Abstract

A novel algorithm for blind image deconvolution using the zero-lag slice (ZLS) of higher-order statistics only is presented. This method first estimates the point-spread function (PSF) using the ZLS of its third-order moment (TOM) and then uses it with one of the known classical image deconvolution methods. The proposed method has simple computations for PSF estimation because it solves a nonlinear problem by using an iterative method with fast convergence. In each iteration, one need only calculate the ZLS of the TOM and estimate the PSF using simple two-dimensional operations. Furthermore, the method presented achieves good results, since the ZLS estimate obtained from the degraded image exhibits high reliability. The good performance of the proposed algorithm is demonstrated by applying it to synthetic and real data sets.

© 2006 Optical Society of America

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References

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  1. D. Kundur and D. Hatzinakos, IEEE Signal Process. Mag. 13, 43 (1996).
    [CrossRef]
  2. W. Lu, Electron. Lett. 39, 425 (2003).
    [CrossRef]
  3. Y. Xu and G. Crebbin, in Proceedings of the International Conference on Image Processing (IEEE, 1996), Vol. 3, p. 77.
  4. C. Y. Chi and C. H. Chen, IEEE Trans. Signal Process. 49, 864 (2001).
    [CrossRef]
  5. M. M. Bronstein, A. M. Bronstein, M. Zibulevsky, and Y. Y. Zeevi, IEEE Trans. Image Process. 14, 726 (2005).
    [CrossRef] [PubMed]
  6. C. L. Niklias and A. P. Petropulu, Higher-Order Spectral Analysis: A Nonlinear Signal Processing Framework (Prentice-Hall, 1993).
  7. W. Lu, IEEE Signal Process. Lett. 12, 725 (2005).
    [CrossRef]

2005 (2)

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

W. Lu, IEEE Signal Process. Lett. 12, 725 (2005).
[CrossRef]

2003 (1)

W. Lu, Electron. Lett. 39, 425 (2003).
[CrossRef]

2001 (1)

C. Y. Chi and C. H. Chen, IEEE Trans. Signal Process. 49, 864 (2001).
[CrossRef]

1996 (2)

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

Y. Xu and G. Crebbin, in Proceedings of the International Conference on Image Processing (IEEE, 1996), Vol. 3, p. 77.

1993 (1)

C. L. Niklias and A. P. Petropulu, Higher-Order Spectral Analysis: A Nonlinear Signal Processing Framework (Prentice-Hall, 1993).

Bronstein, A. M.

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

Bronstein, M. M.

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

Chen, C. H.

C. Y. Chi and C. H. Chen, IEEE Trans. Signal Process. 49, 864 (2001).
[CrossRef]

Chi, C. Y.

C. Y. Chi and C. H. Chen, IEEE Trans. Signal Process. 49, 864 (2001).
[CrossRef]

Crebbin, G.

Y. Xu and G. Crebbin, in Proceedings of the International Conference on Image Processing (IEEE, 1996), Vol. 3, p. 77.

Hatzinakos, D.

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

Kundur, D.

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

Lu, W.

W. Lu, IEEE Signal Process. Lett. 12, 725 (2005).
[CrossRef]

W. Lu, Electron. Lett. 39, 425 (2003).
[CrossRef]

Niklias, C. L.

C. L. Niklias and A. P. Petropulu, Higher-Order Spectral Analysis: A Nonlinear Signal Processing Framework (Prentice-Hall, 1993).

Petropulu, A. P.

C. L. Niklias and A. P. Petropulu, Higher-Order Spectral Analysis: A Nonlinear Signal Processing Framework (Prentice-Hall, 1993).

Xu, Y.

Y. Xu and G. Crebbin, in Proceedings of the International Conference on Image Processing (IEEE, 1996), Vol. 3, p. 77.

Zeevi, Y. Y.

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

Zibulevsky, M.

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

Electron. Lett. (1)

W. Lu, Electron. Lett. 39, 425 (2003).
[CrossRef]

IEEE Signal Process. Lett. (1)

W. Lu, IEEE Signal Process. Lett. 12, 725 (2005).
[CrossRef]

IEEE Signal Process. Mag. (1)

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

IEEE Trans. Image Process. (1)

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

IEEE Trans. Signal Process. (1)

C. Y. Chi and C. H. Chen, IEEE Trans. Signal Process. 49, 864 (2001).
[CrossRef]

Other (2)

Y. Xu and G. Crebbin, in Proceedings of the International Conference on Image Processing (IEEE, 1996), Vol. 3, p. 77.

C. L. Niklias and A. P. Petropulu, Higher-Order Spectral Analysis: A Nonlinear Signal Processing Framework (Prentice-Hall, 1993).

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Figures (4)

Fig. 1
Fig. 1

PSFs used in the synthetic experiments: (a) Gaussian, (b) scatter, (c) asymmetric.

Fig. 2
Fig. 2

Two original images used in the synthetic experiments.

Fig. 3
Fig. 3

Example using a synthetically degraded image with SNR = 30 dB : (a) Estimated PSF obtained by the proposed method, (b) degraded image, (c) image restored using the estimated PSF, (d) image restored using the true PSF.

Fig. 4
Fig. 4

Example using out-of-focus images of an air conditioner controller taken by a digital camera: (a) Seriously blurred image and (b) its restoration; (c) moderately blurred image and (d) its restoration; (e) in-focus image.

Tables (2)

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Table 1 Statistical Results of Synthetic Experiments Obtained by the Proposed Method

Tables Icon

Table 2 NCC (Mean, SD) Between the Estimated and the True ZLSs of the TOM of the PSF a

Equations (10)

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y ( i , j ) = b ( i , j ) * d ( i , j ) + w ( i , j ) ,
x ( i , j ) = y ( i , j ) * f ( i , j ) = b ( i , j ) * d ( i , j ) * f ( i , j ) + w ( i , j ) * f ( i , j ) = b ( i , j ) * s ( i , j ) + n ( i , j ) ,
m x 3 ( i 1 , j 1 , i 2 , j 2 ) = i , j x ( i , j ) x ( i + i 1 , j + j 1 ) x ( i + i 2 , j + j 2 ) ,
m x 2 ( i 1 , j 1 ) = i , j x ( i , j ) x ( i + i 1 , j + j 1 ) .
z ( i 1 , j 1 ) = m b 3 ( i 1 , j 1 , 0 , 0 ) = i , j b 2 ( i , j ) b ( i + i 1 , j + j 1 ) .
Z ( u , v ) = B * ( u , v ) C ( u , v ) ,
c 1 = IFFT 2 { [ Z ( u , v ) B l 1 ( u , v ) B l 1 ( u , v ) B l 1 * ( u , v ) + α V ] } ,
c = c 1 + β ( L l + 1 ) L ( c 2 c 1 ) ,
b ( i , j ) = IFFT 2 [ Z * ( u , v ) C ( u , v ) C ( u , v ) C * ( u , v ) + α U ] ,
NCC = i , j [ s 1 ( i , j ) m 1 ] [ s 2 ( i , j ) m 2 ] { i , j [ s 1 ( i , j ) m 1 ] 2 i , j [ s 2 ( i , j ) m 2 ] 2 } 1 2 ,

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