Unified Functional Framework for Restoration of Image Sequences Degraded by Atmospheric Turbulence

  • Naftali Zon
  • Nahum KiryatiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10746)


We propose a unified functional to address the restoration of turbulence-degraded images. This functional quantifies the association between a given image sequence and a candidate latent image restoration. Minimizing the functional using the alternating direction method of multipliers (ADMM) and Moreau proximity mapping leads to a general algorithmic flow. We show that various known algorithms can be derived as special cases of the general approach. Furthermore, we show that building-blocks used in turbulence recovery algorithms, such as optical flow estimation and blind deblurring, are called for by the general model. The main contribution of this work is the establishment of a unified theoretical framework for the restoration of turbulence-degraded images. It leads to novel turbulence recovery algorithms as well as to better understanding of known ones.



This research was supported in part by the Blavatnik Interdisciplinary Cyber Research Center, Tel Aviv University.


  1. 1.
    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, 2345–2356 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Aubailly, M., Vorontsov, M.A., Carhart, G.W., Valley, M.T.: Automated video enhancement from a stream of atmospherically-distorted images: the lucky-region fusion approach. In: Proceedings of the SPIE, vol. 7463 (2009)Google Scholar
  3. 3.
    Carhart, G.W., Vorontsov, M.A.: Synthetic imaging: nonadaptive anisoplanatic image correction in atmospheric turbulence. Opt. Lett. 23, 745–747 (1998)CrossRefGoogle Scholar
  4. 4.
    Chen, E., Haik, O., Yitzhaki, Y.: Detecting and tracking moving objects in long-distance imaging through turbulent medium. Appl. Opt. 53, 1181–1190 (2014)CrossRefGoogle Scholar
  5. 5.
    Cohen, B., Avrin, V., Belitsky, M., Dinstein, I.: Generation of a restored image from a video sequence recorded under turbulence effects. Opt. Eng. 36, 3312–3317 (1997)CrossRefGoogle Scholar
  6. 6.
    Combettes, P.L., Wajs, V.R.: Signal recovery by proximal forward-backward splitting. Multiscale Model. Simul. 4, 1168–1200 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Eckstein, J., Bertsekas, D.P.: On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program. 55, 293–318 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Elkabetz, A., Yitzhaki, Y.: Background modeling for moving object detection in long-distance imaging through turbulent medium. Appl. Opt. 53, 1132–1141 (2014)CrossRefGoogle Scholar
  9. 9.
    Feller, W.: An Introduction to Probability Theory and Its Applications. Wiley, Hoboken (1968)zbMATHGoogle Scholar
  10. 10.
    Fried, D.L.: Probability of getting a lucky short-exposure image through turbulence. J. Opt. Soc. Am. 68, 1651–1658 (1978)CrossRefGoogle Scholar
  11. 11.
    Gadot, D., Wolf, L.: Patchbatch: a batch augmented loss for optical flow. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2016)Google Scholar
  12. 12.
    Gal, R., Kiryati, N., Sochen, N.A.: Progress in the restoration of image sequences degraded by atmospheric turbulence. Pattern Recogn. Lett. 48, 8–14 (2014)CrossRefGoogle Scholar
  13. 13.
    Hirsch, M., Sra, S., Scholkopf, B., Harmeling, S.: Efficient filter flow for space-variant multiframe blind deconvolution. In: Computer Vision and Pattern Recognition (CVPR), pp. 607–614, June 2010Google Scholar
  14. 14.
    John, S., Vorontsov, M.A.: Multiframe selective information fusion from robust error estimation theory. IEEE Trans. Image Process. 14, 577–584 (2005)CrossRefGoogle Scholar
  15. 15.
    Joshi, N., Cohen, M.: Seeing Mt. Rainier: lucky imaging for multi-image denoising, sharpening, and haze removal. In: Proceedings of the IEEE ICCP (2010)Google Scholar
  16. 16.
    Kopeika, N.S.: A System Engineering Approach to Imaging. SPIE Optical Engineering Press, Bellingham (1998)CrossRefGoogle Scholar
  17. 17.
    Mao, Y., Gilles, J.: Turbulence stabilization. Proc. SPIE 8355, 83550H–83550H-7 (2012)Google Scholar
  18. 18.
    Roggemann, M.C., Stoudt, C.A., Welsh, B.M.: Image-spectrum signal-to-noise-ratio improvements by statistical frame selection for adaptive-optics imaging through atmospheric turbulence. Opt. Eng. 33, 3254–3264 (1994)CrossRefGoogle Scholar
  19. 19.
    Shacham, O., Haik, O., Yitzhaky, Y.: Blind restoration of atmospherically degraded images by automatic best step-edge detection. Pattern Recogn. Lett. 28, 2094–2103 (2007)CrossRefGoogle Scholar
  20. 20.
    Sun, D., Roth, S., Black, M.: A quantitative analysis of current practices in optical flow estimation and the principles behind them. Int. J. Comput. Vis. 106, 115–137 (2014)CrossRefGoogle Scholar
  21. 21.
    Vorontsov, M.A., Carhart, G.W.: Anisoplanatic imaging through turbulent media: image recovery by local information fusion from a set of short-exposure images. J. Opt. Soc. Am. A 18, 1312–1324 (2001)CrossRefGoogle Scholar
  22. 22.
    Yin, W., Osher, S., Goldfarb, D., Darbon, J.: Bregman iterative algorithms for \(l_1\)-minimization with applications to compressed sensing. SIAM J. Imaging Sci. 1, 143–168 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Zak, N.: Restoring an image of a moving object from a turbulence-distorted video. Master’s thesis, School of Electrical Engineering, Tel Aviv University, Israel (2015)Google Scholar
  24. 24.
    Zhu, X., Milanfar, P.: Removing atmospheric turbulence via space-invariant deconvolution. IEEE Trans. Pattern Anal. Mach. Intell. 35, 157–170 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Electrical EngineeringTel Aviv UniversityTel AvivIsrael

Personalised recommendations