Abstract

By applying a bank of 2D Gabor filters to a blurred image, single-frame blind-image deconvolution (SF BID) is formulated as a 3D tensor factorization (TF) problem, with the key contribution that neither origin nor size of the spatially invariant blurring kernel is required to be known or estimated. Mixing matrix, the original image, and its spatial derivatives are identified from the factors in the Tucker3 model of the multi channel version of the blurred image. Previous approaches to 2D Gabor-filter-bank-based SF BID relied on 2D representation of the multichannel version of the blurred image and matrix factorization methods such as nonnegative matrix factorization (NMF) and independent component analysis (ICA). Unlike matrix factorization-based methods 3D TF preserves local structure in the image. Moreover, 3D TF based on the PARAFAC model is unique up to permutation and scales under very mild conditions. To achieve this, NMF and ICA respectively require enforcement of sparseness and statistical independence constraints on the original image and its spatial derivatives. These constraints are generally not satisfied. The 3D TF-based SF BID method is demonstrated on an experimental defocused red–green–blue image.

© 2009 Optical Society of America

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  1. M. R. Banham and A. K. Katsaggelos, IEEE Signal Process. Mag. 14, 24 (1997).
    [CrossRef]
  2. D. Kundur and D. Hatzinakos, IEEE Signal Process. Mag. 13, 43 (1996).
    [CrossRef]
  3. P.Campisi and K.Egiazarian, eds., Blind Image Deconvolution (CRC Press, 2007).
    [CrossRef]
  4. I. Kopriva, Opt. Lett. 30, 3135 (2005).
    [CrossRef] [PubMed]
  5. A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis (Wiley Interscience, 2001).
    [CrossRef]
  6. I. Kopriva, J. Opt. Soc. Am. A 24, 973 (2007).
    [CrossRef]
  7. C. Yi-nan, J. Wei-qi, W. Ling-Xue, Z. Lei, and Y. Hong-sheng, Opt. Commun. 282, 786 (2009).
    [CrossRef]
  8. S. Umeyama, Scripta Technica, Electron. Comm. Jpn. Part 3 84, 1 (2001).
    [CrossRef]
  9. H. A. L. Kiers, J. Chemom. 14, 105 (2000).
    [CrossRef]
  10. L. R. Tucker, Psychometrika 31, 279 (1966).
    [CrossRef] [PubMed]
  11. J. D. Carrol and J. J. Chang, Psychometrika 35, 283 (1970).
    [CrossRef]
  12. R. A. Harshman, in UCLA Working Papers in Phonetics (UCLA, 1970), Vol. 16, p. 1.
  13. E. Acar and B. Yener, IEEE Trans. Knowl. Data Eng. 21, 6 (2009).
    [CrossRef]
  14. J. B. Kruskal, Linear Algebr. Appl. 18, 95 (1977).
    [CrossRef]
  15. N. D. Sidiropoulos and R. Bro, J. Chemom. 14, 229 (2000).
    [CrossRef]
  16. N. Renard, S. Bourennane, and J. Blanc-Talon, IEEE Trans. Geosci. Remote Sens. Lett. 5, 138 (2008).
    [CrossRef]
  17. N. Renard and S. Bourennane, IEEE Tras. Geosci. Remote Sens. 46, 2407 (2008).
    [CrossRef]
  18. B. W. Bader and T. G. Kolda, MATLAB Tensor Toolbox Version 2.2, http://csmr.ca.sandia.gov/~tkolda/TensorToolbox.
  19. L. De Lathauwer, B. De Moor, and J. Vandewalle, SIAM J. Matrix Anal. Appl. 21, 1253 (2000).
    [CrossRef]

2009 (2)

C. Yi-nan, J. Wei-qi, W. Ling-Xue, Z. Lei, and Y. Hong-sheng, Opt. Commun. 282, 786 (2009).
[CrossRef]

E. Acar and B. Yener, IEEE Trans. Knowl. Data Eng. 21, 6 (2009).
[CrossRef]

2008 (2)

N. Renard, S. Bourennane, and J. Blanc-Talon, IEEE Trans. Geosci. Remote Sens. Lett. 5, 138 (2008).
[CrossRef]

N. Renard and S. Bourennane, IEEE Tras. Geosci. Remote Sens. 46, 2407 (2008).
[CrossRef]

2007 (2)

I. Kopriva, J. Opt. Soc. Am. A 24, 973 (2007).
[CrossRef]

P.Campisi and K.Egiazarian, eds., Blind Image Deconvolution (CRC Press, 2007).
[CrossRef]

2005 (1)

2001 (2)

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

S. Umeyama, Scripta Technica, Electron. Comm. Jpn. Part 3 84, 1 (2001).
[CrossRef]

2000 (3)

H. A. L. Kiers, J. Chemom. 14, 105 (2000).
[CrossRef]

N. D. Sidiropoulos and R. Bro, J. Chemom. 14, 229 (2000).
[CrossRef]

L. De Lathauwer, B. De Moor, and J. Vandewalle, SIAM J. Matrix Anal. Appl. 21, 1253 (2000).
[CrossRef]

1997 (1)

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

1996 (1)

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

1977 (1)

J. B. Kruskal, Linear Algebr. Appl. 18, 95 (1977).
[CrossRef]

1970 (2)

J. D. Carrol and J. J. Chang, Psychometrika 35, 283 (1970).
[CrossRef]

R. A. Harshman, in UCLA Working Papers in Phonetics (UCLA, 1970), Vol. 16, p. 1.

1966 (1)

L. R. Tucker, Psychometrika 31, 279 (1966).
[CrossRef] [PubMed]

Acar, E.

E. Acar and B. Yener, IEEE Trans. Knowl. Data Eng. 21, 6 (2009).
[CrossRef]

Bader, B. W.

B. W. Bader and T. G. Kolda, MATLAB Tensor Toolbox Version 2.2, http://csmr.ca.sandia.gov/~tkolda/TensorToolbox.

Banham, M. R.

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

Blanc-Talon, J.

N. Renard, S. Bourennane, and J. Blanc-Talon, IEEE Trans. Geosci. Remote Sens. Lett. 5, 138 (2008).
[CrossRef]

Bourennane, S.

N. Renard and S. Bourennane, IEEE Tras. Geosci. Remote Sens. 46, 2407 (2008).
[CrossRef]

N. Renard, S. Bourennane, and J. Blanc-Talon, IEEE Trans. Geosci. Remote Sens. Lett. 5, 138 (2008).
[CrossRef]

Bro, R.

N. D. Sidiropoulos and R. Bro, J. Chemom. 14, 229 (2000).
[CrossRef]

Carrol, J. D.

J. D. Carrol and J. J. Chang, Psychometrika 35, 283 (1970).
[CrossRef]

Chang, J. J.

J. D. Carrol and J. J. Chang, Psychometrika 35, 283 (1970).
[CrossRef]

De Lathauwer, L.

L. De Lathauwer, B. De Moor, and J. Vandewalle, SIAM J. Matrix Anal. Appl. 21, 1253 (2000).
[CrossRef]

De Moor, B.

L. De Lathauwer, B. De Moor, and J. Vandewalle, SIAM J. Matrix Anal. Appl. 21, 1253 (2000).
[CrossRef]

Harshman, R. A.

R. A. Harshman, in UCLA Working Papers in Phonetics (UCLA, 1970), Vol. 16, p. 1.

Hatzinakos, D.

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

Hong-sheng, Y.

C. Yi-nan, J. Wei-qi, W. Ling-Xue, Z. Lei, and Y. Hong-sheng, Opt. Commun. 282, 786 (2009).
[CrossRef]

Hyvärinen, A.

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

Karhunen, J.

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

Katsaggelos, A. K.

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

Kiers, H. A. L.

H. A. L. Kiers, J. Chemom. 14, 105 (2000).
[CrossRef]

Kolda, T. G.

B. W. Bader and T. G. Kolda, MATLAB Tensor Toolbox Version 2.2, http://csmr.ca.sandia.gov/~tkolda/TensorToolbox.

Kopriva, I.

Kruskal, J. B.

J. B. Kruskal, Linear Algebr. Appl. 18, 95 (1977).
[CrossRef]

Kundur, D.

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

Lei, Z.

C. Yi-nan, J. Wei-qi, W. Ling-Xue, Z. Lei, and Y. Hong-sheng, Opt. Commun. 282, 786 (2009).
[CrossRef]

Ling-Xue, W.

C. Yi-nan, J. Wei-qi, W. Ling-Xue, Z. Lei, and Y. Hong-sheng, Opt. Commun. 282, 786 (2009).
[CrossRef]

Oja, E.

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

Renard, N.

N. Renard, S. Bourennane, and J. Blanc-Talon, IEEE Trans. Geosci. Remote Sens. Lett. 5, 138 (2008).
[CrossRef]

N. Renard and S. Bourennane, IEEE Tras. Geosci. Remote Sens. 46, 2407 (2008).
[CrossRef]

Sidiropoulos, N. D.

N. D. Sidiropoulos and R. Bro, J. Chemom. 14, 229 (2000).
[CrossRef]

Tucker, L. R.

L. R. Tucker, Psychometrika 31, 279 (1966).
[CrossRef] [PubMed]

Umeyama, S.

S. Umeyama, Scripta Technica, Electron. Comm. Jpn. Part 3 84, 1 (2001).
[CrossRef]

Vandewalle, J.

L. De Lathauwer, B. De Moor, and J. Vandewalle, SIAM J. Matrix Anal. Appl. 21, 1253 (2000).
[CrossRef]

Wei-qi, J.

C. Yi-nan, J. Wei-qi, W. Ling-Xue, Z. Lei, and Y. Hong-sheng, Opt. Commun. 282, 786 (2009).
[CrossRef]

Yener, B.

E. Acar and B. Yener, IEEE Trans. Knowl. Data Eng. 21, 6 (2009).
[CrossRef]

Yi-nan, C.

C. Yi-nan, J. Wei-qi, W. Ling-Xue, Z. Lei, and Y. Hong-sheng, Opt. Commun. 282, 786 (2009).
[CrossRef]

Electron. Comm. Jpn. Part 3 (1)

S. Umeyama, Scripta Technica, Electron. Comm. Jpn. Part 3 84, 1 (2001).
[CrossRef]

IEEE Signal Process. Mag. (2)

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

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

IEEE Trans. Geosci. Remote Sens. Lett. (1)

N. Renard, S. Bourennane, and J. Blanc-Talon, IEEE Trans. Geosci. Remote Sens. Lett. 5, 138 (2008).
[CrossRef]

IEEE Trans. Knowl. Data Eng. (1)

E. Acar and B. Yener, IEEE Trans. Knowl. Data Eng. 21, 6 (2009).
[CrossRef]

IEEE Tras. Geosci. Remote Sens. (1)

N. Renard and S. Bourennane, IEEE Tras. Geosci. Remote Sens. 46, 2407 (2008).
[CrossRef]

J. Chemom. (2)

N. D. Sidiropoulos and R. Bro, J. Chemom. 14, 229 (2000).
[CrossRef]

H. A. L. Kiers, J. Chemom. 14, 105 (2000).
[CrossRef]

J. Opt. Soc. Am. A (1)

Linear Algebr. Appl. (1)

J. B. Kruskal, Linear Algebr. Appl. 18, 95 (1977).
[CrossRef]

Opt. Commun. (1)

C. Yi-nan, J. Wei-qi, W. Ling-Xue, Z. Lei, and Y. Hong-sheng, Opt. Commun. 282, 786 (2009).
[CrossRef]

Opt. Lett. (1)

Psychometrika (2)

L. R. Tucker, Psychometrika 31, 279 (1966).
[CrossRef] [PubMed]

J. D. Carrol and J. J. Chang, Psychometrika 35, 283 (1970).
[CrossRef]

SIAM J. Matrix Anal. Appl. (1)

L. De Lathauwer, B. De Moor, and J. Vandewalle, SIAM J. Matrix Anal. Appl. 21, 1253 (2000).
[CrossRef]

Other (4)

B. W. Bader and T. G. Kolda, MATLAB Tensor Toolbox Version 2.2, http://csmr.ca.sandia.gov/~tkolda/TensorToolbox.

R. A. Harshman, in UCLA Working Papers in Phonetics (UCLA, 1970), Vol. 16, p. 1.

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

P.Campisi and K.Egiazarian, eds., Blind Image Deconvolution (CRC Press, 2007).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

RGB experimental image obtained by digital camera in manually defocused mode. Images courtesy of (left) Wiley-Blackwell and (right) Cambridge University Press.

Fig. 2
Fig. 2

RGB image restored by 3D TF SF BID algorithm. Images courtesy of (left) Wiley-Blackwell and (right) Cambridge University Press.

Fig. 3
Fig. 3

RGB image restored by WP SDICA BID algorithm [6]. Images courtesy of (left) Wiley-Blackwell and (right) Cambridge University Press.

Equations (7)

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

G ( i 1 , i 2 ) = s = M M t = M M H ( s , t ) F ( i 1 s , i 2 t ) ,
G ( i 1 , i 2 ) = a 1 F ( i 1 , i 2 ) + a 2 F i 1 ( i 1 , i 2 ) + a 3 F i 2 ( i 1 , i 2 ) + ,
G i 3 ( i 1 , i 2 ) = a i 3 , 1 F ( i 1 , i 2 ) + a i 3 , 2 F i 1 ( i 1 , i 2 ) + a i 3 , 3 F i 2 ( i 1 , i 2 ) + , i 3 = 2 , , I 3 ,
G ̱ R ̱ × 1 A ( 1 ) × 2 A ( 2 ) × 3 A ( 3 ) ,
G ( 3 ) A F ( 3 ) ,
A A ( 3 ) ,
F ̱ R ̱ × 1 A ( 1 ) × 2 A ( 2 ) G ̱ × 3 ( A ( 3 ) ) ,

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