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Boosting normalized sparsity regularization for blind image deconvolution

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Abstract

We focus on blind image deconvolution, which has attracted intensive attentions since Fergus et al.’s influential work in 2006. Among the current literature, the daring idea of imposing the normalized sparsity measure on blind image deblurring is a recent spotlight, which is, nevertheless, far from practical use in terms of estimating accuracy, efficiency, as well as robustness. To boost its performance, we propose a novel method via coupling the normalized sparsity measure with the total generalized variation, which, however, does not fit the blind deblurring problem. By use of operator splitting and alternating direction method of multipliers, a numerical scheme is derived, leading to a more accurate, efficient, and robust blind deblurring algorithm. Numerous blind deblurring results on both benchmark data and real-world blurred images demonstrate the competitive or even better performance compared against the state of the art.

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Notes

  1. www.wisdom.weizmann.ac.il/~levina/papers/LevinEtalCVPR2011Code.zip

  2. Since March, 2013, the authors of [15] have successively released two executable software (implemented in C++) for blind motion deblurring, i.e., Robust Motion Deblurring System. The first version is v3.0.1 which implements the algorithm as detailed in [15], and the second version is v3.1 which incorporates the algorithms in both [15] and [14] for more accurate blur kernel estimation. The notation [15+14] means that we use the second version, i.e., v3.1, to produce the deblurred images.

References

  1. Chambolle, A., Lions, P.-L.: Image recovery via total variation minimization and related problems. Numer. Math. 76, 167–188 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  2. Fergus, R., Singh, B., Hertzmann, A., Roweis, S.T., Freeman, W.: Removing camera shake from a single photograph. ACM Trans. Graph. 25(3), 787–794 (2006)

    Article  Google Scholar 

  3. Babacan, S.D., Molina, R., Katsaggelos, A.K.: Variational Bayesian blind deconvolution using a total variation prior. IEEE Trans. Image Process. 18(1), 12–26 (2009)

    Article  MathSciNet  Google Scholar 

  4. Shao, W.-Z., Deng, H.-S., Ge, Q., Li, H.-B., Wei, Z.-H.: Regularized motion blur-kernel estimation with adaptive sparse image prior learning. Pattern Recognit. 51, 402–424 (2016)

    Article  Google Scholar 

  5. Levin, A., Weiss, Y., Durand, F., Freeman, W.T.: Efficient marginal likelihood optimization in blind deconvolution. IEEE CVPR (2011). doi:10.1109/CVPR.2011.5995308

    Google Scholar 

  6. Levin, A., Weiss, Y., Durand, F., Freeman, W.T.: Understanding blind deconvolution algorithms. IEEE Trans. Pattern Anal. Mach. Intell. 33(12), 2354–2367 (2011)

    Article  Google Scholar 

  7. Chan, T.F., Wong, C.K.: Total variation blind deconvolution. IEEE Trans. Image Process. 7(3), 370–375 (1998)

    Article  Google Scholar 

  8. Liao, H., Ng, M.K.: Blind deconvolution using generalized cross-validation approach to regularization parameter estimation. IEEE Trans. Image Process. 20, 670–680 (2011)

    Article  MathSciNet  Google Scholar 

  9. Kotera, J., Sroubek, F., Milanfar, P.: Blind deconvolution using alternating maximum a posteriori estimation with heavy-tailed priors. R. Wilson et al. (eds.): CAIP, Part II, LNCS 8048, pp. 59–66. (2013). doi:10.1007/978-3-642-40246-3-8

  10. Cho, S., Lee, S.: Fast motion deblurring. ACM Trans. Graph. 28(5), 145 (2009)

    Article  Google Scholar 

  11. Liu, R.W., Wu, D., Wu, C.S., Xiong, N.X.: Hybrid regularized Blur Kernel estimation for single-image blind deconvolutionl’. IEEE SMC (2015). doi:10.1109/SMC.2015.318

    Google Scholar 

  12. Krishnan, D., Tay, T., Fergus, R.: Blind deconvolution using a normalized sparsity measure. IEEE CVPR (2011). doi:10.1109/CVPR.2011.5995521

    Google Scholar 

  13. Shan, Q., Jia, J., Agarwala, A.: High-quality motion deblurring from a single image. ACM Trans. Graph. 27, 3 (2008)

    Google Scholar 

  14. Xu, L., Jia, J.: Two-phase kernel estimation for robust motion deblurring. ECCV 6311, 157–170 (2010). doi:10.1007/978-3-642-15549-9_12

  15. Xu, L., Zheng, S., Jia, J.: Unnatural \(L_{0}\) sparse representation for natural image deblurring. IEEE CVPR (2013). doi:10.1109/CVPR.2013.147

    Google Scholar 

  16. Daniele, P., Paolo, F.: Total variation blind deconvolution: the devil is in the details. IEEE CVPR (2014). doi:10.1109/CVPR.2014.372

    Google Scholar 

  17. Welk, M., Raudaschl, P., Schwarzbauer, T., et al.: Fast and Robust linear motion deblurring. Signal Image Video Process. 9, 1221 (2015)

    Article  Google Scholar 

  18. Kerouh, F., Serir, A.: Wavelet-based blind blur reduction. Signal Image Video Process. 9, 1587 (2015)

    Article  Google Scholar 

  19. Wang, W., Ng, M.K.: Convex regularized inverse filtering methods for blind image deconvolution. Signal Image Video Process. (2016). doi:10.1007/s11760-016-0924-3

    Google Scholar 

  20. Wang, R., Tao, D.: “Recent progress in image deblurring.” arXiv:1409.6838, unpublished

  21. Bredies, K., Kunisch, K., Pock, T.: Total generalized variation. SIAMJ Imaging Sci. 3(3), 492–526 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  22. Sun, Y., Li, Z., Wu, M.: A rank-constrained matrix representation for hypergraph-based subspace clustering. Math. Probl. Eng. 3, 1–12 (2015)

    MathSciNet  Google Scholar 

  23. Money, J.H., Kang, S.H.: Total variation minimizing blind deconvolution with shock filter reference. Image Vis. Comput. 26(2), 302–314 (2008)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  25. Chan, T.F., Marquina, A., Mulet, P.: Higher order total variation-based image restoration. SIAM J. Sci. Comput. 22(2), 503–516 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  26. Krishnan, D., Fergus, R.: Fast image deconvolution using hyper-laplacian priors. Adv. Neural Inf. Process. Syst. Proc. Conf. 22, 1033–1041 (2009)

    Google Scholar 

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Acknowledgements

We would like to show our gratitude to the anonymous reviewers for their serious, pertinent, and very helpful comments on the manuscript. This research was supported in part by the Natural Science Foundation (NSF) of China (61402239, 61302178, 61602257), the NSF of Jiangsu Province (BK20130868, BK20160904), and the NSF of Guangxi Province (2014GXNSFAA118360), the NSF for Jiangsu Institutions (15KJB520028, 16KJB520035), and the Jiangsu Key Lab. of Image and Video Understanding for Social Safety (Nanjing University of Science and Technology, 30920140122007).

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Authors and Affiliations

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

    Chang-Xing Yang & Wen-Ze Shao

  2. Jiangsu Key Laboratory of Image and Video Understanding for Social Safety, Nanjing University of Science and Technology, Nanjing, China

    Wen-Ze Shao

  3. School of Science, Guangxi University of Science and Technology, Liuzhou, China

    Li-Li Huang

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  1. Chang-Xing Yang
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Correspondence to Wen-Ze Shao.

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Yang, CX., Shao, WZ. & Huang, LL. Boosting normalized sparsity regularization for blind image deconvolution. SIViP 11, 681–688 (2017). https://doi.org/10.1007/s11760-016-1010-6

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