Skip to main content
Springer Nature Link
Log in

Kullback–Leibler Divergence Based Composite Prior Modeling for Bayesian Super-Resolution

  • Published:
Journal of Scientific Computing Aims and scope Submit manuscript

Abstract

This paper proposes to adaptively combine the known total variation model and more recent Frobenius norm regularization for multi-frame image super-resolution (SR). In contrast to existing literature, in this paper both the composite prior modeling and posterior variational optimization are achieved in the Bayesian framework by utilizing the Kullback–Leibler divergence, and hyper-parameters related to the composite prior and noise statistics are all determined automatically, resulting in a spatially adaptive SR reconstruction method. Experimental results demonstrate that the new approach can generate a super-resolved image with higher signal-to-noise ratio and better visual perception, not only image details better preserved but also staircase effects better suppressed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Ng, M.K., Shen, H., Lam, E.Y., Zhang, L.: A total variation regularization based super-resolution reconstruction algorithm for digital video. EURASIP J. Adv. Signal Process. (74585), 1–16 (2007)

  2. Cristani, M., Cheng, D.S., Murino, V., Pannullo, D.: Distilling information with super-resolution for video surveillance. In: Proceedings of the ACM 2nd international workshop on Video surveillance and sensor, networks, pp. 2–11 (2004)

  3. Li, F., Jia, X., Fraser, D., Andrew, L.: Super resolution for remote sensing images based on a universal hidden Markov tree model. IEEE Trans. Geosci. Remote Sens. 48(3), 1270–1278 (2010)

    Article  Google Scholar 

  4. Yang, J., Wright, J., Huang, T., Ma, Y.: Image superresolution via sparse representation. IEEE Trans. Image Process. 19(11), 2861–2873 (2010)

    Article  MathSciNet  Google Scholar 

  5. Robinson, M.D., Chiu, S.J., Lo, J.Y., Toth, C.A., Izatt, J.A., Farsiu, S.: Novel applications of super-resolution in medical imaging. In: Milanfar, Peyman (ed.) Super-Resolution Imaging, pp. 383–412. CRC Press, Boca Raton (2010)

    Google Scholar 

  6. Kang, M., Chaudhuri, S. (ed.): Super-resolution image reconstruction. IEEE Signal Process. Mag. 20(3), 19–20 (2003)

  7. Milanfar, P.: Super-Resolution Imaging. CRC Press, New York (2011)

    Google Scholar 

  8. Katsaggelos, A.K., Molina, R., Mateos, J.: Super Resolution of Images and Video. Morgan and Claypool, San Rafael (2007)

    Google Scholar 

  9. Hardie, R.C., Barnard, K.J., Armstrong, E.E.: Join MAP registration and high resolution image estimation using a sequence of undersampled images. IEEE Trans. Image Process. 6(12), 1621–1633 (1997)

    Article  Google Scholar 

  10. He, H., Kondi, L.P.: MAP based resolution enhancement of video sequences using a Huber-Markov random field image prior model. Int. Conf. Image Process. 3, 933–936 (2003)

    Google Scholar 

  11. Marquina, A., Osher, S.J.: Image super-resolution by TV-regularization and Bregman iteration. J. Sci. Comput. 37(3), 367–382 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  12. Farsiu, S., Robinson, M.D., Elad, M., Milanfar, P.: Fast and robust multiframe super resolution. IEEE Trans. Image Process. 13(10), 1327–1344 (2004)

    Article  Google Scholar 

  13. Zeng, W.L., Lu, X.B.: A robust variational approach to super-resolution with nonlocal TV regularisation term. The Imaging Science Journal (2012) accepted

  14. Babacan, S.D., Molina, R., Katsaggelos, A.K.: Variational Bayesian super resolution. IEEE Trans. Image Process. 20(4), 984–999 (2011)

    Article  MathSciNet  Google Scholar 

  15. Lefkimmiatis, S., Bourquard, A., Unser, M.: Hessian-based norm regularization for image restoration with biomedical applications. IEEE Trans. Image Process. 21(3), 983–995 (2012)

    Article  MathSciNet  Google Scholar 

  16. Lysaker, M., Tai, X.-C.: Iterative image restoration combining total variation minimization and a second-order functional. Int. J. Comput. Vision. 66(1), 5–18 (2006)

    Article  MATH  Google Scholar 

  17. Yang, J., Zhang, Y., Yin, W.: A fast alternating direction method for TVL1-L2 signal reconstruction from partial fourier data. IEEE J. Sel. Top. Signal Process. 4(2), 288–297 (2010)

    Article  Google Scholar 

  18. Shao, W.-Z., Deng, H.-S., Wei, Z.-H.: Multi-Parseval frame-based nonconvex sparse image deconvolution. Opt. Eng. 51(6), 067008–067008-12 (2012)

    Article  Google Scholar 

  19. Li, F., Shen, C., Fan, J., Shen, C.: Image restoration combining a total variational filter and a fourth-order filter. J. Visual Commun. Image Represent 18(4), 322–330 (2007)

    Article  Google Scholar 

  20. Mignotte, M.: Fusion of regularization terms for image restoration. J. Electron. Imaging 19, 033004 (2010)

    Article  MathSciNet  Google Scholar 

  21. Afonso, M.V., Bioucas-Dias, J.M., Figueiredo, M.A.T.: Fast image recovery using variable splitting and constrained optimization. IEEE Trans. Image Process. 19(9), 2345–2356 (2010)

    Article  MathSciNet  Google Scholar 

  22. Villena, S., Vega, M., Babacan, S.D., Molina, R., Katsaggelos, A.K.: Using the Kullback-Leibler divergence to combine image priors in super-resolution image reconstruction. IEEE 17th international conference on image processing, pp. 893–896 (2010)

  23. Oliveira, J., Figueiredo, M., Bioucas-Dias, J.: Adaptative total variation image deblurring: a majorization-minimization approach. Signal Process. 89(9), 1683–1693 (2009)

    Article  MATH  Google Scholar 

  24. Tipping, M.E., Bishop, C.M.: Bayesian Image Super-Resolution. Advances in Neural Information Processing Systems (15). MIT Press, Cambridge (2003)

    Google Scholar 

  25. Kanemura, A., Maeda, S.-I., Ishii, S.: Superresolution with compound Markov random fields via the variational EM algorithm. Neural Netw. 22(7), 1025–1034 (2009)

    Article  Google Scholar 

  26. Pickup, L.C., Capel, D.P., Roberts, S.J., Zisserman, A.: Bayesian methods for image super-resolution. Comput. J. 52(1), 101–113 (2009)

    Article  Google Scholar 

  27. Zomet, A., Rav-Acha, A., Peleg, S.: Robust super-resolution. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 645–650 (2001)

  28. Shao, W. Z., Deng, H. S., Wei, Z. H.: A posterior mean approach for MRF-based spatially adaptive multi-frame image super-resolution. Signal Image Video Process. (2013). doi:10.1007/s11760-013-0458-x

Download references

Acknowledgments

Many thanks are given to the reviewers for their detailed and insightful comments, which have helped to significantly strengthen this manuscript. Wen-Ze Shao is grateful to Professor Yi-Zhong Ma and Dr. Min Wu for their kind supports in the past years. He also shows many thanks to other kind people for helping him through his lost and sad years. The work is supported in part by the Natural Science Foundation of Jiangsu Province (BK20130868), the Natural Science Research Foundation for Jiangsu Universities (13KJB510022), the Talent Introduction Foundation and Natural Science Foundation of Nanjing University of Posts and Telecommunications (NY212014, NY212039), and the Natural Science Foundation of China (61203270, 61071167).

Author information

Authors and Affiliations

  1. College of Telecommunications and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

    Wen-Ze Shao

  2. School of Mathematics and Statistics, Nanjing Audit University, Nanjing, 211815, China

    Hai-Song Deng

  3. School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing, 210094, China

    Zhi-Hui Wei

Authors
  1. Wen-Ze Shao
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Hai-Song Deng
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Zhi-Hui Wei
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Wen-Ze Shao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shao, WZ., Deng, HS. & Wei, ZH. Kullback–Leibler Divergence Based Composite Prior Modeling for Bayesian Super-Resolution. J Sci Comput 60, 60–78 (2014). https://doi.org/10.1007/s10915-013-9784-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10915-013-9784-y

Keywords

Mathematics Subject Classification