Skip to main content
SpringerLink
Log in

A Blur-SURE-Based Approach to Kernel Estimation for Motion Deblurring

  • Representation, Processing, Analysis, and Understanding of Images
  • Published:
Pattern Recognition and Image Analysis Aims and scope Submit manuscript

Abstract

Blind motion deblurring is a highly challenging inverse problem in image processing and low-level computer vision. In this paper, we propose a novel approach to identify the parameters (blur length and orientation) of motion blur from an observed image. The kernel estimation is based on a novel criterion — the minimization of a blurred Stein’s unbiased risk estimate (blur-SURE): an unbiased estimate of a filtered mean squared error. By incorporating a simple Wiener filtering into the blur-SURE, the motion blur is estimated by minimizing this new objective functional with high accuracy. We then perform non-blind deconvolution using the high-quality SURE-LET algorithm with the estimated kernel. The results of synthetic and real experiments are quite competitive with other state-of-the-art algorithms under a wide range of degradation scenarios both numerically and visually.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Fergus, B. Singh, A. Hertzmann, S. T. Roweis, and W. T. Freeman, “Removing camera shake from a single photograph,” ACM Trans. Graphics 25 (3), 787–794 (2006).

    Article  MATH  Google Scholar 

  2. Q. Shan, J. Jia, and A. Agarwala, “High-quality motion deblurring from a single image,” ACM Trans. Graphics 27 (3), Article No. 73 (2008).

    Google Scholar 

  3. A. Levin, Y. Weiss, F. Durand, and W. T. Freeman, “Understanding and evaluating blind deconvolution algorithms,” in Proc. 2009 IEEE Conf. on Computer Vision and Pattern Recognition (Miami, FL, USA, 2009), pp. 1964–1971.

    Google Scholar 

  4. D. Kundur and D. Hatzinakos, “Blind image deconvolution,” IEEE Signal Process. Mag. 13 (3), 43–64 (1996).

    Article  Google Scholar 

  5. R. Molina, J. Núñez, F. J. Cortijo, and J. Mateos, “Image restoration in astronomy: a Bayesian perspective,” IEEE Signal Process. Mag. 18 (2), 11–29 (2001).

    Article  Google Scholar 

  6. A. S. Carasso, “Linear and nonlinear image deblurring: A documented study,” SIAM J. Numer. Anal. 36 (6), 1659–1689 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  7. T. E. Bishop, S. D. Babacan, B. Amizic, A. K. Katsaggelos, T. Chan, and R. Molina, “Blind image deconvolution: Problem formulation and existing approaches,” in Blind Image Deconvolution: Theory and Applications, Ed. by P. Campisi and K. Egiazarian (CRC Press, Boca Raton, 2007), Chapter 1, pp. 1–42.

    Google Scholar 

  8. B. Amizic, R. Molina, and A. K. Katsaggelos, “Sparse Bayesian blind image deconvolution with parameter estimation,” EURASIP J. Image Video Process. 2012 (20), 15 pages (2012).

    Google Scholar 

  9. L. Yuan, J. Sun, L. Quan, and H.-Y. Shum, “Image deblurring with blurred/noisy image pairs,” ACM Trans. Graphics 26 (3), Article No. 1 (2007).

    Google Scholar 

  10. O. Whyte, J. Sivic, A. Zisserman, and J. Ponce, “Non-uniform deblurring for shaken images,” in Proc. 2010 IEEE Computer Society Conf. on Computer Vision and Pattern Recognition (San Francisco, CA, USA, 2010), pp. 491–498.

    Google Scholar 

  11. S. Cho and S. Lee, “Fast motion deblurring,” ACM Trans. Graphics 28 (5), Article No. 145 (2009).

    Google Scholar 

  12. A. Levin, Y. Weiss, F. Durand, and W. T. Freeman, “Efficient marginal likelihood optimization in blind deconvolution,” in Proc. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR 2011) (Colorado Springs, CO, USA, 2011), pp. 2657–2664.

    Google Scholar 

  13. N. Joshi, R. Szeliski, and D. J. Kriegman, “PSF estimation using sharp edge prediction,” in Proc. 2008 IEEE Conf. on Computer Vision and Pattern Recognition (CVPR 2008) (Anchorage, AK, USA, 2008), pp. 1–8.

    Google Scholar 

  14. M. Hirsch, C. J. Schuler, S. Harmeling, and B. Schölkopf, “Fast removal of non-uniform camera shake,” in Proc. 2011 IEEE Int. Conf. on Computer Vision (ICCV2011x) (Barcelona, Spain, 2011), pp. 463–470.

    Google Scholar 

  15. J. Gast, A. Sellent, and S. Roth, “Parametric object motion from blur,” in Proc. 2016 29th IEEE Conf. on Computer Vision and Pattern Recognition (CVPR 2016) (Las Vegas, NV, USA, 2016), pp. 1846–1854.

    Google Scholar 

  16. J. Pan, R. Liu, Z. Su, and G. Liu, “Motion blur kernel estimation via salient edges and low rank prior,” in Proc. 2014 IEEE Int. Conf. on Multimedia and Expo (ICME) (Chengdu, China, 2014), pp. 1–6.

    Google Scholar 

  17. D. Krishnan and R. Fergus, “Fast image deconvolution using hyper-Laplacian priors,” in Advances in Neural Information Processing Systems 22: Proc. Annual Conf. NIPS 2009 (Vancouver, Canada, 2015), pp. 1033–1041.

    Google Scholar 

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

    Article  Google Scholar 

  19. B. Amizic, S. D. Babacan, R. Molina, and A. K. Katsaggelos, “Sparse Bayesian blind image deconvolution with parameter estimation,” in Proc. 2010 18th European Signal Processing Conf. (Aalborg, Denmark, 2010), pp. 626–630.

    Google Scholar 

  20. F. Krahmer, Y. Lin, B. McAdoo, K. Ott, J. Wang, D. Widemann, and B. Wohlberg, “Blind image deconvolution: Motion blur estimation,” Technical Report, IMA Preprint Series # 2133-5 (Institute for Mathematics and its Applications, University of Minnesota, 2006).

    Google Scholar 

  21. J. P. Oliveira, M. A. T. Figueiredom, and J. M. Bioucas-Dias, “Parametric blur estimation for blind restoration of natural images: Linear motion and out-of-focus,” IEEE Trans. Image Process. 23 (1), 466–477 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  22. M. Ebrahimi Moghaddam and M. Jamzad, “Motion blur identification in noisy images using mathematical models and statistical measures,” Pattern Recogn. 40 (7), 1946–1957 (2007).

    Article  Google Scholar 

  23. J. P. Oliveira, M. A. T. Figueiredo, and J. M. Bioucas-Dias, “Blind estimation of motion blur parameters for image deconvolution,” in Pattern Recognition and Image Analysis, IbPRIA 2007, Ed. by J. Marti, J. M. Benedi, A. M. Mendonça, and J. Serrat, Lecture Notes in Computer Science (Springer, Berlin, Heidelberg, 2007), Vol. 4478, pp. 604–611.

    Google Scholar 

  24. W. T. Freeman and E. H. Adelson, “The design and use of steerable filters,” IEEE Trans. Pattern Anal. Mach. Intell. 13 (9), 891–906 (1991).

    Article  Google Scholar 

  25. J. Biemond, R. L. Lagendijk, and R. M. Mersereau, “Iterative methods for image deblurring,” Proc. IEEE 78 (5), 856–883 (1990).

    Article  Google Scholar 

  26. H. Ji and C. Liu, “Motion blur identification from image gradients,” in Proc. 2008 IEEE Conf. on Computer Vision and Pattern Recognition (CVPR 2008) (Anchorage, AK, USA, 2008), pp. 1–8.

    Google Scholar 

  27. H. Sun, M. Desvignes, and Y. Yunhui, “Motion blur adaptive identification from natural image model,” in Proc. 2009 16th IEEE Int. Conf. on Image Processing (ICIP 2009) (Cairo, Egypt, 2009), pp. 137–140.

    Google Scholar 

  28. H. Sun, M. Desvignes, Y. Yan, and W. Liu, “Motion blur parameters identification from Radon transform image gradients,” in Proc. 2009 35th Annual Conf. of IEEE Industrial Electronics (IECON 2009) (Porto, Portugal, 2009), pp. 2098–2103.

    Google Scholar 

  29. S. Dai and Y. Wu, “Motion from blur,” in Proc. 2008 IEEE Conf. on Computer Vision and Pattern Recognition (CVPR 2008) (Anchorage, AK, USA 2008), pp. 1–8.

    Google Scholar 

  30. S. J. Reeves and R. M. Mersereau, “Blur identification by the method of generalized cross-validation,” IEEE Trans. Image Process. 1 (3), 301–311 (1992).

    Article  Google Scholar 

  31. Y. Yitzhaky, I. Mor, A. Lantzman, and N. S. Kopeika, “Direct method for restoration of motion-blurred images,” J. Opt. Soc. Am. A. 15 (6), 1512–1519 (1998).

    Article  Google Scholar 

  32. A. Levin, “Blind motion deblurring using image statistics,” Advances in Neural Information Processing Systems 19: Proc. Annual Conf. NIPS 2006 (Vancouver, Canada, 2006), pp. 841–848.

    Google Scholar 

  33. C. M. Stein, “Estimation of the mean of a multivariate normal distribution,” Ann. Stat. 9 (6) 1135–1151 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  34. T. Blu and F. Luisier, “The SURE-LET approach to image denoising,” IEEE Trans. Image Process. 16 (11), 2778–2786 (2007).

    Article  MathSciNet  Google Scholar 

  35. Y. C. Eldar, “Generalized SURE for exponential families: Applications to regularization,” IEEE Trans. Signal Process. 57 (2), 471–481 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  36. J.-C. Pesquet, A. Benazza-Benyahia, and C. Chaux, “A SURE approach for digital signal/image deconvolution problems,” IEEE Trans. Signal Process. 57 (12), 4616–4632 (2009).

    Article  MathSciNet  Google Scholar 

  37. C. Vonesch, S. Ramani, and M. Unser, “Recursive risk estimation for non-linear image deconvolution with a wavelet-domain sparsity constraint,” in Proc. 2008 15th IEEE Int. Conf. on Image Processing (ICIP 2008) (San Diego, CA, USA, 2008), pp. 665–668.

    Google Scholar 

  38. R. Giryes, M. Elad, and Y. C. Eldar, “The projected GSURE for automatic parameter tuning in iterative shrinkage methods,” Appl. Comput. Harmonic Anal. 30 (3), 407–422 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  39. F. Xue, F. Luisier, and T. Blu, “SURE-LET image deconvolution using multiple Wiener filters,” in Proc. 2012 19th IEEE Int. Conf. on Image Processing (ICIP 2012) (Orlando, FL, USA, 2012), pp. 3037–3040.

    Google Scholar 

  40. F. Xue, F. Luisier, and T. Blu, “Multi-Wiener SURE-LET deconvolution,” IEEE Trans. Image Process. 22 (5), 1954–1968 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  41. F. Xue and T. Blu, “SURE-based blind Gaussian deconvolution,” in Proc. 2012 IEEE Statistical Signal Processing Workshop (SSP) (Ann Arbor, MI, USA), pp. 452–455.

  42. F. Xue and T. Blu, “A novel SURE-based criterion for parametric PSF estimation,” IEEE Trans. Image Process. 24 (2), 595–607 (2015).

    Article  MathSciNet  Google Scholar 

  43. F. Xue, J. Liu, S. Jiao, S. Liu, M. Zhao, Z. Niu, “SURE-type functionals as criteria for parametric PSF estimation,” J. Math. Imaging Vis. 54 (1), 78–105 (2016).

    Article  MathSciNet  Google Scholar 

  44. N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series, With Engineering Applications (Wiley, New York, 1964).

    Google Scholar 

  45. O. Michailovich and A. Tannenbaum, “Blind deconvolution of medical ultrasound images: A parametric inverse filtering approach,” IEEE Trans. Image Process. 16 (12), 3005–3019 (2007).

    Article  MathSciNet  Google Scholar 

  46. T. S. Cho, S. Paris, B. K. P. Horn, and W. T. Freeman, “Blur kernel estimation using the radon transform,” in Proc. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR 2011) (Colorado Springs, CO, USA, 2011), pp. 241–248.

    Google Scholar 

  47. S. Cho and S. Lee, “Fast motion deblurring,” ACM Trans. Graphics (SIGGRAPH Asia 2009) 28 (5), article no. 145 (2009).

    Google Scholar 

  48. L. Xu, J. Jia, “Two-phase kernel estimation for robust motion deblurring,” in Computer Vision — ECCV2010, Proc. 11th European Conf. on Computer Vision, Part I, Ed. by K. Daniilidis, P. Maragos, and N. Paragios, Lecture Notes in Computer Science (Springer, Berlin, Heidelberg, 2010), Vol. 6311, pp. 157–170.

  49. P. Pankajakshan, L. Blanc-Féraud, B. Zhang, Z. Kam, J. Olivo-Marin, and J. Zerubia, “Parametric blind deconvolution for confocal laser scanning microscopy (CLSM)-proof of concept,” Research Report RR-6493 (INRIA, 2008). https://hal.inria.fr/inria-00269265

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Foreign Languages, Renmin University of China, Beijing, 100872, China

    Jing Li

Authors
  1. Jing Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jing Li.

Additional information

The article is published in the original.

Jing Li was born in Hebei, China, in 1986. She received her Bachelor degree from School of Foreign Languages, Peking University, in 2011; Master degree in Translation and Interpretation in Public Services from Faculty of Humanities, Universidad de Alcalá, in 2012, and PhD in Humanities from Universidad Carlos III de Madrid, in 2015. She is currently with School of Foreign Languages, Renmin University of China, Beijing, China. Her main research interests include computational linguistics, corpus-based analysis, data processing and analysis.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, J. A Blur-SURE-Based Approach to Kernel Estimation for Motion Deblurring. Pattern Recognit. Image Anal. 29, 240–251 (2019). https://doi.org/10.1134/S1054661819010164

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1054661819010164

Keywords

Search

Navigation