Abstract

We propose a maximum a posteriori blind Poissonian images deconvolution approach with framelet regularization for the image and total variation (TV) regularization for the point spread function. Compared with the TV based methods, our algorithm not only suppresses noise effectively but also recovers edges and detailed information. Moreover, the split Bregman method is exploited to solve the resulting minimization problem. Comparative results on both simulated and real images are reported.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Campisi and K. Egiazarian, eds., Blind Image Deconvolution: Theory and Applications (CRC, 2007).
  2. N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
    [CrossRef]
  3. Z. Xu and E. Y. Lam, Opt. Lett. 34, 1453 (2009).
    [CrossRef]
  4. L. Yan, H. Fang, and S. Zhong, Opt. Lett. 37, 2778 (2012).
    [CrossRef]
  5. D. A. Hope and S. M. Jefferies, Opt. Lett. 36, 867 (2011).
    [CrossRef]
  6. T. F. Chan and C. Wong, IEEE Trans. Image Process. 7, 370 (1998).
    [CrossRef]
  7. J. Cai, H. Ji, C. Liu, and Z. Shen, IEEE Trans. Image Process. 21, 562 (2012).
    [CrossRef]
  8. S. Lefkimmiatis, A. Bourquard, and M. Unser, IEEE Trans. Image Process. 21, 983 (2012).
    [CrossRef]
  9. T. Goldstein and S. Osher, SIAM J. Imaging Sci. 2, 323 (2009).
    [CrossRef]
  10. J. Cai, Framelet toolbox version 2.02, http://www.math.uiowa.edu/~jiancai/code/SplitBreg_Deblur.zip .
  11. http://www.cmnh.org/site/AtTheMuseum/PlanetariumandObservatory/AstronomyLectures.aspx .
  12. http://www.astrospider.com/images/moon/moon002.jpg .

2012 (3)

J. Cai, H. Ji, C. Liu, and Z. Shen, IEEE Trans. Image Process. 21, 562 (2012).
[CrossRef]

S. Lefkimmiatis, A. Bourquard, and M. Unser, IEEE Trans. Image Process. 21, 983 (2012).
[CrossRef]

L. Yan, H. Fang, and S. Zhong, Opt. Lett. 37, 2778 (2012).
[CrossRef]

2011 (1)

2009 (2)

Z. Xu and E. Y. Lam, Opt. Lett. 34, 1453 (2009).
[CrossRef]

T. Goldstein and S. Osher, SIAM J. Imaging Sci. 2, 323 (2009).
[CrossRef]

2006 (1)

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef]

1998 (1)

T. F. Chan and C. Wong, IEEE Trans. Image Process. 7, 370 (1998).
[CrossRef]

Blanc-Feraud, L.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef]

Bourquard, A.

S. Lefkimmiatis, A. Bourquard, and M. Unser, IEEE Trans. Image Process. 21, 983 (2012).
[CrossRef]

Cai, J.

J. Cai, H. Ji, C. Liu, and Z. Shen, IEEE Trans. Image Process. 21, 562 (2012).
[CrossRef]

Chan, T. F.

T. F. Chan and C. Wong, IEEE Trans. Image Process. 7, 370 (1998).
[CrossRef]

Dey, N.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef]

Fang, H.

Goldstein, T.

T. Goldstein and S. Osher, SIAM J. Imaging Sci. 2, 323 (2009).
[CrossRef]

Hope, D. A.

Jefferies, S. M.

Ji, H.

J. Cai, H. Ji, C. Liu, and Z. Shen, IEEE Trans. Image Process. 21, 562 (2012).
[CrossRef]

Kam, Z.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef]

Lam, E. Y.

Lefkimmiatis, S.

S. Lefkimmiatis, A. Bourquard, and M. Unser, IEEE Trans. Image Process. 21, 983 (2012).
[CrossRef]

Liu, C.

J. Cai, H. Ji, C. Liu, and Z. Shen, IEEE Trans. Image Process. 21, 562 (2012).
[CrossRef]

Olivo-Marin, J. C.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef]

Osher, S.

T. Goldstein and S. Osher, SIAM J. Imaging Sci. 2, 323 (2009).
[CrossRef]

Roux, P.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef]

Shen, Z.

J. Cai, H. Ji, C. Liu, and Z. Shen, IEEE Trans. Image Process. 21, 562 (2012).
[CrossRef]

Unser, M.

S. Lefkimmiatis, A. Bourquard, and M. Unser, IEEE Trans. Image Process. 21, 983 (2012).
[CrossRef]

Wong, C.

T. F. Chan and C. Wong, IEEE Trans. Image Process. 7, 370 (1998).
[CrossRef]

Xu, Z.

Yan, L.

Zerubia, J.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef]

Zhong, S.

Zimmer, C.

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef]

IEEE Trans. Image Process. (3)

T. F. Chan and C. Wong, IEEE Trans. Image Process. 7, 370 (1998).
[CrossRef]

J. Cai, H. Ji, C. Liu, and Z. Shen, IEEE Trans. Image Process. 21, 562 (2012).
[CrossRef]

S. Lefkimmiatis, A. Bourquard, and M. Unser, IEEE Trans. Image Process. 21, 983 (2012).
[CrossRef]

Microsc. Res. Tech. (1)

N. Dey, L. Blanc-Feraud, C. Zimmer, P. Roux, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, Microsc. Res. Tech. 69, 260 (2006).
[CrossRef]

Opt. Lett. (3)

SIAM J. Imaging Sci. (1)

T. Goldstein and S. Osher, SIAM J. Imaging Sci. 2, 323 (2009).
[CrossRef]

Other (4)

J. Cai, Framelet toolbox version 2.02, http://www.math.uiowa.edu/~jiancai/code/SplitBreg_Deblur.zip .

http://www.cmnh.org/site/AtTheMuseum/PlanetariumandObservatory/AstronomyLectures.aspx .

http://www.astrospider.com/images/moon/moon002.jpg .

P. Campisi and K. Egiazarian, eds., Blind Image Deconvolution: Theory and Applications (CRC, 2007).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

Restoration of a simulated degraded image. (a) Degraded image, image restoration by (b) RLTV, (c) RLSATV, and (d) BPIDFR.

Fig. 2.
Fig. 2.

NMSE versus the iteration number of the three methods for the brain image.

Fig. 3.
Fig. 3.

Restoration of a Saturn image [11]. (a) Degraded image, image restoration by (b) RLTV, (c) RLSATV, and (d) BPIDFR.

Fig. 4.
Fig. 4.

Restoration of a lunar soil image [12]. (a) Degraded image, restoration by (b) RLTV, (c) RLSATV, and (d) BPIDFR.

Tables (1)

Tables Icon

Table 1. NMSE of Degraded Image and the Best Restored Image (with the Lowest NSME) by Different Algorithms

Equations (9)

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

g=P(Hu)=P(Uh),
p(g|u,h)=i=1N(Hu)igiexp(Hu)igi!.
p(u)exp(τWu1),p(h)exp(αh1),
E(u,h)=i=1N[(Hu)igilog(Hu)i]+τWu1+αh1+lu0,
htk+1=hk1αdiv(hk|hk|){(Uk)T[gUkhk]},hk+1=htk+1i=1N(htk+1)i,
minu,d1,d2,d3i=1N[(d1)igilog(d1)i]+τd21+ld30(d3)+12γ(d1Hub122+d2Wub222+d3ub322),
uk+1=HT(d1kb1k)+WT(d2kb2k)+d3kb3kHTH+2I,
{d1k+1=12(sk+(sk)2+4γg),d2k+1=max{Wuk+1+b2k1τγ,0}Wuk+1+b2kWuk+1+b2k1,d3k+1=max{uk+1+b3k,0},
{b1k+1=b1k+Huk+1d1k+1,b2k+1=b2k+Wuk+1d2k+1,b3k+1=b3k+uk+1d3k+1.

Metrics