Abstract

A multichannel blind deconvolution algorithm that incorporates the maximum-likelihood image restoration by several estimates of the differently blurred point-spread function (PSF) into the Ayers–Dainty iterative algorithm is proposed. The algorithm uses no restrictions on the image and the PSFs except for the assumption that they are positive. The algorithm employs no cost functions, input parameters, a priori probability distributions, or the analytically specified transfer functions. The iterative algorithm permits its application in the presence of different kinds of distortion. The work presents results of digital modeling and the results of processing real telescope data from several satellites. The proof of convergence of the algorithm to the positive estimates of object and the PSFs is given. The convergence of the Ayers–Dainty algorithm with a single processed frame is not obvious in the general case; therefore it is useful to have confidence in its convergence in a multiframe case. The dependence of convergence on the number of processed frames is discussed. Formulas for evaluating the quality of the algorithm performance on each iteration and the rule of stopping its work in accordance with this quality are proposed. A method of building the monotonically converging subsequence of the image estimates of all the images obtained in the iterative process is also proposed.

© 2006 Optical Society of America

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  1. M. Banham and A. Katsaggelos, "Digital image restoration," IEEE Signal Process. Mag. 14, 24-41 (1997).
    [CrossRef]
  2. G. R. Ayers and J. C. Dainty, "Iterative blind deconvolution method and its applications," Opt. Lett. 13, 547-549 (1988).
    [CrossRef] [PubMed]
  3. R. Lane and R. Bates, "Automatic multichannel deconvolution," J. Opt. Soc. Am. A 4, 180-188 (1987).
    [CrossRef]
  4. D. Kundur and D. Hatzinakos, "A novel blind deconvolution scheme for image restoration using recursive filtering," IEEE Trans. Signal Process. 46, 375-390 (1998).
    [CrossRef]
  5. C. Ong and J. Chambers, "An enhanced NAS-RIF algorithm for blind image deconvolution," IEEE Trans. Image Process. 8, 988-992 (1999).
    [CrossRef]
  6. M. Ng, R. Plemmons, and S. Qiao, "Regularization of RIF blind image deconvolution," IEEE Trans. Image Process. 9, 1130-1138 (2000).
    [CrossRef]
  7. R. G. Lane, "Blind deconvolution of speckle images," J. Opt. Soc. Am. A 9, 1508-1514 (1992).
    [CrossRef]
  8. E. Thiebaut and J. M. Conan, "Strict a priori constraints for maximum-likelihood blind deconvolution," J. Opt. Soc. Am. A 12, 485-492 (March 1995).
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    [CrossRef]
  10. H. Pai and A. C. Bovik, "Exact multichannel blind image restoration," IEEE Signal Process. Lett. 4, 217-220 (1997).
    [CrossRef]
  11. H. Pai and A. C. Bovik, "On eigenstructure-based direct multichannel blind image restoration", IEEE Trans. Image Process. 10, 1434-1446 (2001).
    [CrossRef]
  12. P. A. Bakut and Y. V. Zhulina, "Measuring and compensating phase distortions in the images of short exposition," Opt. J. 65, 5-61 (1998) (in Russian).
  13. A. A. Kuriksha and Y. V. Zhulina, "Reconstruction of distorted optical images in the presence of Poisson signal fluctuations in the photoreceiver," J. Commun. Technol. Electron. 45, 287-293 (2000).
  14. T. J. Schulz, B. E. Stribling, and J. J. Miller, "Multiframe blind deconvolution with real data: imagery of the Hubble Space Telescope," Opt. Express 1, 355-362 (1997).
    [CrossRef] [PubMed]
  15. T. J. Schulz, "Multiframe blind deconvolution of astronomical images," J. Opt. Soc. Am. A 10, 1064-1073 (1993).
    [CrossRef]
  16. S. M. Jefferies and J. C. Christou, "Restoration of astronomical images by iterative blind deconvolution," Astrophys. J. 63, 862-874 (1993).
    [CrossRef]
  17. M. G. Lofdahl, "Multi-frame blind deconvolution with linear equality constraints," in Image Reconstruction from Incomplete Data II, P. J. Bones, M. A. Fiddy and R. P. Millane, eds., Proc. SPIE 4792, 146-155 (2002).
    [CrossRef]
  18. B. L. K. Davey, R. G. Lane, and R. H. T. Bates, "Blind deconvolution of noisy complex-valued image," Opt. Commun. 69, 353-356 (1989).
    [CrossRef]
  19. L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D 60, 259-268 (1992).
    [CrossRef]
  20. C. Vogel and M. Oman, "Iterative methods for total variation denoising," SIAM (Soc. Ind. Appl. Math.) J. Sci. Comput. 17, 227-238 (1996).
  21. C. Vogel and M. Oman, "Fast, robust total variation-based reconstruction of noisy, blurred images," IEEE Trans. Image Process. 7, 813-824 (1998).
    [CrossRef]
  22. T. Chan, G. Golub, and P. Mulet, "A nonlinear primal-dual method for total variation-based image restoration," SIAM (Soc. Ind. Appl. Math.) J. Sci. Comput. 20, 1964-1977 (1999).
  23. D. Geman and G. Reynolds, "Constrained restoration and the recovery of discontinuities," IEEE Trans. Pattern Anal. Mach. Intell. 14, 367-383 (1992).
    [CrossRef]
  24. Y.-L. You and M. Kaveh, "A regularization approach to joint blur identification and image restoration," IEEE Trans. Image Process. 5, 416-28 (1996).
    [CrossRef] [PubMed]
  25. A. Bovik, Handbook of Image and Video Processing (Academic, 2000).
  26. T. F. Chan, S. Osher, and J. Shen, "The digital TV filter and nonlinear denoising," IEEE Trans. Image Process. 10, 231-241 (2001).
    [CrossRef]
  27. T. Chan and C. Wong, "Total variation blind deconvolution," IEEE Trans. Image Process. 7, 370-375 (1998).
    [CrossRef]
  28. T. F. Chan and C. K. Wong, "Convergence of the alternating minimization algorithm for blind deconvolution," Linear Algebr. Appl. 316, 259-285 (2000).
    [CrossRef]
  29. G. Harikumar and Y. Bresler, "Perfect blind restoration of images blurred by multiple filters: Theory and efficient algorithms," IEEE Trans. Image Process. 8, 202-219 (1999).
    [CrossRef]
  30. G. Harikumar and Y. Bresler, "Efficient algorithms for the blind recovery of images blurred by multiple filters," in Proceedings of IEEE International Conference on Image Processing (IEEE, 1996), Vol. 3, pp. 97-100.
  31. S. Pillai and B. Liang, "Blind image deconvolution using a robust GCD approach," IEEE Trans. Image Process. 8, 295-301 (1999).
    [CrossRef]
  32. G. Giannakis and R. Heath, "Blind identification of multichannel FIR blurs and perfect image restoration," IEEE Trans. Image Process. 9, 1877-1896 (2000).
    [CrossRef]
  33. G. Xu, H. Liu, L. Tong, and T. Kailath, "A least-squares approach to blind channel identification," IEEE Trans. Signal Process. 43, 2983-2993 (1995).
  34. F. Sroubek and J. Flusser, "Multichannel blind iterative image restoration," IEEE Trans. Image Process. 12, 1094-1106 (2003).
    [CrossRef]

2003 (1)

F. Sroubek and J. Flusser, "Multichannel blind iterative image restoration," IEEE Trans. Image Process. 12, 1094-1106 (2003).
[CrossRef]

2002 (1)

M. G. Lofdahl, "Multi-frame blind deconvolution with linear equality constraints," in Image Reconstruction from Incomplete Data II, P. J. Bones, M. A. Fiddy and R. P. Millane, eds., Proc. SPIE 4792, 146-155 (2002).
[CrossRef]

2001 (2)

H. Pai and A. C. Bovik, "On eigenstructure-based direct multichannel blind image restoration", IEEE Trans. Image Process. 10, 1434-1446 (2001).
[CrossRef]

T. F. Chan, S. Osher, and J. Shen, "The digital TV filter and nonlinear denoising," IEEE Trans. Image Process. 10, 231-241 (2001).
[CrossRef]

2000 (4)

T. F. Chan and C. K. Wong, "Convergence of the alternating minimization algorithm for blind deconvolution," Linear Algebr. Appl. 316, 259-285 (2000).
[CrossRef]

G. Giannakis and R. Heath, "Blind identification of multichannel FIR blurs and perfect image restoration," IEEE Trans. Image Process. 9, 1877-1896 (2000).
[CrossRef]

A. A. Kuriksha and Y. V. Zhulina, "Reconstruction of distorted optical images in the presence of Poisson signal fluctuations in the photoreceiver," J. Commun. Technol. Electron. 45, 287-293 (2000).

M. Ng, R. Plemmons, and S. Qiao, "Regularization of RIF blind image deconvolution," IEEE Trans. Image Process. 9, 1130-1138 (2000).
[CrossRef]

1999 (4)

C. Ong and J. Chambers, "An enhanced NAS-RIF algorithm for blind image deconvolution," IEEE Trans. Image Process. 8, 988-992 (1999).
[CrossRef]

G. Harikumar and Y. Bresler, "Perfect blind restoration of images blurred by multiple filters: Theory and efficient algorithms," IEEE Trans. Image Process. 8, 202-219 (1999).
[CrossRef]

S. Pillai and B. Liang, "Blind image deconvolution using a robust GCD approach," IEEE Trans. Image Process. 8, 295-301 (1999).
[CrossRef]

T. Chan, G. Golub, and P. Mulet, "A nonlinear primal-dual method for total variation-based image restoration," SIAM (Soc. Ind. Appl. Math.) J. Sci. Comput. 20, 1964-1977 (1999).

1998 (3)

C. Vogel and M. Oman, "Fast, robust total variation-based reconstruction of noisy, blurred images," IEEE Trans. Image Process. 7, 813-824 (1998).
[CrossRef]

T. Chan and C. Wong, "Total variation blind deconvolution," IEEE Trans. Image Process. 7, 370-375 (1998).
[CrossRef]

D. Kundur and D. Hatzinakos, "A novel blind deconvolution scheme for image restoration using recursive filtering," IEEE Trans. Signal Process. 46, 375-390 (1998).
[CrossRef]

1997 (3)

M. Banham and A. Katsaggelos, "Digital image restoration," IEEE Signal Process. Mag. 14, 24-41 (1997).
[CrossRef]

H. Pai and A. C. Bovik, "Exact multichannel blind image restoration," IEEE Signal Process. Lett. 4, 217-220 (1997).
[CrossRef]

T. J. Schulz, B. E. Stribling, and J. J. Miller, "Multiframe blind deconvolution with real data: imagery of the Hubble Space Telescope," Opt. Express 1, 355-362 (1997).
[CrossRef] [PubMed]

1996 (2)

C. Vogel and M. Oman, "Iterative methods for total variation denoising," SIAM (Soc. Ind. Appl. Math.) J. Sci. Comput. 17, 227-238 (1996).

Y.-L. You and M. Kaveh, "A regularization approach to joint blur identification and image restoration," IEEE Trans. Image Process. 5, 416-28 (1996).
[CrossRef] [PubMed]

1995 (1)

G. Xu, H. Liu, L. Tong, and T. Kailath, "A least-squares approach to blind channel identification," IEEE Trans. Signal Process. 43, 2983-2993 (1995).

1994 (1)

1993 (2)

T. J. Schulz, "Multiframe blind deconvolution of astronomical images," J. Opt. Soc. Am. A 10, 1064-1073 (1993).
[CrossRef]

S. M. Jefferies and J. C. Christou, "Restoration of astronomical images by iterative blind deconvolution," Astrophys. J. 63, 862-874 (1993).
[CrossRef]

1992 (3)

L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D 60, 259-268 (1992).
[CrossRef]

R. G. Lane, "Blind deconvolution of speckle images," J. Opt. Soc. Am. A 9, 1508-1514 (1992).
[CrossRef]

D. Geman and G. Reynolds, "Constrained restoration and the recovery of discontinuities," IEEE Trans. Pattern Anal. Mach. Intell. 14, 367-383 (1992).
[CrossRef]

1989 (1)

B. L. K. Davey, R. G. Lane, and R. H. T. Bates, "Blind deconvolution of noisy complex-valued image," Opt. Commun. 69, 353-356 (1989).
[CrossRef]

1988 (1)

1987 (1)

Ayers, G. R.

Bakut, P. A.

P. A. Bakut and Y. V. Zhulina, "Measuring and compensating phase distortions in the images of short exposition," Opt. J. 65, 5-61 (1998) (in Russian).

Banham, M.

M. Banham and A. Katsaggelos, "Digital image restoration," IEEE Signal Process. Mag. 14, 24-41 (1997).
[CrossRef]

Bates, R.

Bates, R. H. T.

B. L. K. Davey, R. G. Lane, and R. H. T. Bates, "Blind deconvolution of noisy complex-valued image," Opt. Commun. 69, 353-356 (1989).
[CrossRef]

Bovik, A.

A. Bovik, Handbook of Image and Video Processing (Academic, 2000).

Bovik, A. C.

H. Pai and A. C. Bovik, "On eigenstructure-based direct multichannel blind image restoration", IEEE Trans. Image Process. 10, 1434-1446 (2001).
[CrossRef]

H. Pai and A. C. Bovik, "Exact multichannel blind image restoration," IEEE Signal Process. Lett. 4, 217-220 (1997).
[CrossRef]

Bresler, Y.

G. Harikumar and Y. Bresler, "Perfect blind restoration of images blurred by multiple filters: Theory and efficient algorithms," IEEE Trans. Image Process. 8, 202-219 (1999).
[CrossRef]

G. Harikumar and Y. Bresler, "Efficient algorithms for the blind recovery of images blurred by multiple filters," in Proceedings of IEEE International Conference on Image Processing (IEEE, 1996), Vol. 3, pp. 97-100.

Chambers, J.

C. Ong and J. Chambers, "An enhanced NAS-RIF algorithm for blind image deconvolution," IEEE Trans. Image Process. 8, 988-992 (1999).
[CrossRef]

Chan, T.

T. Chan, G. Golub, and P. Mulet, "A nonlinear primal-dual method for total variation-based image restoration," SIAM (Soc. Ind. Appl. Math.) J. Sci. Comput. 20, 1964-1977 (1999).

T. Chan and C. Wong, "Total variation blind deconvolution," IEEE Trans. Image Process. 7, 370-375 (1998).
[CrossRef]

Chan, T. F.

T. F. Chan, S. Osher, and J. Shen, "The digital TV filter and nonlinear denoising," IEEE Trans. Image Process. 10, 231-241 (2001).
[CrossRef]

Christou, J. C.

S. M. Jefferies and J. C. Christou, "Restoration of astronomical images by iterative blind deconvolution," Astrophys. J. 63, 862-874 (1993).
[CrossRef]

Conan, J. M.

Dainty, J. C.

Davey, B. L. K.

B. L. K. Davey, R. G. Lane, and R. H. T. Bates, "Blind deconvolution of noisy complex-valued image," Opt. Commun. 69, 353-356 (1989).
[CrossRef]

Fatemi, E.

L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D 60, 259-268 (1992).
[CrossRef]

Flusser, J.

F. Sroubek and J. Flusser, "Multichannel blind iterative image restoration," IEEE Trans. Image Process. 12, 1094-1106 (2003).
[CrossRef]

Galatsanos, N. P.

Geman, D.

D. Geman and G. Reynolds, "Constrained restoration and the recovery of discontinuities," IEEE Trans. Pattern Anal. Mach. Intell. 14, 367-383 (1992).
[CrossRef]

Giannakis, G.

G. Giannakis and R. Heath, "Blind identification of multichannel FIR blurs and perfect image restoration," IEEE Trans. Image Process. 9, 1877-1896 (2000).
[CrossRef]

Golub, G.

T. Chan, G. Golub, and P. Mulet, "A nonlinear primal-dual method for total variation-based image restoration," SIAM (Soc. Ind. Appl. Math.) J. Sci. Comput. 20, 1964-1977 (1999).

Harikumar, G.

G. Harikumar and Y. Bresler, "Perfect blind restoration of images blurred by multiple filters: Theory and efficient algorithms," IEEE Trans. Image Process. 8, 202-219 (1999).
[CrossRef]

G. Harikumar and Y. Bresler, "Efficient algorithms for the blind recovery of images blurred by multiple filters," in Proceedings of IEEE International Conference on Image Processing (IEEE, 1996), Vol. 3, pp. 97-100.

Hatzinakos, D.

D. Kundur and D. Hatzinakos, "A novel blind deconvolution scheme for image restoration using recursive filtering," IEEE Trans. Signal Process. 46, 375-390 (1998).
[CrossRef]

Heath, R.

G. Giannakis and R. Heath, "Blind identification of multichannel FIR blurs and perfect image restoration," IEEE Trans. Image Process. 9, 1877-1896 (2000).
[CrossRef]

Jefferies, S. M.

S. M. Jefferies and J. C. Christou, "Restoration of astronomical images by iterative blind deconvolution," Astrophys. J. 63, 862-874 (1993).
[CrossRef]

Kailath, T.

G. Xu, H. Liu, L. Tong, and T. Kailath, "A least-squares approach to blind channel identification," IEEE Trans. Signal Process. 43, 2983-2993 (1995).

Katsaggelos, A.

M. Banham and A. Katsaggelos, "Digital image restoration," IEEE Signal Process. Mag. 14, 24-41 (1997).
[CrossRef]

Kaveh, M.

Y.-L. You and M. Kaveh, "A regularization approach to joint blur identification and image restoration," IEEE Trans. Image Process. 5, 416-28 (1996).
[CrossRef] [PubMed]

Kundur, D.

D. Kundur and D. Hatzinakos, "A novel blind deconvolution scheme for image restoration using recursive filtering," IEEE Trans. Signal Process. 46, 375-390 (1998).
[CrossRef]

Kuriksha, A. A.

A. A. Kuriksha and Y. V. Zhulina, "Reconstruction of distorted optical images in the presence of Poisson signal fluctuations in the photoreceiver," J. Commun. Technol. Electron. 45, 287-293 (2000).

Lane, R.

Lane, R. G.

R. G. Lane, "Blind deconvolution of speckle images," J. Opt. Soc. Am. A 9, 1508-1514 (1992).
[CrossRef]

B. L. K. Davey, R. G. Lane, and R. H. T. Bates, "Blind deconvolution of noisy complex-valued image," Opt. Commun. 69, 353-356 (1989).
[CrossRef]

Liang, B.

S. Pillai and B. Liang, "Blind image deconvolution using a robust GCD approach," IEEE Trans. Image Process. 8, 295-301 (1999).
[CrossRef]

Liu, H.

G. Xu, H. Liu, L. Tong, and T. Kailath, "A least-squares approach to blind channel identification," IEEE Trans. Signal Process. 43, 2983-2993 (1995).

Lofdahl, M. G.

M. G. Lofdahl, "Multi-frame blind deconvolution with linear equality constraints," in Image Reconstruction from Incomplete Data II, P. J. Bones, M. A. Fiddy and R. P. Millane, eds., Proc. SPIE 4792, 146-155 (2002).
[CrossRef]

Miller, J. J.

Mulet, P.

T. Chan, G. Golub, and P. Mulet, "A nonlinear primal-dual method for total variation-based image restoration," SIAM (Soc. Ind. Appl. Math.) J. Sci. Comput. 20, 1964-1977 (1999).

Ng, M.

M. Ng, R. Plemmons, and S. Qiao, "Regularization of RIF blind image deconvolution," IEEE Trans. Image Process. 9, 1130-1138 (2000).
[CrossRef]

Oman, M.

C. Vogel and M. Oman, "Fast, robust total variation-based reconstruction of noisy, blurred images," IEEE Trans. Image Process. 7, 813-824 (1998).
[CrossRef]

C. Vogel and M. Oman, "Iterative methods for total variation denoising," SIAM (Soc. Ind. Appl. Math.) J. Sci. Comput. 17, 227-238 (1996).

Ong, C.

C. Ong and J. Chambers, "An enhanced NAS-RIF algorithm for blind image deconvolution," IEEE Trans. Image Process. 8, 988-992 (1999).
[CrossRef]

Osher, S.

T. F. Chan, S. Osher, and J. Shen, "The digital TV filter and nonlinear denoising," IEEE Trans. Image Process. 10, 231-241 (2001).
[CrossRef]

L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D 60, 259-268 (1992).
[CrossRef]

Pai, H.

H. Pai and A. C. Bovik, "On eigenstructure-based direct multichannel blind image restoration", IEEE Trans. Image Process. 10, 1434-1446 (2001).
[CrossRef]

H. Pai and A. C. Bovik, "Exact multichannel blind image restoration," IEEE Signal Process. Lett. 4, 217-220 (1997).
[CrossRef]

Pillai, S.

S. Pillai and B. Liang, "Blind image deconvolution using a robust GCD approach," IEEE Trans. Image Process. 8, 295-301 (1999).
[CrossRef]

Plemmons, R.

M. Ng, R. Plemmons, and S. Qiao, "Regularization of RIF blind image deconvolution," IEEE Trans. Image Process. 9, 1130-1138 (2000).
[CrossRef]

Qiao, S.

M. Ng, R. Plemmons, and S. Qiao, "Regularization of RIF blind image deconvolution," IEEE Trans. Image Process. 9, 1130-1138 (2000).
[CrossRef]

Reynolds, G.

D. Geman and G. Reynolds, "Constrained restoration and the recovery of discontinuities," IEEE Trans. Pattern Anal. Mach. Intell. 14, 367-383 (1992).
[CrossRef]

Rudin, L.

L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D 60, 259-268 (1992).
[CrossRef]

Schulz, T. J.

Shen, J.

T. F. Chan, S. Osher, and J. Shen, "The digital TV filter and nonlinear denoising," IEEE Trans. Image Process. 10, 231-241 (2001).
[CrossRef]

Sroubek, F.

F. Sroubek and J. Flusser, "Multichannel blind iterative image restoration," IEEE Trans. Image Process. 12, 1094-1106 (2003).
[CrossRef]

Stark, H.

Stribling, B. E.

Thiebaut, E.

Tong, L.

G. Xu, H. Liu, L. Tong, and T. Kailath, "A least-squares approach to blind channel identification," IEEE Trans. Signal Process. 43, 2983-2993 (1995).

Vogel, C.

C. Vogel and M. Oman, "Fast, robust total variation-based reconstruction of noisy, blurred images," IEEE Trans. Image Process. 7, 813-824 (1998).
[CrossRef]

C. Vogel and M. Oman, "Iterative methods for total variation denoising," SIAM (Soc. Ind. Appl. Math.) J. Sci. Comput. 17, 227-238 (1996).

Wong, C.

T. Chan and C. Wong, "Total variation blind deconvolution," IEEE Trans. Image Process. 7, 370-375 (1998).
[CrossRef]

Xu, G.

G. Xu, H. Liu, L. Tong, and T. Kailath, "A least-squares approach to blind channel identification," IEEE Trans. Signal Process. 43, 2983-2993 (1995).

Yang, Y.

You, Y.-L.

Y.-L. You and M. Kaveh, "A regularization approach to joint blur identification and image restoration," IEEE Trans. Image Process. 5, 416-28 (1996).
[CrossRef] [PubMed]

Zhulina, Y. V.

A. A. Kuriksha and Y. V. Zhulina, "Reconstruction of distorted optical images in the presence of Poisson signal fluctuations in the photoreceiver," J. Commun. Technol. Electron. 45, 287-293 (2000).

P. A. Bakut and Y. V. Zhulina, "Measuring and compensating phase distortions in the images of short exposition," Opt. J. 65, 5-61 (1998) (in Russian).

Astrophys. J. (1)

S. M. Jefferies and J. C. Christou, "Restoration of astronomical images by iterative blind deconvolution," Astrophys. J. 63, 862-874 (1993).
[CrossRef]

IEEE Signal Process. Lett. (1)

H. Pai and A. C. Bovik, "Exact multichannel blind image restoration," IEEE Signal Process. Lett. 4, 217-220 (1997).
[CrossRef]

IEEE Signal Process. Mag. (1)

M. Banham and A. Katsaggelos, "Digital image restoration," IEEE Signal Process. Mag. 14, 24-41 (1997).
[CrossRef]

IEEE Trans. Image Process. (11)

C. Ong and J. Chambers, "An enhanced NAS-RIF algorithm for blind image deconvolution," IEEE Trans. Image Process. 8, 988-992 (1999).
[CrossRef]

M. Ng, R. Plemmons, and S. Qiao, "Regularization of RIF blind image deconvolution," IEEE Trans. Image Process. 9, 1130-1138 (2000).
[CrossRef]

H. Pai and A. C. Bovik, "On eigenstructure-based direct multichannel blind image restoration", IEEE Trans. Image Process. 10, 1434-1446 (2001).
[CrossRef]

C. Vogel and M. Oman, "Fast, robust total variation-based reconstruction of noisy, blurred images," IEEE Trans. Image Process. 7, 813-824 (1998).
[CrossRef]

Y.-L. You and M. Kaveh, "A regularization approach to joint blur identification and image restoration," IEEE Trans. Image Process. 5, 416-28 (1996).
[CrossRef] [PubMed]

T. F. Chan, S. Osher, and J. Shen, "The digital TV filter and nonlinear denoising," IEEE Trans. Image Process. 10, 231-241 (2001).
[CrossRef]

T. Chan and C. Wong, "Total variation blind deconvolution," IEEE Trans. Image Process. 7, 370-375 (1998).
[CrossRef]

G. Harikumar and Y. Bresler, "Perfect blind restoration of images blurred by multiple filters: Theory and efficient algorithms," IEEE Trans. Image Process. 8, 202-219 (1999).
[CrossRef]

S. Pillai and B. Liang, "Blind image deconvolution using a robust GCD approach," IEEE Trans. Image Process. 8, 295-301 (1999).
[CrossRef]

G. Giannakis and R. Heath, "Blind identification of multichannel FIR blurs and perfect image restoration," IEEE Trans. Image Process. 9, 1877-1896 (2000).
[CrossRef]

F. Sroubek and J. Flusser, "Multichannel blind iterative image restoration," IEEE Trans. Image Process. 12, 1094-1106 (2003).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

D. Geman and G. Reynolds, "Constrained restoration and the recovery of discontinuities," IEEE Trans. Pattern Anal. Mach. Intell. 14, 367-383 (1992).
[CrossRef]

IEEE Trans. Signal Process. (2)

D. Kundur and D. Hatzinakos, "A novel blind deconvolution scheme for image restoration using recursive filtering," IEEE Trans. Signal Process. 46, 375-390 (1998).
[CrossRef]

G. Xu, H. Liu, L. Tong, and T. Kailath, "A least-squares approach to blind channel identification," IEEE Trans. Signal Process. 43, 2983-2993 (1995).

J. Commun. Technol. Electron. (1)

A. A. Kuriksha and Y. V. Zhulina, "Reconstruction of distorted optical images in the presence of Poisson signal fluctuations in the photoreceiver," J. Commun. Technol. Electron. 45, 287-293 (2000).

J. Opt. Soc. Am. A (5)

Linear Algebr. Appl. (1)

T. F. Chan and C. K. Wong, "Convergence of the alternating minimization algorithm for blind deconvolution," Linear Algebr. Appl. 316, 259-285 (2000).
[CrossRef]

Opt. Commun. (1)

B. L. K. Davey, R. G. Lane, and R. H. T. Bates, "Blind deconvolution of noisy complex-valued image," Opt. Commun. 69, 353-356 (1989).
[CrossRef]

Opt. Express (1)

Opt. J. (1)

P. A. Bakut and Y. V. Zhulina, "Measuring and compensating phase distortions in the images of short exposition," Opt. J. 65, 5-61 (1998) (in Russian).

Opt. Lett. (1)

Physica D (1)

L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D 60, 259-268 (1992).
[CrossRef]

Proc. SPIE (1)

M. G. Lofdahl, "Multi-frame blind deconvolution with linear equality constraints," in Image Reconstruction from Incomplete Data II, P. J. Bones, M. A. Fiddy and R. P. Millane, eds., Proc. SPIE 4792, 146-155 (2002).
[CrossRef]

SIAM (2)

C. Vogel and M. Oman, "Iterative methods for total variation denoising," SIAM (Soc. Ind. Appl. Math.) J. Sci. Comput. 17, 227-238 (1996).

T. Chan, G. Golub, and P. Mulet, "A nonlinear primal-dual method for total variation-based image restoration," SIAM (Soc. Ind. Appl. Math.) J. Sci. Comput. 20, 1964-1977 (1999).

Other (2)

A. Bovik, Handbook of Image and Video Processing (Academic, 2000).

G. Harikumar and Y. Bresler, "Efficient algorithms for the blind recovery of images blurred by multiple filters," in Proceedings of IEEE International Conference on Image Processing (IEEE, 1996), Vol. 3, pp. 97-100.

Cited By

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Figures (16)

Fig. 1
Fig. 1

Real image of the satellite Lacrosse-2.

Fig. 2
Fig. 2

Real image of the satellite Lacrosse-4.

Fig. 3
Fig. 3

Real image of the satellite Global Star.

Fig. 4
Fig. 4

Real image of the International Space Station.

Fig. 5
Fig. 5

Digitally modeled image of the satellite Ecco, frame 1.

Fig. 6
Fig. 6

Digitally modeled image of the satellite Ecco, frame 2.

Fig. 7
Fig. 7

Restoration of the satellite Ecco, 10th iteration.

Fig. 8
Fig. 8

Restoration of the satellite Ecco, 135th iteration.

Fig. 9
Fig. 9

Restoration of the satellite Lacrosse-2, 50th iteration, twice enlarged image.

Fig. 10
Fig. 10

Restoration of the satellite Lacrosse-2, 50th iteration, four times enlarged image.

Fig. 11
Fig. 11

Restoration of the satellite Lacrosse-4, 59th iteration, twice enlarged image.

Fig. 12
Fig. 12

Restoration of the satellite Lacrosse-4, 59th iteration, four times-enlarged image.

Fig. 13
Fig. 13

Drawing of the Lacrosse satellite taken from the Internet.

Fig. 14
Fig. 14

Restoration of the satellite Global Star, 67th iteration, twice enlarged image.

Fig. 15
Fig. 15

Restoration of the ISS, 159th iteration, twice enlarged image.

Fig. 16
Fig. 16

(Color online) Picture of the ISS from the Internet.

Equations (32)

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O ( r ) = h ( r - r 1 ) E ( r 1 ) d 2 r 1 + n ( r ) ,
E ( k ) ( r ) = E ( + ) ( k ) ( r ) - E ( - ) ( k ) ( r ) ,
G ( k ) ( ω ) = G ( + ) ( k ) ( ω ) - G ( - ) ( k ) ( ω ) ,
h m ( k ) ( r ) = h m ( + ) ( k ) ( r ) - h m ( - ) ( k ) ( r ) .
H m ( k ) ( ω ) = H m ( + ) ( k ) ( ω ) - H m ( - ) ( k ) ( ω ) ,
H m ( k ) ( ω ) G ( + ) ( k - 1 ) ( ω ) = C m ( ω ) .
H m ( k ) ( ω ) = C m ( ω ) G ( + ) ( k - 1 ) ( ω ) + ε ( k ) .
δ ln [ G ( k ) (⋅) ] δG ( k ) ( ω ) = 0 ,
ln [ G ( k ) (⋅) ] = - m = 1 M | H m ( + ) ( k ) ( ω ) G ( k ) ( ω ) - C m ( ω ) | 2  ×  d 2 ω .
G ( k ) ( ω ) = m = 1 M μ m ( k ) ( ω ) C m ( ω ) ,
μ m ( k ) ( ω ) = H m ( + ) ( k ) * ( ω ) m = 1 M | H m ( + ) ( k ) * ( ω ) | 2 .
μ m ( k ) ( ω ) = H m ( + ) ( k ) * ( ω ) m = 1 M | H m ( + ) ( k ) * ( ω ) | 2 + ε 0 ( k ) .
Num = min ω { m = 1 M | H m ( + ) ( k ) * ω | 2 } > 0
Num E = min ω { | G ( + ) { k - 1 } ( ω ) | } .
O ^ m ( k ) ( r ) = h m ( + ) ( k ) ( r - r 1 ) × E ( + ) ( k ) ( r 1 ) d 2 r 1 ( m = 1 , , M ) .
Q m ( k ) ( r ) = O ^ m ( k ) ( r + r 1 ) O m ( r 1 ) d 2 r 1
( m = 1 , , M ) .
Qn m ( k ) ( r ) = Q m ( k ) ( r ) [ O ^ m ( k ) ( r 1 ) ] 2 d 2 r 1 [ O m ( r 1 ) ] 2 d 2 r 1
( m = 1 , , M ) .
Qn max m ( k ) = max r { Q m ( k ) ( r ) } .
Qn max ( k ) = 1 M m = 1 M Qn max m ( k ) .
H m ( ρ ) = 1 A Δ ( r ) e m ( r ) Δ ( r - ρ ) e - m ( r - ρ ) d 2 r .
G m ( k ) ( ω ) H m ( + ) ( k ) ( ω ) = C m ( ω ) .
G m ( k ) ( ω ) = G m ( + ) ( k ) ( ω ) - G m ( - ) ( k ) ( ω ) ,
[ H m ( + ) ( k ) ( ω ) - H m ( - ) ( k ) ( ω ) ] G ( + ) ( k - 1 ) ( ω ) = C m ( ω ) .
[ G m ( + ) ( k ) ( ω ) - G m ( - ) ( k ) ( ω ) ] H m ( + ) ( k ) ( ω ) = C m ( ω ) .
G m ( k ) ( ω ) G ( + ) ( k - 1 ) ( ω ) + Q m ( k ) ( ω ) = 1 ( m = 1 , , M ) ,
Q m ( k ) ( ω ) = H m ( - ) ( k ) ( ω ) H m ( + ) ( k ) ( ω ) .
μ ˜ m ( k ) ( ω ) = | H m ( + ) ( k ) ( ω ) | 2 m = 1 M | H m ( + ) ( k ) ( ω ) | 2 ,
Q ( k ) ( ω ) = m = 1 M μ ˜ m ( k ) ( ω ) Q m ( k ) ( ω ) .
G ( k ) ( ω ) G ( + ) ( k - 1 ) ( ω ) + Q ( k ) ( ω ) = 1.
M   > =   ln ( 1 - P conv ) ln log P ,

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