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Convex regularized inverse filtering methods for blind image deconvolution

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Abstract

In this paper, we study a regularized inverse filtering method for blind image deconvolution. The main idea is to make use of nonnegativity and support constraints, and to incorporate regularization terms to establish a convex programming model which aims to determine an inverse filter for image deconvolution. Because of the convexity of the proposed energy functional, the existence of the solution can be guaranteed. We employ the alternating direction method of multipliers to solve the resulting optimization problem. In this paper, we consider three possible regularization methods in the inverse filtering, namely total variation, nonlocal total variation, and framelet approaches. Experimental results of these regularization methods are reported to show that the performance of the proposed methods is better than the other testing methods for several testing images.

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Notes

  1. The detailed comparison of different sizes of inverse filters can be found in Experiment 3.

References

  1. Kundur, D., Hatzinakos, D.: Blind image deconvolution. IEEE Signal Process. Mag. 13, 43–64 (1996)

  2. Ayers, G.R., Dainty, J.C.: Iterative blind deconvolution method and its applications. Opt. Lett. 13, 547–549 (1988)

    Article  Google Scholar 

  3. McCallum, B.C.: Blind deconvolution by simulated annealing. Opt. Commun. 75, 101–105 (1990)

    Article  Google Scholar 

  4. Kundur, D.: Blind deconvolution of still images using recursive inverse filtering. M. A. Sc. thesis, Univ. Toronto, Toronto, Ont., Canada (1995)

  5. Kundur, D., Hatzinakos, D.: A novel blind deconvolution scheme for image restoration using recursive filtering. IEEE Trans. Signal Process. 46, 375–390 (1998)

    Article  MathSciNet  Google Scholar 

  6. Ong, C.A., Chambers, J.A.: An enhanced NAS-RIF algorithm for blind image deconvolution. IEEE Trans. Image Process. 8(7), 988–992 (1999)

    Article  Google Scholar 

  7. Xue, M., Yang, L., Zou, C., He, Z.: A modified NAS-RIF blind lmage restoration algorithm for noisy binary images. In: 6th International Conference on Signal Processing (2002)

  8. Matsuyama, M., Tanji, Y., Tanaka, M.: Enhancing the ability of NAS-RIF algorithm for blind image deconvolution. In: IEEE International Symposium on Circuits and Systems, May 28–31. Geneva, Switzerland (2000)

  9. Masuda, H., Kuroki, N., Numa, M., Hirano, K.: Layered blind deconvolution with interband prediction. Trans. IEICE 381–D(12), 2712–2717 (1998)

  10. Ng, M.K., Plemmons, R.J., Qiao, S.: Regularization of RIF blind image deconvolution. IEEE Trans. Image Process. 9(6), 1130–1134 (2000)

    Article  Google Scholar 

  11. Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  13. You, Y., Kaveh, M.: Blind image restoration by anisotropic regularization. IEEE Trans. Image Process. 8(3), 396–407 (1999)

    Article  Google Scholar 

  14. Chan, S., Gill, P., Nguyen, T.: An augmented Lagrangian method for total variation image restoration. IEEE Trans. Image Process. 20, 3011–3097 (2011)

    MathSciNet  Google Scholar 

  15. Tofighi, Mohammad, Yorulmaz, Onur, Köse, Kivanç, Cansen Yıldırım, Deniz, Çetin-Atalay, Rengül, Enis Çetin, A.: Phase and TV based convex sets for blind deconvolution of microscopic images. IEEE J. Sel. Top. Signal Process. 10(1), 81–91 (2016)

    Article  Google Scholar 

  16. Huang, Y., Ng, M.: Lipschitz and total-variational regularization for blind deconvolution. Commun. Comput. Phys. 4, 195–206 (2008)

    MathSciNet  Google Scholar 

  17. Lou, Y., Zhang, X., Osher, S., Bertozzi, A.: Image recovery via nonlocal operators. J. Sci. Comput. 42, 185–197 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  18. Peyre, G., Bougleux, S., Cohen, L.: Non-local regularization of inverse problems. ECCV, Part III, LNCS 5304, 57–68 (2008)

    MATH  Google Scholar 

  19. Zhang, X., Burger, M., Bresson, X., Osher, S.: Bregmanized nonlocal regularization for deconvolution and sparse reconstruction. SIAM J. Imaging Sci. 3(3), 253–276 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  20. Wang, W., Ng, M.K.: A nonlocal total variation model for image decomposition: illumination and reflectance. Numer. Math.: Theory Methods Appl. 7, 334–355 (2014)

    MathSciNet  MATH  Google Scholar 

  21. Cai, Jian-Feng., Ji, Hui., Liu, Chaoqiang., Shen, Zuowei.: Blind motion deblurring using multiple images. UCLA Cam Report 09–59

  22. Cai, J.-F., Ji, H., Liu, C., Shen, Z.: High-quality curvelet-based motion deblurring from an image pair. UCLA Cam Report 09-60

  23. Cai, J.-F., Ji, H., Liu, C., Shen, Z.: Blind motion deblurring from a single image using sparse approximation. UCLA Cam Report 09–61

  24. Chai, Anwei, Shen, Zuowei: Deconvolution: a wavelet frame approach. Numer. Math. 106, 529–587 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  25. Wang, W., Ng, M.K.: On Algorithms for automatic deblurring from a single image. J. Comput. Math. 30(1), 80–100 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  26. Goldstein, Tom, Osher, Stanley: The split Bregman method for L1 regularized problems. SIAM J. Imaging Sci. 2, 323–343 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  27. Cai, J., Osher, S., Shen, Z.: Split Bregman methods and frame based image restoration. SIAM J. Multiscale Model. Simul. 8, 337–369 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  28. Eckstein, J., Bertsekas, D.: On the Douglas–Rachford splitting method and the proximal point algorithm for maximal monotone operators. Mathematical Programming 55, North-Holland (1992)

  29. Ng, M., Yuan, X., Wang, F.: Inexact alternating direction methods for image recovery. SIAM J. Sci. Comput. 33(4), 1643–1668 (2011)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

Research of Wei Wang is supported by National Natural Science Foundation of China (Grant No. 11201341). Research of Michael K. Ng is supported by RGC GRF Grant Nos. 202013, 12301214 and HKBU FRG Grant No. FRG2/14-15/087.

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Authors and Affiliations

  1. Department of Mathematics, Tongji University, Shanghai, China

    Wei Wang

  2. Centre for Mathematical Imaging and Vision and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Michael K. Ng

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  1. Wei Wang
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  2. Michael K. Ng
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Correspondence to Wei Wang.

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Wang, W., Ng, M.K. Convex regularized inverse filtering methods for blind image deconvolution. SIViP 10, 1353–1360 (2016). https://doi.org/10.1007/s11760-016-0924-3

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