Abstract

Performances of iterative blind deconvolution methods for motion-blurred images are usually reduced depending on the accuracy of the required initial guess of the blur. We examine this dependency, and a two-stage restoration procedure is proposed: First we perform a direct technique with a single straightforward process to produce a rough initial estimate of the blur, and then an iterative technique is employed to refine the blur estimate. Two common iterative techniques (the expectation-maximization and the Richardson–Lucy methods) are examined here and implemented in the combined direct–iterative modification for a variety of motion blur types. Results show that the combined method significantly improves the reliability of the deconvolution process.

© 2006 Optical Society of America

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  1. Y. Yitzhaky, R. Milberg, S. Yohayev, and N. S. Kopeika, "Comparison of direct blind deconvolution methods for motion-blurred images," Appl. Opt. 38, 4325-4332 (1999).
    [CrossRef]
  2. D. Slepian, "Restoration of photographs blurred by image motion," Bell Syst. Tech. J. 46, 2353-2362 (1967).
  3. M. M. Sondhi, "Image restoration: the removal of spatially invariant degradations," Proc. IEEE 60, 842-853 (1972).
    [CrossRef]
  4. M. Cannon, "Blind deconvolution of spatially invariant image blurs with phase," IEEE Trans. Acoust. Speech Signal Process. ASSP-24, 58-63 (1976).
    [CrossRef]
  5. Y. Yitzhaky and N. S. Kopeika, "Identification of blur parameters from motion blurred images," Graph. Models Image Process. 59, 310-320 (1997).
    [CrossRef]
  6. Y. Yitzhaky, I. Mor, A. Lantzman, and N. S. Kopeika, "Direct method for restoration of motion-blurred images," J. Opt. Soc. Am. A 15, 1512-1519 (1998).
    [CrossRef]
  7. M. I. Sezan and A. M. Tekalp, "Survey of recent developments in digital image restoration," Opt. Eng. 29, 393-404 (1990).
    [CrossRef]
  8. G. Pavlovic and A. M. Tekalp, "Maximum likelihood parametric blur identification based on a continuous spatial domain model," IEEE Trans. Image Process. 1, 496-504 (1992).
    [CrossRef] [PubMed]
  9. R. L. Lagendijk, J. Biemond, and D. E. Boekee, "Identification and restoration of noisy blurred images using the expectation-maximization algorithm," IEEE Trans. Acoust. Speech Signal Process. 38, 1180-1191 (1990).
    [CrossRef]
  10. R. L. Lagendijk, A. M. Tekalp, and J. Biemond, "Maximum likelihood image and blur identification: a unifying approach," Opt. Eng. 29, 422-435 (1990).
    [CrossRef]
  11. L. B. Lucy, "An iterative technique for the rectification of observed distributions," Astron. J. 79, 745-754 (1974).
    [CrossRef]
  12. W. H. Richardson, "Bayesian-based iterative method of image restoration," J. Opt. Soc. Am. 62, 55-59 (1972).
    [CrossRef]
  13. D. S. C. Biggs and M. Andrews, "Acceleration of iterative image restoration algorithms," Appl. Opt. 36, 1766-1775 (1997).
    [CrossRef] [PubMed]
  14. A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data," J. R. Stat. Soc. Ser. B Methodol. 39, 1-38 (1997).
  15. N. S. Kopeika, A System Engineering Approach to Imaging (SPIE Press, 1998).
  16. W. K. Pratt, "Vector space formulation of two-dimensional signal processing operations," Comput. Graph. Image Process. 4, 1-24 (1975).
    [CrossRef]
  17. N. B. Nill and B. H. Bouzas, "Objective image quality measure derived from digital image power spectra," Opt. Eng. 31, 813-825 (1992).
    [CrossRef]
  18. P. Marziliano, F. Dufaux, S. Winkler, and T. Ebrahimi, "A no-reference perceptual blur metric," In Proceedings of IEEE International Conference on Image Processing (IEEE Press, 2002), Vol. 3, pp. 57-60.
    [CrossRef]
  19. Y. Yitzhaky and A. Stern "Restoration of interlaced images degraded by variable velocity motion," Opt. Eng. 42, 3557-3565 (2003).
    [CrossRef]
  20. Y. Yitzhaky, G. Boshusha, Y. Levy, and N. S. Kopeika, "Restoration of an image degraded by vibrations using only a single frame," Opt. Eng. 39, 2083-2091 (2000).

2003 (1)

Y. Yitzhaky and A. Stern "Restoration of interlaced images degraded by variable velocity motion," Opt. Eng. 42, 3557-3565 (2003).
[CrossRef]

1999 (1)

1998 (1)

1997 (3)

D. S. C. Biggs and M. Andrews, "Acceleration of iterative image restoration algorithms," Appl. Opt. 36, 1766-1775 (1997).
[CrossRef] [PubMed]

A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data," J. R. Stat. Soc. Ser. B Methodol. 39, 1-38 (1997).

Y. Yitzhaky and N. S. Kopeika, "Identification of blur parameters from motion blurred images," Graph. Models Image Process. 59, 310-320 (1997).
[CrossRef]

1992 (2)

N. B. Nill and B. H. Bouzas, "Objective image quality measure derived from digital image power spectra," Opt. Eng. 31, 813-825 (1992).
[CrossRef]

G. Pavlovic and A. M. Tekalp, "Maximum likelihood parametric blur identification based on a continuous spatial domain model," IEEE Trans. Image Process. 1, 496-504 (1992).
[CrossRef] [PubMed]

1990 (3)

R. L. Lagendijk, J. Biemond, and D. E. Boekee, "Identification and restoration of noisy blurred images using the expectation-maximization algorithm," IEEE Trans. Acoust. Speech Signal Process. 38, 1180-1191 (1990).
[CrossRef]

R. L. Lagendijk, A. M. Tekalp, and J. Biemond, "Maximum likelihood image and blur identification: a unifying approach," Opt. Eng. 29, 422-435 (1990).
[CrossRef]

M. I. Sezan and A. M. Tekalp, "Survey of recent developments in digital image restoration," Opt. Eng. 29, 393-404 (1990).
[CrossRef]

1976 (1)

M. Cannon, "Blind deconvolution of spatially invariant image blurs with phase," IEEE Trans. Acoust. Speech Signal Process. ASSP-24, 58-63 (1976).
[CrossRef]

1975 (1)

W. K. Pratt, "Vector space formulation of two-dimensional signal processing operations," Comput. Graph. Image Process. 4, 1-24 (1975).
[CrossRef]

1974 (1)

L. B. Lucy, "An iterative technique for the rectification of observed distributions," Astron. J. 79, 745-754 (1974).
[CrossRef]

1972 (2)

W. H. Richardson, "Bayesian-based iterative method of image restoration," J. Opt. Soc. Am. 62, 55-59 (1972).
[CrossRef]

M. M. Sondhi, "Image restoration: the removal of spatially invariant degradations," Proc. IEEE 60, 842-853 (1972).
[CrossRef]

1967 (1)

D. Slepian, "Restoration of photographs blurred by image motion," Bell Syst. Tech. J. 46, 2353-2362 (1967).

Andrews, M.

Biemond, J.

R. L. Lagendijk, J. Biemond, and D. E. Boekee, "Identification and restoration of noisy blurred images using the expectation-maximization algorithm," IEEE Trans. Acoust. Speech Signal Process. 38, 1180-1191 (1990).
[CrossRef]

R. L. Lagendijk, A. M. Tekalp, and J. Biemond, "Maximum likelihood image and blur identification: a unifying approach," Opt. Eng. 29, 422-435 (1990).
[CrossRef]

Biggs, D. S. C.

Boekee, D. E.

R. L. Lagendijk, J. Biemond, and D. E. Boekee, "Identification and restoration of noisy blurred images using the expectation-maximization algorithm," IEEE Trans. Acoust. Speech Signal Process. 38, 1180-1191 (1990).
[CrossRef]

Bouzas, B. H.

N. B. Nill and B. H. Bouzas, "Objective image quality measure derived from digital image power spectra," Opt. Eng. 31, 813-825 (1992).
[CrossRef]

Cannon, M.

M. Cannon, "Blind deconvolution of spatially invariant image blurs with phase," IEEE Trans. Acoust. Speech Signal Process. ASSP-24, 58-63 (1976).
[CrossRef]

Dempster, A. P.

A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data," J. R. Stat. Soc. Ser. B Methodol. 39, 1-38 (1997).

Dufaux, F.

P. Marziliano, F. Dufaux, S. Winkler, and T. Ebrahimi, "A no-reference perceptual blur metric," In Proceedings of IEEE International Conference on Image Processing (IEEE Press, 2002), Vol. 3, pp. 57-60.
[CrossRef]

Ebrahimi, T.

P. Marziliano, F. Dufaux, S. Winkler, and T. Ebrahimi, "A no-reference perceptual blur metric," In Proceedings of IEEE International Conference on Image Processing (IEEE Press, 2002), Vol. 3, pp. 57-60.
[CrossRef]

Kopeika, N. S.

Lagendijk, R. L.

R. L. Lagendijk, A. M. Tekalp, and J. Biemond, "Maximum likelihood image and blur identification: a unifying approach," Opt. Eng. 29, 422-435 (1990).
[CrossRef]

R. L. Lagendijk, J. Biemond, and D. E. Boekee, "Identification and restoration of noisy blurred images using the expectation-maximization algorithm," IEEE Trans. Acoust. Speech Signal Process. 38, 1180-1191 (1990).
[CrossRef]

Laird, N. M.

A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data," J. R. Stat. Soc. Ser. B Methodol. 39, 1-38 (1997).

Lantzman, A.

Lucy, L. B.

L. B. Lucy, "An iterative technique for the rectification of observed distributions," Astron. J. 79, 745-754 (1974).
[CrossRef]

Marziliano, P.

P. Marziliano, F. Dufaux, S. Winkler, and T. Ebrahimi, "A no-reference perceptual blur metric," In Proceedings of IEEE International Conference on Image Processing (IEEE Press, 2002), Vol. 3, pp. 57-60.
[CrossRef]

Milberg, R.

Mor, I.

Nill, N. B.

N. B. Nill and B. H. Bouzas, "Objective image quality measure derived from digital image power spectra," Opt. Eng. 31, 813-825 (1992).
[CrossRef]

Pavlovic, G.

G. Pavlovic and A. M. Tekalp, "Maximum likelihood parametric blur identification based on a continuous spatial domain model," IEEE Trans. Image Process. 1, 496-504 (1992).
[CrossRef] [PubMed]

Pratt, W. K.

W. K. Pratt, "Vector space formulation of two-dimensional signal processing operations," Comput. Graph. Image Process. 4, 1-24 (1975).
[CrossRef]

Richardson, W. H.

Rubin, D. B.

A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data," J. R. Stat. Soc. Ser. B Methodol. 39, 1-38 (1997).

Sezan, M. I.

M. I. Sezan and A. M. Tekalp, "Survey of recent developments in digital image restoration," Opt. Eng. 29, 393-404 (1990).
[CrossRef]

Slepian, D.

D. Slepian, "Restoration of photographs blurred by image motion," Bell Syst. Tech. J. 46, 2353-2362 (1967).

Sondhi, M. M.

M. M. Sondhi, "Image restoration: the removal of spatially invariant degradations," Proc. IEEE 60, 842-853 (1972).
[CrossRef]

Stern, A.

Y. Yitzhaky and A. Stern "Restoration of interlaced images degraded by variable velocity motion," Opt. Eng. 42, 3557-3565 (2003).
[CrossRef]

Tekalp, A. M.

G. Pavlovic and A. M. Tekalp, "Maximum likelihood parametric blur identification based on a continuous spatial domain model," IEEE Trans. Image Process. 1, 496-504 (1992).
[CrossRef] [PubMed]

M. I. Sezan and A. M. Tekalp, "Survey of recent developments in digital image restoration," Opt. Eng. 29, 393-404 (1990).
[CrossRef]

R. L. Lagendijk, A. M. Tekalp, and J. Biemond, "Maximum likelihood image and blur identification: a unifying approach," Opt. Eng. 29, 422-435 (1990).
[CrossRef]

Winkler, S.

P. Marziliano, F. Dufaux, S. Winkler, and T. Ebrahimi, "A no-reference perceptual blur metric," In Proceedings of IEEE International Conference on Image Processing (IEEE Press, 2002), Vol. 3, pp. 57-60.
[CrossRef]

Yitzhaky, Y.

Y. Yitzhaky and A. Stern "Restoration of interlaced images degraded by variable velocity motion," Opt. Eng. 42, 3557-3565 (2003).
[CrossRef]

Y. Yitzhaky, R. Milberg, S. Yohayev, and N. S. Kopeika, "Comparison of direct blind deconvolution methods for motion-blurred images," Appl. Opt. 38, 4325-4332 (1999).
[CrossRef]

Y. Yitzhaky, I. Mor, A. Lantzman, and N. S. Kopeika, "Direct method for restoration of motion-blurred images," J. Opt. Soc. Am. A 15, 1512-1519 (1998).
[CrossRef]

Y. Yitzhaky and N. S. Kopeika, "Identification of blur parameters from motion blurred images," Graph. Models Image Process. 59, 310-320 (1997).
[CrossRef]

Yohayev, S.

Appl. Opt. (2)

Astron. J. (1)

L. B. Lucy, "An iterative technique for the rectification of observed distributions," Astron. J. 79, 745-754 (1974).
[CrossRef]

Bell Syst. Tech. J. (1)

D. Slepian, "Restoration of photographs blurred by image motion," Bell Syst. Tech. J. 46, 2353-2362 (1967).

Comput. Graph. Image Process. (1)

W. K. Pratt, "Vector space formulation of two-dimensional signal processing operations," Comput. Graph. Image Process. 4, 1-24 (1975).
[CrossRef]

Graph. Models Image Process. (1)

Y. Yitzhaky and N. S. Kopeika, "Identification of blur parameters from motion blurred images," Graph. Models Image Process. 59, 310-320 (1997).
[CrossRef]

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

M. Cannon, "Blind deconvolution of spatially invariant image blurs with phase," IEEE Trans. Acoust. Speech Signal Process. ASSP-24, 58-63 (1976).
[CrossRef]

R. L. Lagendijk, J. Biemond, and D. E. Boekee, "Identification and restoration of noisy blurred images using the expectation-maximization algorithm," IEEE Trans. Acoust. Speech Signal Process. 38, 1180-1191 (1990).
[CrossRef]

IEEE Trans. Image Process. (1)

G. Pavlovic and A. M. Tekalp, "Maximum likelihood parametric blur identification based on a continuous spatial domain model," IEEE Trans. Image Process. 1, 496-504 (1992).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

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

J. R. Stat. Soc. Ser. B Methodol. (1)

A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data," J. R. Stat. Soc. Ser. B Methodol. 39, 1-38 (1997).

Opt. Eng. (4)

N. B. Nill and B. H. Bouzas, "Objective image quality measure derived from digital image power spectra," Opt. Eng. 31, 813-825 (1992).
[CrossRef]

Y. Yitzhaky and A. Stern "Restoration of interlaced images degraded by variable velocity motion," Opt. Eng. 42, 3557-3565 (2003).
[CrossRef]

M. I. Sezan and A. M. Tekalp, "Survey of recent developments in digital image restoration," Opt. Eng. 29, 393-404 (1990).
[CrossRef]

R. L. Lagendijk, A. M. Tekalp, and J. Biemond, "Maximum likelihood image and blur identification: a unifying approach," Opt. Eng. 29, 422-435 (1990).
[CrossRef]

Proc. IEEE (1)

M. M. Sondhi, "Image restoration: the removal of spatially invariant degradations," Proc. IEEE 60, 842-853 (1972).
[CrossRef]

Other (3)

Y. Yitzhaky, G. Boshusha, Y. Levy, and N. S. Kopeika, "Restoration of an image degraded by vibrations using only a single frame," Opt. Eng. 39, 2083-2091 (2000).

P. Marziliano, F. Dufaux, S. Winkler, and T. Ebrahimi, "A no-reference perceptual blur metric," In Proceedings of IEEE International Conference on Image Processing (IEEE Press, 2002), Vol. 3, pp. 57-60.
[CrossRef]

N. S. Kopeika, A System Engineering Approach to Imaging (SPIE Press, 1998).

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Figures (7)

Fig. 1
Fig. 1

Original cameraman image used in the simulation examples (256 × 256 pixels).

Fig. 2
Fig. 2

Block diagram of the degradation and the combined direct–iterative blind deconvolution processes.

Fig. 3
Fig. 3

(a) Cameraman image degraded by a 33-pixel portion of a low-frequency sinusoidal motion blur; (b) image restored by a direct method; (c) image restored by the proposed direct–iterative RL method; and (d) real, initial, and final estimated PSFs.

Fig. 4
Fig. 4

Average ACF that produces the initial PSF estimation of the direct method from the blurred image of Fig. 3(a). The distance between a global minimum and the center of the ACF (33 pixels in this case) is the blur extent estimation of the direct method.

Fig. 5
Fig. 5

Same as Fig. 3, but for a 27-pixel high-frequency sinusoidal motion blur type.

Fig. 6
Fig. 6

Same as Fig. 3, but for another motion type obtained by using a different portion of a low-frequency sinusoidal blur with a 20-pixel extent and with a restoration using the EM iterative method.

Fig. 7
Fig. 7

(a) Real-motion-blurred image taken from a moving car,[6] (b) comparison of PSFs estimated by the direct-only method and by the proposed direct–iterative EM and RL methods for a blur extent estimated as 26 pixels, (c) image restored by the direct–iterative EM method, and (d) image restored by the direct–iterative RL method.

Tables (1)

Tables Icon

Table 1 Sensitivity of the Iterative Process (with 100 Iterations) to the Initial Point-Spread Function Guess (Cameraman Image) a

Equations (40)

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

Δ G ( u , ν ) = G ( u , ν ) W ( ν ) W ( u ) ,
R l ( j ) = 1 M i = M M l ( i + j ) l ( i ) ,   integer   j [ M , M ] ,
l ( i ) = 0 for   i [ 0 , M ] ,
S ¯ Δ G S Δ PSF ,
S Δ PSF = | H W ( u ) | 2 ,
MTF ( u ) [ S ¯ ΔG ( u ) ] 1 / 2 | W ( u ) | .
PTF ( u ) = 1 2 π 0 2 π ln [ MTF ( α ) ] cot u α 2  d α .
H = MTF   exp ( j PTF ) .
g ( i , j ) = m , n S h h ( m , n ) f ( i m , j n ) + ω ( i , j ) ,
m , n S h h ( m , n ) = 1.
g = H f + ω ,
P ( f i | g k ) = P ( g k | f i ) P ( f i ) j P ( g k | f j ) P ( f i ) ;
i = { 1 , I } , j = { 1 , J } , k = { 1 , K } ,
f ^ 1 ( i , j ) = m = i i + K 1 n = j j + L 1 g ( m , n ) h ^ 1 ( m i + 1 , n j + 1 ) p = a b q = c d h ^ 1 ( m p + 1 , n q + 1 ) ,
f ^ r + 1 ( i , j ) = f ^ r ( i , j ) m = i i + K 1 n = j j + L 1 g ( m , n ) h ^ r ( m i + 1 , n j + 1 ) p = a b q = c d f ^ r ( p , q ) h ^ r ( m p + 1 , n q + 1 ) ,
f ^ r + 1 = f ^ r ( h ^ r g h ^ r f ^ r ) Ψ ( f ^ r ) ,
h ^ r + 1 = h ^ r ( f ^ r g h ^ r f ^ r ) Ω ( h ^ r ) ,
f ^ r + λ = f ^ r + λ f [ Ψ ( f ^ r ) f ^ r ] ,
h ^ r + λ = h ^ r + λ h [ Ω ( h ^ r ) h ^ r ] ,
λ f = i N j N { [ f ^ r + 1 ( i , j ) f ^ r ( i , j ) ] [ f ^ r ( i , j ) f ^ r 1 ( i , j ) ] } i N j N { [ f ^ r ( i , j ) f ^ r 1 ( i , j ) ] 2 } ,
λ h = i N j N { [ h ^ r + 1 ( i , j ) h ^ r ( i , j ) ] [ h ^ r ( i , j ) h ^ r 1 ( i , j ) ] } i N j N { [ h ^ r ( i , j ) h ^ r 1 ( i , j ) ] 2 } .
f ( i , j ) = k , l S a a ( k , l ) f ( i k , j l ) + ν ( i , j ) ,
f = A f + ν ,
θ = ( θ 1 , θ 2 , , θ M ) t = [ h ( m , n ) , a ( k , l ) , σ ω       2 , σ ν     2 ] .
θ ^ ml = arg { max θ Θ L * ( θ ) } = arg { max log θ Θ p ( g ; θ ) } ,
p ( f ; A , Q ν ) = [ det | I A | 2 2 π N 2 det | Q ν | ] 1 / 2 × exp [ 1 2 f t ( I - A ) t Q ν     1 ( I A ) f ] .
p ( g / f ; H , Q ω ) = 1 2 π N 2 det | Q ω | × exp [ 1 2 ( g - Hf ) t Q ω     1 ( g H f ) ] ,
L ( θ ) = log ( det | P | ) + g t P 1 g ,
P = cov ( g ) = σ ν     2 H ( I A ) 1 ( I A ) 1 H t + σ ω     2 I .
p ( i , j ) = σ ν     2 h ( i , j ) [ 1 a ( i , j ) ] 1 [ 1 a ( i , j ) ] 1 × h ( i , j ) + σ ω       2 .
L ( θ ; θ ^ ( k ) ) = E { log p ( X ; θ ) / Y ; θ ^ ( k ) } ,
θ ^ ( k + 1 ) = arg { max L θ Θ ( θ ;    θ ^ ( k ) ) } ,
V ( k ) = cov ( f / g ; θ ( k ) ) = [ ( I A ) t Q ν     1 ( I A ) + H t Q ω     1 H ] 1 ,
f ^ ( k ) = E ( f / g ; θ ( k ) ) = V ( k ) H t Q ω     1 g ;
r ^ f f ( k ) ( p , q ) = k , l S a a ^ ( k , l ) r ^ f f ( k ) ( p k , q l ) , ( p , q ) S a ,
σ ^ ν 2 = r ^ f f ( k ) ( 0 , 0 ) k , l S a a ^ ( k , l ) r ^ f f ( k ) ( k , l ) ,
r ^ f g ( k ) ( p , q ) = m , n S h h ^ ( m , n ) r ^ f f ( k ) ( p m , q n ) , ( p , q ) S h ,
σ ^ ω 2 = 1 N 2 i , j = 1 N g ( i , j ) 2 m , n S h h ^ ( m , n ) × r ^ f g ( k ) ( m , n ) ,
r ^ f f ( k ) ( p , q ) = V ( k ) ( p , q ) + 1 N 2 i , j = 1 N f ^ ( k ) ( i , j ) f ^ ( k ) ( i p , j q ) ,
r ^ f g ( k ) ( p , q ) = i , j = 1 N f ^ ( k ) ( i , j ) g ( k ) ( i p , j q ) .

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