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RDEPS: A Combined Reaction-Diffusion Equation and Photometric Similarity Filter for Optical Image Restoration

  • Xueqing ZhaoEmail author
  • Pavlos Mavridis
  • Tobias Schreck
  • Arjan Kuijper
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10073)

Abstract

Restoration of optical images degraded by atmospheric turbulence and various types of noise is still an open problem. In this paper, we propose an optical image restoration method based on a Reaction-Diffusion Equation and Photometric Similarity (RDEPS). We exploit photometric similarity and geometric closeness of the optical image by combining a photometric similarity function and a appropriately defined reaction-diffusion equation. Our resulting RDEPS filter is used to restore images degraded by atmospheric turbulence and noise, including Gaussian noise and impulse noise. Extensive experimental results show that our method outperforms other recently developed methods in terms of PSNR and SSIM. Moreover, the computational efficiency analysis shows that our RDEPS provides efficient restoration of optical images.

Notes

Acknowledgement

This work supported by Doctor Scientific Research Foundation, Xi’an Polytechnic University, the Special Scientific Research Project of Education Department of Shaanxi Provincial Government (No. 16JK1328), and China Scholarship Council (CSC) Fund.

References

  1. 1.
    Anantrasirichai, N., Achim, A., Kingsbury, N.G., Bull, D.R.: Atmospheric turbulence mitigation using complex wavelet-based fusion. IEEE Trans. Image Process. 22(6), 2398–2408 (2013)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Arboleda, C., Wang, Z., Stampanoni, M.: Wavelet-based noise-model driven denoising algorithm for differential phase contrast mammography. Opt. Express 21(9), 10572–10589 (2013)CrossRefGoogle Scholar
  3. 3.
    Chen, F., Zhang, L., Yu, H.: External patch prior guided internal clustering for image denoising. In: 2015 IEEE International Conference on Computer Vision, ICCV, pp. 603–611 (2015)Google Scholar
  4. 4.
    Chen, G., Xie, W., Zhao, Y.: Wavelet-based denoising: a brief review. In: Intelligent Control and Information Processing (ICICIP). pp. 570–574, June 2013Google Scholar
  5. 5.
    Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Trans. Image Process. 16(8), 2080–2095 (2007)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Domingues Jr., M.O., Mendes, O., da Costa, A.M.: On wavelet techniques in atmospheric sciences. Adv. Space Res. 35(5), 831–842 (2005). Fundamentals of Space Environment ScienceCrossRefGoogle Scholar
  7. 7.
    Furhad, M.H., Tahtali, M., Lambert, A.: Restoring atmospheric-turbulence-degraded images. Appl. Opt. 55(19), 5082–5090 (2016)CrossRefGoogle Scholar
  8. 8.
    Ghimpeţeanu, G., Batard, T., Bertalmío, M., Levine, S.: Denoising an Image by denoising its components in a moving frame. In: Elmoataz, A., Lezoray, O., Nouboud, F., Mammass, D. (eds.) ICISP 2014. LNCS, vol. 8509, pp. 375–383. Springer, Heidelberg (2014). doi: 10.1007/978-3-319-07998-1_43 Google Scholar
  9. 9.
    Irum, I., Shahid, M., Sharif, M., Raza, M.: A review of image denoising methods. J. Eng. Sci. Technol. Rev. 8(5), 41–48 (2015)Google Scholar
  10. 10.
    Ji, Z., Xia, Y., Sun, Q., Xia, D., Feng, D.D.: Local Gaussian distribution fitting based FCM algorithm for brain MR image segmentation. In: Zhang, Y., Zhou, Z.-H., Zhang, C., Li, Y. (eds.) IScIDE 2011. LNCS, vol. 7202, pp. 318–325. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-31919-8_41 CrossRefGoogle Scholar
  11. 11.
    Jiang, J., Zhang, L., Yang, J.: Mixed noise removal by weighted encoding with sparse nonlocal regularization. IEEE Trans. Image Process. 23(6), 2651–2662 (2014)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Kuijper, A.: Geometrical PDEs based on second-order derivatives of gauge coordinates in image processing. Image Vis. Comput. 27(8), 1023–1034 (2009)CrossRefGoogle Scholar
  13. 13.
    Li, D., Mersereau, R.M., Simske, S.J.: Atmospheric turbulence-degraded image restoration using principal components analysis. IEEE Geosci. Remote Sensing Lett. 4(3), 340–344 (2007)CrossRefGoogle Scholar
  14. 14.
    Li, D., Simske, S.J.: Atmospheric turbulence degraded-image restoration by kurtosis minimization. IEEE Geosci. Remote Sens. Lett. 6(2), 244–247 (2009)CrossRefGoogle Scholar
  15. 15.
    Weickert, J.: Anisotropic Diffusion in Image Processing, vol. 1. Teubner, Stuttgart (1998)zbMATHGoogle Scholar
  16. 16.
    Niknejad, M., Rabbani, H., Babaie-Zadeh, M.: Image restoration using gaussian mixture models with spatially constrained patch clustering. IEEE Trans. Image Process. 24(11), 3624–3636 (2015)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Sampat, M.P., Wang, Z., Gupta, S., Bovik, A.C., Markey, M.K.: Complex wavelet structural similarity: a new image similarity index. IEEE Trans. Image Process. 18(11), 2385–2401 (2009)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Song, C., Ma, K., Li, A., Chen, X., Xu, X.: Diffraction-limited image reconstruction with SURE for atmospheric turbulence removal. Infrared Phys. Technol. 71, 171–174 (2015)CrossRefGoogle Scholar
  19. 19.
    Wang, X., Zhao, X., Guo, F., Ma, J.: Impulsive noise detection by double noise detector and removal using adaptive neural-fuzzy inference system. AEU-Int. J. Electron. Commun. 65(5), 429–434 (2011). ElsevierCrossRefGoogle Scholar
  20. 20.
    Xue, B., Cao, L., Cui, L., Bai, X., Cao, X., Zhou, F.: Analysis of non-Kolmogorov weak turbulence effects on infrared imaging by atmospheric turbulence MTF. Opt. Commun. 300, 114–118 (2013)CrossRefGoogle Scholar
  21. 21.
    Yan, L., Jin, M., Fang, H., Liu, H., Zhang, T.: Atmospheric-turbulence-degraded astronomical image restoration by minimizing second-order central moment. IEEE Geosci. Remote Sens. Lett. 9(4), 672–676 (2012)CrossRefGoogle Scholar
  22. 22.
    Yang, A., Lu, M., Teng, S., Sun, J.: Phase estimation based blind deconvolution for turbulence degraded images. In: 2013 International Conference on Virtual Reality and Visualization (ICVRV), pp. 273–276, September 2013Google Scholar
  23. 23.
    Zhao, X., Wang, X.: Novel adaptive high-performance and nonlinear filtering algorithm for mixed noise removal. J. Electron. Imaging 21(2), 023005 (2012)CrossRefGoogle Scholar
  24. 24.
    Zhu, X., Milanfar, P.: Removing atmospheric turbulence via space-invariant deconvolution. IEEE Trans. Pattern Anal. Mach. Intell. 35(1), 157–170 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Xueqing Zhao
    • 1
    • 2
    Email author
  • Pavlos Mavridis
    • 2
  • Tobias Schreck
    • 2
  • Arjan Kuijper
    • 3
    • 4
  1. 1.School of Computer ScienceXi’an Polytechnic UniversityXi’anChina
  2. 2.Institute for Computer Graphics and Knowledge VisualizationGraz University of TechnologyGrazAustria
  3. 3.Fraunhofer IGDDarmstadtGermany
  4. 4.Technische Universität DarmstadtDarmstadtGermany

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