Abstract

We consider the recovery of degraded videos without complete knowledge about the degradation. A spatially shift-invariant but temporally shift-varying video formation model is used. This leads to a simple multiframe degradation model that relates each original video frame with multiple observed frames and point spread functions (PSFs). We propose a variational method that simultaneously reconstructs each video frame and the associated PSFs from the corresponding observed frames. Total variation (TV) regularization is used on both the video frames and the PSFs to further reduce the ill-posedness and to better preserve edges. In order to make TV minimization practical for video sequences, we propose an efficient splitting method that generalizes some recent fast single-image TV minimization methods to the multiframe case. Both synthetic and real videos are used to show the performance of the proposed method.

© 2010 Optical Society of America

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References

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  1. H. Andrew and B. Hunt, Digital Image Restoration (Prentice-Hall, 1977).
  2. S. D. Babacan, R. Molina, and A. K. Katsaggelos, “Variational Bayesian blind deconvolution using a total variation prior,” IEEE Trans. Image Process. 18, 12–26 (2009).
    [CrossRef]
  3. T. Chan and C. Wong, “Total variation blind deconvolution,” IEEE Trans. Image Process. 7, 370–375 (1998).
    [CrossRef]
  4. O. Haik and Y. Yitzhaky, “Effects of image restoration on automatic acquisition of moving objects in thermal video sequences degraded by the atmosphere,” Appl. Opt. 46, 8562–8572 (2007).
    [CrossRef] [PubMed]
  5. H. Zhu, Y. Lu, and Q. Wu, “Blind image deconvolution subject to bandwidth and total variation constraints,” Opt. Lett. 32, 2550–2552 (2007).
    [CrossRef]
  6. I. Kopriva, “Approach to blind image deconvolution by multiscale subband decomposition and independent component analysis,” J. Opt. Soc. Am. A 24, 973–983 (2007).
    [CrossRef]
  7. D. Kundur and D. Hatzinakos, “Blind image deconvolution,” IEEE Signal. Process. Mag. 13, 43–64 (1996).
    [CrossRef]
  8. C. L. Matson, K. Borelli, S. Jefferies, C. C. Beckner, Jr., E. K. Hege, and M. Lloyd-Hart, “Fast and optimal multiframe blind deconvolution algorithm for high-resolution ground-based imaging of space objects,” Appl. Opt. 48, A75–A92 (2009).
    [CrossRef]
  9. R. Molina, J. Mateos, and A. K. Katsaggelos, “Blind deconvolution using a variational approach to parameter, image, and blur estimation,” IEEE Trans. Image Process. 15, 3715–3727(2006).
    [CrossRef] [PubMed]
  10. F. Sroubek and J. Flusser, “Multichannel blind iterative image restoration,” IEEE Trans. Image Process. 12, 1094–1106 (2003).
    [CrossRef]
  11. F. Sroubek and J. Flusser, “Multichannel blind deconvolution of spatially misaligned images,” IEEE Trans. Image Process. 14, 874–883 (2005).
    [CrossRef] [PubMed]
  12. Y. You and M. Kaveh, “A regularization approach to joint blur identification and image restoration,” IEEE Trans. Image Process. 5, 416–428 (1996).
    [CrossRef] [PubMed]
  13. A. M. Tekalp, Digital Video Processing (Prentice-Hall, 1995).
  14. T. Chan, G. Golub, and P. Mulet, “A nonlinear primal-dual method for total variation-based image restoration,” SIAM J. Sci. Comput. 20, 1964–1977 (1999).
    [CrossRef]
  15. T. Chan and K. Chen, “An optimization-based multilevel algorithm for total variation image denoising,” Multiscale Model. Simul. 5, 615–645 (2006).
    [CrossRef]
  16. A. Katsaggelos and K. Lay, “Maximum likelihood blur identification and image restoration using the EM algorithm,” IEEE Trans. Signal Process. 39, 729–733 (1991).
    [CrossRef]
  17. D. Krishnan, P. Lin, and X. Tai, “An efficient operator splitting method for noise removal in images,” Commun. Comput. Phys. 1, 847–858 (2006).
  18. L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D (Amsterdam) 60, 259–268 (1992).
    [CrossRef]
  19. C. Vogel and M. Oman, “Iterative method for total variation denoising,” SIAM J. Sci. Comput. 17, 227–238 (1996).
    [CrossRef]
  20. D. Tzikas, A. Likas, and N. Galatsanos, “Variational Bayesian sparse kernel-based blind image deconvolution with student’s-t priors,” IEEE Trans. Image Process. 18, 753–764 (2009).
    [CrossRef] [PubMed]
  21. G. Harikumar and Y. Bresler, “Exact image deconvolution from multiple FIR blurs,” IEEE Trans. Image Process. 8, 846–862 (1999).
    [CrossRef]
  22. 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]
  23. A. Rav-Acha and S. Peleg, “Two motion-blurred images are better than one,” Pattern Recogn. Lett. 26, 311–317 (2005).
    [CrossRef]
  24. Y. Huang, M. Ng, and Y. Wen, “A fast total variation minimization method for image restoration,” Multiscale Model. Simul. 7, 774–795 (2008).
    [CrossRef]
  25. Y. Huang, M. Ng, and Y. Wen, “A new total variation method for multiplicative noise removal,” SIAM J. Imaging Sci. 2, 20–40 (2009).
    [CrossRef]
  26. A. J. Patti, M. I. Sezan, and A. M. Tekalp, “Superresolution video reconstruction with arbitrary sampling lattices and nonzero aperture time,” IEEE Trans. Image Process. 6, 1064–1076 (1997).
    [CrossRef] [PubMed]
  27. A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision 20, 73 (2004).
    [CrossRef]
  28. M. Ng, L. Qi, Y. Yang, and Y. Huang, “On semismooth Newton’s methods for total variation minimization,” J. Math. Imaging Vision 27, 265–276 (2007).
    [CrossRef]

2009

D. Tzikas, A. Likas, and N. Galatsanos, “Variational Bayesian sparse kernel-based blind image deconvolution with student’s-t priors,” IEEE Trans. Image Process. 18, 753–764 (2009).
[CrossRef] [PubMed]

Y. Huang, M. Ng, and Y. Wen, “A new total variation method for multiplicative noise removal,” SIAM J. Imaging Sci. 2, 20–40 (2009).
[CrossRef]

S. D. Babacan, R. Molina, and A. K. Katsaggelos, “Variational Bayesian blind deconvolution using a total variation prior,” IEEE Trans. Image Process. 18, 12–26 (2009).
[CrossRef]

C. L. Matson, K. Borelli, S. Jefferies, C. C. Beckner, Jr., E. K. Hege, and M. Lloyd-Hart, “Fast and optimal multiframe blind deconvolution algorithm for high-resolution ground-based imaging of space objects,” Appl. Opt. 48, A75–A92 (2009).
[CrossRef]

2008

Y. Huang, M. Ng, and Y. Wen, “A fast total variation minimization method for image restoration,” Multiscale Model. Simul. 7, 774–795 (2008).
[CrossRef]

2007

2006

R. Molina, J. Mateos, and A. K. Katsaggelos, “Blind deconvolution using a variational approach to parameter, image, and blur estimation,” IEEE Trans. Image Process. 15, 3715–3727(2006).
[CrossRef] [PubMed]

T. Chan and K. Chen, “An optimization-based multilevel algorithm for total variation image denoising,” Multiscale Model. Simul. 5, 615–645 (2006).
[CrossRef]

D. Krishnan, P. Lin, and X. Tai, “An efficient operator splitting method for noise removal in images,” Commun. Comput. Phys. 1, 847–858 (2006).

2005

F. Sroubek and J. Flusser, “Multichannel blind deconvolution of spatially misaligned images,” IEEE Trans. Image Process. 14, 874–883 (2005).
[CrossRef] [PubMed]

A. Rav-Acha and S. Peleg, “Two motion-blurred images are better than one,” Pattern Recogn. Lett. 26, 311–317 (2005).
[CrossRef]

2004

A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision 20, 73 (2004).
[CrossRef]

2003

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

1999

G. Harikumar and Y. Bresler, “Exact image deconvolution from multiple FIR blurs,” IEEE Trans. Image Process. 8, 846–862 (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]

T. Chan, G. Golub, and P. Mulet, “A nonlinear primal-dual method for total variation-based image restoration,” SIAM J. Sci. Comput. 20, 1964–1977 (1999).
[CrossRef]

1998

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

1997

A. J. Patti, M. I. Sezan, and A. M. Tekalp, “Superresolution video reconstruction with arbitrary sampling lattices and nonzero aperture time,” IEEE Trans. Image Process. 6, 1064–1076 (1997).
[CrossRef] [PubMed]

1996

C. Vogel and M. Oman, “Iterative method for total variation denoising,” SIAM J. Sci. Comput. 17, 227–238 (1996).
[CrossRef]

Y. You and M. Kaveh, “A regularization approach to joint blur identification and image restoration,” IEEE Trans. Image Process. 5, 416–428 (1996).
[CrossRef] [PubMed]

D. Kundur and D. Hatzinakos, “Blind image deconvolution,” IEEE Signal. Process. Mag. 13, 43–64 (1996).
[CrossRef]

1992

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

1991

A. Katsaggelos and K. Lay, “Maximum likelihood blur identification and image restoration using the EM algorithm,” IEEE Trans. Signal Process. 39, 729–733 (1991).
[CrossRef]

Andrew, H.

H. Andrew and B. Hunt, Digital Image Restoration (Prentice-Hall, 1977).

Babacan, S. D.

S. D. Babacan, R. Molina, and A. K. Katsaggelos, “Variational Bayesian blind deconvolution using a total variation prior,” IEEE Trans. Image Process. 18, 12–26 (2009).
[CrossRef]

Beckner, C. C.

Borelli, K.

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, “Exact image deconvolution from multiple FIR blurs,” IEEE Trans. Image Process. 8, 846–862 (1999).
[CrossRef]

Chambolle, A.

A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision 20, 73 (2004).
[CrossRef]

Chan, T.

T. Chan and K. Chen, “An optimization-based multilevel algorithm for total variation image denoising,” Multiscale Model. Simul. 5, 615–645 (2006).
[CrossRef]

T. Chan, G. Golub, and P. Mulet, “A nonlinear primal-dual method for total variation-based image restoration,” SIAM J. Sci. Comput. 20, 1964–1977 (1999).
[CrossRef]

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

Chen, K.

T. Chan and K. Chen, “An optimization-based multilevel algorithm for total variation image denoising,” Multiscale Model. Simul. 5, 615–645 (2006).
[CrossRef]

Fatemi, E.

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

Flusser, J.

F. Sroubek and J. Flusser, “Multichannel blind deconvolution of spatially misaligned images,” IEEE Trans. Image Process. 14, 874–883 (2005).
[CrossRef] [PubMed]

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

Galatsanos, N.

D. Tzikas, A. Likas, and N. Galatsanos, “Variational Bayesian sparse kernel-based blind image deconvolution with student’s-t priors,” IEEE Trans. Image Process. 18, 753–764 (2009).
[CrossRef] [PubMed]

Golub, G.

T. Chan, G. Golub, and P. Mulet, “A nonlinear primal-dual method for total variation-based image restoration,” SIAM J. Sci. Comput. 20, 1964–1977 (1999).
[CrossRef]

Haik, O.

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, “Exact image deconvolution from multiple FIR blurs,” IEEE Trans. Image Process. 8, 846–862 (1999).
[CrossRef]

Hatzinakos, D.

D. Kundur and D. Hatzinakos, “Blind image deconvolution,” IEEE Signal. Process. Mag. 13, 43–64 (1996).
[CrossRef]

Hege, E. K.

Huang, Y.

Y. Huang, M. Ng, and Y. Wen, “A new total variation method for multiplicative noise removal,” SIAM J. Imaging Sci. 2, 20–40 (2009).
[CrossRef]

Y. Huang, M. Ng, and Y. Wen, “A fast total variation minimization method for image restoration,” Multiscale Model. Simul. 7, 774–795 (2008).
[CrossRef]

M. Ng, L. Qi, Y. Yang, and Y. Huang, “On semismooth Newton’s methods for total variation minimization,” J. Math. Imaging Vision 27, 265–276 (2007).
[CrossRef]

Hunt, B.

H. Andrew and B. Hunt, Digital Image Restoration (Prentice-Hall, 1977).

Jefferies, S.

Katsaggelos, A.

A. Katsaggelos and K. Lay, “Maximum likelihood blur identification and image restoration using the EM algorithm,” IEEE Trans. Signal Process. 39, 729–733 (1991).
[CrossRef]

Katsaggelos, A. K.

S. D. Babacan, R. Molina, and A. K. Katsaggelos, “Variational Bayesian blind deconvolution using a total variation prior,” IEEE Trans. Image Process. 18, 12–26 (2009).
[CrossRef]

R. Molina, J. Mateos, and A. K. Katsaggelos, “Blind deconvolution using a variational approach to parameter, image, and blur estimation,” IEEE Trans. Image Process. 15, 3715–3727(2006).
[CrossRef] [PubMed]

Kaveh, M.

Y. You and M. Kaveh, “A regularization approach to joint blur identification and image restoration,” IEEE Trans. Image Process. 5, 416–428 (1996).
[CrossRef] [PubMed]

Kopriva, I.

Krishnan, D.

D. Krishnan, P. Lin, and X. Tai, “An efficient operator splitting method for noise removal in images,” Commun. Comput. Phys. 1, 847–858 (2006).

Kundur, D.

D. Kundur and D. Hatzinakos, “Blind image deconvolution,” IEEE Signal. Process. Mag. 13, 43–64 (1996).
[CrossRef]

Lay, K.

A. Katsaggelos and K. Lay, “Maximum likelihood blur identification and image restoration using the EM algorithm,” IEEE Trans. Signal Process. 39, 729–733 (1991).
[CrossRef]

Likas, A.

D. Tzikas, A. Likas, and N. Galatsanos, “Variational Bayesian sparse kernel-based blind image deconvolution with student’s-t priors,” IEEE Trans. Image Process. 18, 753–764 (2009).
[CrossRef] [PubMed]

Lin, P.

D. Krishnan, P. Lin, and X. Tai, “An efficient operator splitting method for noise removal in images,” Commun. Comput. Phys. 1, 847–858 (2006).

Lloyd-Hart, M.

Lu, Y.

Mateos, J.

R. Molina, J. Mateos, and A. K. Katsaggelos, “Blind deconvolution using a variational approach to parameter, image, and blur estimation,” IEEE Trans. Image Process. 15, 3715–3727(2006).
[CrossRef] [PubMed]

Matson, C. L.

Molina, R.

S. D. Babacan, R. Molina, and A. K. Katsaggelos, “Variational Bayesian blind deconvolution using a total variation prior,” IEEE Trans. Image Process. 18, 12–26 (2009).
[CrossRef]

R. Molina, J. Mateos, and A. K. Katsaggelos, “Blind deconvolution using a variational approach to parameter, image, and blur estimation,” IEEE Trans. Image Process. 15, 3715–3727(2006).
[CrossRef] [PubMed]

Mulet, P.

T. Chan, G. Golub, and P. Mulet, “A nonlinear primal-dual method for total variation-based image restoration,” SIAM J. Sci. Comput. 20, 1964–1977 (1999).
[CrossRef]

Ng, M.

Y. Huang, M. Ng, and Y. Wen, “A new total variation method for multiplicative noise removal,” SIAM J. Imaging Sci. 2, 20–40 (2009).
[CrossRef]

Y. Huang, M. Ng, and Y. Wen, “A fast total variation minimization method for image restoration,” Multiscale Model. Simul. 7, 774–795 (2008).
[CrossRef]

M. Ng, L. Qi, Y. Yang, and Y. Huang, “On semismooth Newton’s methods for total variation minimization,” J. Math. Imaging Vision 27, 265–276 (2007).
[CrossRef]

Oman, M.

C. Vogel and M. Oman, “Iterative method for total variation denoising,” SIAM J. Sci. Comput. 17, 227–238 (1996).
[CrossRef]

Osher, S.

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

Patti, A. J.

A. J. Patti, M. I. Sezan, and A. M. Tekalp, “Superresolution video reconstruction with arbitrary sampling lattices and nonzero aperture time,” IEEE Trans. Image Process. 6, 1064–1076 (1997).
[CrossRef] [PubMed]

Peleg, S.

A. Rav-Acha and S. Peleg, “Two motion-blurred images are better than one,” Pattern Recogn. Lett. 26, 311–317 (2005).
[CrossRef]

Qi, L.

M. Ng, L. Qi, Y. Yang, and Y. Huang, “On semismooth Newton’s methods for total variation minimization,” J. Math. Imaging Vision 27, 265–276 (2007).
[CrossRef]

Rav-Acha, A.

A. Rav-Acha and S. Peleg, “Two motion-blurred images are better than one,” Pattern Recogn. Lett. 26, 311–317 (2005).
[CrossRef]

Rudin, L.

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

Sezan, M. I.

A. J. Patti, M. I. Sezan, and A. M. Tekalp, “Superresolution video reconstruction with arbitrary sampling lattices and nonzero aperture time,” IEEE Trans. Image Process. 6, 1064–1076 (1997).
[CrossRef] [PubMed]

Sroubek, F.

F. Sroubek and J. Flusser, “Multichannel blind deconvolution of spatially misaligned images,” IEEE Trans. Image Process. 14, 874–883 (2005).
[CrossRef] [PubMed]

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

Tai, X.

D. Krishnan, P. Lin, and X. Tai, “An efficient operator splitting method for noise removal in images,” Commun. Comput. Phys. 1, 847–858 (2006).

Tekalp, A. M.

A. J. Patti, M. I. Sezan, and A. M. Tekalp, “Superresolution video reconstruction with arbitrary sampling lattices and nonzero aperture time,” IEEE Trans. Image Process. 6, 1064–1076 (1997).
[CrossRef] [PubMed]

A. M. Tekalp, Digital Video Processing (Prentice-Hall, 1995).

Tzikas, D.

D. Tzikas, A. Likas, and N. Galatsanos, “Variational Bayesian sparse kernel-based blind image deconvolution with student’s-t priors,” IEEE Trans. Image Process. 18, 753–764 (2009).
[CrossRef] [PubMed]

Vogel, C.

C. Vogel and M. Oman, “Iterative method for total variation denoising,” SIAM J. Sci. Comput. 17, 227–238 (1996).
[CrossRef]

Wen, Y.

Y. Huang, M. Ng, and Y. Wen, “A new total variation method for multiplicative noise removal,” SIAM J. Imaging Sci. 2, 20–40 (2009).
[CrossRef]

Y. Huang, M. Ng, and Y. Wen, “A fast total variation minimization method for image restoration,” Multiscale Model. Simul. 7, 774–795 (2008).
[CrossRef]

Wong, C.

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

Wu, Q.

Yang, Y.

M. Ng, L. Qi, Y. Yang, and Y. Huang, “On semismooth Newton’s methods for total variation minimization,” J. Math. Imaging Vision 27, 265–276 (2007).
[CrossRef]

Yitzhaky, Y.

You, Y.

Y. You and M. Kaveh, “A regularization approach to joint blur identification and image restoration,” IEEE Trans. Image Process. 5, 416–428 (1996).
[CrossRef] [PubMed]

Zhu, H.

Appl. Opt.

Commun. Comput. Phys.

D. Krishnan, P. Lin, and X. Tai, “An efficient operator splitting method for noise removal in images,” Commun. Comput. Phys. 1, 847–858 (2006).

IEEE Signal. Process. Mag.

D. Kundur and D. Hatzinakos, “Blind image deconvolution,” IEEE Signal. Process. Mag. 13, 43–64 (1996).
[CrossRef]

IEEE Trans. Image Process.

S. D. Babacan, R. Molina, and A. K. Katsaggelos, “Variational Bayesian blind deconvolution using a total variation prior,” IEEE Trans. Image Process. 18, 12–26 (2009).
[CrossRef]

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

R. Molina, J. Mateos, and A. K. Katsaggelos, “Blind deconvolution using a variational approach to parameter, image, and blur estimation,” IEEE Trans. Image Process. 15, 3715–3727(2006).
[CrossRef] [PubMed]

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

F. Sroubek and J. Flusser, “Multichannel blind deconvolution of spatially misaligned images,” IEEE Trans. Image Process. 14, 874–883 (2005).
[CrossRef] [PubMed]

Y. You and M. Kaveh, “A regularization approach to joint blur identification and image restoration,” IEEE Trans. Image Process. 5, 416–428 (1996).
[CrossRef] [PubMed]

D. Tzikas, A. Likas, and N. Galatsanos, “Variational Bayesian sparse kernel-based blind image deconvolution with student’s-t priors,” IEEE Trans. Image Process. 18, 753–764 (2009).
[CrossRef] [PubMed]

G. Harikumar and Y. Bresler, “Exact image deconvolution from multiple FIR blurs,” IEEE Trans. Image Process. 8, 846–862 (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]

A. J. Patti, M. I. Sezan, and A. M. Tekalp, “Superresolution video reconstruction with arbitrary sampling lattices and nonzero aperture time,” IEEE Trans. Image Process. 6, 1064–1076 (1997).
[CrossRef] [PubMed]

IEEE Trans. Signal Process.

A. Katsaggelos and K. Lay, “Maximum likelihood blur identification and image restoration using the EM algorithm,” IEEE Trans. Signal Process. 39, 729–733 (1991).
[CrossRef]

J. Math. Imaging Vision

A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision 20, 73 (2004).
[CrossRef]

M. Ng, L. Qi, Y. Yang, and Y. Huang, “On semismooth Newton’s methods for total variation minimization,” J. Math. Imaging Vision 27, 265–276 (2007).
[CrossRef]

J. Opt. Soc. Am. A

Multiscale Model. Simul.

Y. Huang, M. Ng, and Y. Wen, “A fast total variation minimization method for image restoration,” Multiscale Model. Simul. 7, 774–795 (2008).
[CrossRef]

T. Chan and K. Chen, “An optimization-based multilevel algorithm for total variation image denoising,” Multiscale Model. Simul. 5, 615–645 (2006).
[CrossRef]

Opt. Lett.

Pattern Recogn. Lett.

A. Rav-Acha and S. Peleg, “Two motion-blurred images are better than one,” Pattern Recogn. Lett. 26, 311–317 (2005).
[CrossRef]

Physica D (Amsterdam)

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

SIAM J. Imaging Sci.

Y. Huang, M. Ng, and Y. Wen, “A new total variation method for multiplicative noise removal,” SIAM J. Imaging Sci. 2, 20–40 (2009).
[CrossRef]

SIAM J. Sci. Comput.

C. Vogel and M. Oman, “Iterative method for total variation denoising,” SIAM J. Sci. Comput. 17, 227–238 (1996).
[CrossRef]

T. Chan, G. Golub, and P. Mulet, “A nonlinear primal-dual method for total variation-based image restoration,” SIAM J. Sci. Comput. 20, 1964–1977 (1999).
[CrossRef]

Other

A. M. Tekalp, Digital Video Processing (Prentice-Hall, 1995).

H. Andrew and B. Hunt, Digital Image Restoration (Prentice-Hall, 1977).

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Figures (8)

Fig. 1
Fig. 1

Cameraman image (first row) and satellite image (second row). From left to right, the original image, one of the observed images, the restored image by TVCP, and the proposed method, respectively.

Fig. 2
Fig. 2

Left, true PSFs; middle, restored PSFs by TVCP; right, restored PSFs by the proposed method.

Fig. 3
Fig. 3

Left, true PSFs; middle, restored PSFs by TVCP; right, restored PSFs by the proposed method.

Fig. 4
Fig. 4

Thirty-first, thirty-second, and thirty-third observed frames (top), the corresponding estimated frames (middle), and PSFs (bottom) of the book video.

Fig. 5
Fig. 5

Enlarged portions of the recorded frames (left) and the restored frames (right) of the thirty-second frame in Fig. 4.

Fig. 6
Fig. 6

Twenty-fifth, twenty-sixth, and twenty-seventh observed frames (top), corresponding estimated frames (middle), and PSFs (bottom) of the map video.

Fig. 7
Fig. 7

Enlarged portions of the recorded frames (left) and the restored frames (right) of the twenty-sixth frame in Fig. 6.

Fig. 8
Fig. 8

Relative successive difference of a PSF versus the number of iterations. Left, PSF of frame 33 of the book video; right, PSF of frame 27 of the map video.

Tables (1)

Tables Icon

Table 1 PSNRs (dB) of Image and PSFs, CPU Time (s), and Parameter Values of the Two Methods

Equations (15)

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

g ( x , t ) = 1 T a t T a t Ω h ( x y , τ ) f ( y , τ ) d y d τ + n ( x , t ) ,
y ( τ | u , t k ) = u + ( τ t k ) v k for     τ ( t k T a , t k ] ,
y ( τ | u , t i ) = u + d i , k + ( τ t i ) v i for     τ ( t i T a , t i ] .
g ( x , t i ) = 1 T a t i T a t i ( Ω h ( x u d i , k ( τ t i ) v i , τ ) f ( u , t k ) d u ) d τ + n ( x , t i ) , = 1 T a Ω ( t i T a t i h ( x u d i , k ( τ t i ) v i , τ ) ) f ( u , t k ) d u + n ( x , t i ) .
h i , k ( y ) = 1 T a t i T a t i h ( y d i , k ( τ t i ) v i ) τ ,
g ( x , t i ) = Ω h i , k ( x u ) f ( u , t k ) d u + n ( x , t i ) ,
g i = h i , k f k + n i .
J ( f k , h ¯ k ) = i g i h i , k f k 2 2 + α R ( f k ) + β Q ( h ¯ k ) .
u TV = 1 j , k n | ( x u ) j , k | 2 + | ( y u ) j , k | 2 .
R ( f k ) = min u α u α f k u 2 2 + u TV .
p r , s l + 1 = p r , s l + δ γ ( γ div p l f k ) r , s 1 + δ γ | ( γ div p l f k ) r , s | ,
F k ( w ) = i H i , k * ( w ) G i ( w ) + α u U ( w ) i | H i , k ( w ) | 2 + α u .
Q ( h ¯ k ) = i ( min v i λ i , k / β h i , k v i 2 2 + v i TV ) .
min h i , k , v i g i f k h i , k 2 2 + λ i , k h i , k v i 2 2 + β v i TV .
H i , k ( w ) = F k * ( w ) G i ( w ) + λ i , k V i ( w ) | F k ( w ) | 2 + λ i , k .

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