Skip to main content
Log in

Fast and Robust linear motion deblurring

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

We investigate efficient algorithmic realisations for robust deconvolution of grey-value images with known space-invariant point-spread function, with emphasis on 1D motion blur scenarios. The goal is to make deconvolution suitable as preprocessing step in automated image processing environments with tight time constraints. Candidate deconvolution methods are selected for their restoration quality, robustness and efficiency. Evaluation of restoration quality and robustness on synthetic and real-world test images leads us to focus on a combination of Wiener filtering with few iterations of robust and regularised Richardson–Lucy deconvolution. We discuss algorithmic optimisations for specific scenarios. In the case of uniform linear motion blur in coordinate direction, it is possible to achieve real-time performance (less than 50 ms) in single-threaded CPU computation on images of \(256\times 256\) pixels. For more general space-invariant blur settings, still favourable computation times are obtained. Exemplary parallel implementations demonstrate that the proposed method also achieves real-time performance for general 1D motion blurs in a multi-threaded CPU setting and for general 2D blurs on a GPU.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Almeida, M.S.C., Almeida, L.B.: Blind and semi-blind deblurring of natural images. IEEE Trans. Image Process. 19(1), 36–52 (2010)

    Article  MathSciNet  Google Scholar 

  2. Bar, L., Sochen, N., Kiryati, N.: Image deblurring in the presence of salt-and-pepper noise. In: Kimmel, R., Sochen, N., Weickert, J. (eds.) Scale Space and PDE Methods in Computer Vision, Lecture Notes in Computer Science, vol. 3459, pp. 107–118. Springer, Berlin (2005)

    Chapter  Google Scholar 

  3. Bronstein, I.N., Semendyaev, K.A.: Taschenbuch der Mathematik. Teubner, Leipzig (1979)

    Google Scholar 

  4. Chan, T.F., Yip, A.M., Park, F.E.: Simultaneous total variation image inpainting and blind deconvolution. Int. J. Imaging Syst. Technol. 15(1), 92–102 (2005)

    Article  Google Scholar 

  5. Colton, D., Kress, R.: Inverse Acoustic and Electromagnetic Scattering Theory. Springer, Berlin (1992)

    Book  MATH  Google Scholar 

  6. Dey, N., Blanc-Feraud, L., Zimmer, C., Roux, P., Kam, Z., Olivo-Marin, J.C., Zerubia, J.: Richardson–Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution. Microsc. Res. Tech. 69, 260–266 (2006)

    Article  Google Scholar 

  7. Elhayek, A., Welk, M., Weickert, J.: Simultaneous interpolation and deconvolution model for the 3-D reconstruction of cell images. In: Mester, R., Felsberg, M. (eds.) Pattern Recognition, Lecture Notes in Computer Science, vol. 6835, pp. 316–325. Springer, Berlin (2011)

    Google Scholar 

  8. Hirsch, M., Schuler, C.J., Harmeling, S., Schölkopf, B.: Fast removal of non-uniform camera shake. In: Proceedings of IEEE International Conference on Computer Vision, pp. 463–470, Barcelona (2011)

  9. Huber, P.J.: Robust Statistics. Wiley, New York (1981)

    Book  MATH  Google Scholar 

  10. Klosowski, J.T., Krishnan, S.: Real-time image deconvolution on the GPU. In: Owens, J.D., Lin, I.J., Zhang, Y.J., Beretta, G.B. (eds.) Parallel Processing for Imaging Applications, Proceedings of SPIE, vol. 7872, pp. 1033–1041. SPIE Press, Bellingham (2011)

    Google Scholar 

  11. Krishnan, D., Fergus, R.: Fast image deconvolution using hyper-Laplacian priors. In: Advances in Neural Information Processing Systems, pp. 1033–1041 (2009)

  12. Lucy, L.B.: An iterative technique for the rectification of observed distributions. Astron. J. 79(6), 745–754 (1974)

    Article  Google Scholar 

  13. McDonnell, M.J.: Box-filtering techniques. Comput. Graph. Image Process. 17(1), 65–70 (1981)

    Article  Google Scholar 

  14. Richardson, W.H.: Bayesian-based iterative method of image restoration. J. Opt. Soc. Am. 62(1), 55–59 (1972)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  16. Snyder, D., Schulz, T.J., O’Sullivan, J.A.: Deblurring subject to nonnegativity constraints. IEEE Trans. Image Process. 40(5), 1143–1150 (1992)

    Article  MATH  Google Scholar 

  17. van Cittert, P.H.: Zum Einfluß der Spaltbreite auf die Intensitätsverteilung in Spektrallinien. II. Zeitschrift für Physik 65, 298–308 (1933)

    Google Scholar 

  18. Wang, Y., Yang, J., Yin, W., Zhang, Y.: A new alternating minimization algorithm for total variation image reconstruction. SIAM J. Imaging Sci. 1(3), 248–272 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  19. Welk, M.: Robust variational approaches to positivity-constrained image deconvolution. Technical Report 261, Department of Mathematics, Saarland University, Saarbrücken, Germany (2010)

  20. Welk, M., Theis, D., Brox, T., Weickert, J.: PDE-based deconvolution with forward-backward diffusivities and diffusion tensors. In: Kimmel, R., Sochen, N., Weickert, J. (eds.) Scale Space and PDE Methods in Computer Vision, Lecture Notes in Computer Science, vol. 3459, pp. 585–597. Springer, Berlin (2005)

    Chapter  Google Scholar 

  21. Welk, M., Theis, D., Weickert, J.: Variational deblurring of images with uncertain and spatially variant blurs. In: Kropatsch, W., Sablatnig, R., Hanbury, A. (eds.) Pattern Recognition, Lecture Notes in Computer Science, vol. 3663, pp. 485–492. Springer, Berlin (2005)

    Google Scholar 

  22. Wiener, N.: Extrapolation, Interpolation and Smoothing of Stationary Time Series with Engineering Applications. MIT Press, Cambridge (1949)

    MATH  Google Scholar 

  23. You, Y.L., Kaveh, M.: Anisotropic blind image restoration. In: Proceedings of 1996 IEEE International Conference on Image Processing, vol. 2, pp. 461–464. Lausanne, Switzerland (1996)

Download references

Acknowledgments

It is gratefully acknowledged that work on this project was funded by Standortagentur Tirol, Innsbruck, and done in cooperation with Datacon GmbH, Radfeld, and WESTCAM Projektmanagement GmbH, Mils.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Martin Welk.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Welk, M., Raudaschl, P., Schwarzbauer, T. et al. Fast and Robust linear motion deblurring. SIViP 9, 1221–1234 (2015). https://doi.org/10.1007/s11760-013-0563-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-013-0563-x

Keywords

Navigation