ f ̂ T ) i j ] 2

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