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Image Restoration Based on PDEs and a Non-local Algorithm

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Advances in Multimedia Information Processing - PCM 2010 (PCM 2010)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 6298))

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Abstract

Image restoration based on partial differential equations (PDEs) is an effective approach. However, most of the methods are based on using a local window, such as a 3×3 mask, operating on images. As a consequence, the anisotropic diffusion process seeks the local mode of a density when performing repeatedly, which may degrade the image details. However, a non-local (NL) algorithm can take advantage of all the possible self-predictions provided by the image. In this paper, image restoration based on PDEs is discussed and a NL algorithm is proposed. Experiments show that this method using the NL algorithm can improve the performance efficiently and significantly.

Project supported by the Natural Science Foundation of Fujian Province of China (No.2009J01301, 2008J0032, 2009J05087), and Science and Technology Planning Project of Xiamen (3502Z20083006).

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References

  1. Koenderink, J.J.: The structure of images. Biol Cybernet 50(5), 363–370 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  2. Hummel: A representations based on zero-crossing in scale-space. In: Fischler, M., Firschein, O. (eds.) Readings in Computer Vision: Issues problems Principles and Paradigms (1986)

    Google Scholar 

  3. Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. J. IEEE Trans.on PAMI 12(7), 629–639 (1990)

    Google Scholar 

  4. Catte, F., Coll, T., Lions, P.L., Morel, J.M., et al.: Image selective smoothing and edge detection by nonlinear diffusion. J. SIAM Number. Anal 29(1), 182–193 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  5. Alvarez, L., lions, P.L., Morel, J.M.: Image selective smoothing and edge detection by nonlinear diffusion. J. SIAM Numer Anal 29(3), 845–866 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  6. Barash, D., Comaniciu, D.: A Common Framework for Nonlinear Diffusion, Adaptive Smoothing, Bilateral Filtering and Mean Shift. J. Image and Vision Computing 22(1), 73–81 (2004)

    Article  Google Scholar 

  7. Buades, A., Coll, B., Morel, J.-M.: A non-local algorithm for image denoising. C. In: IEEE Computer Society Conference on CVPR., vol. 2, pp. 60–65 (2005)

    Google Scholar 

  8. Bettahar, S., Stambouli, A.B.: Shock filter coupled to curvature diffusion for image denoising and sharpening. J. Image Vis Comput. 26(11), 1481–1489 (2008)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Communication Engineering, Xiamen University, Xiamen, Fujian, China

    Lei Xu, Xiaoling Zhang & Jin Xie

  2. Centre for Signal Processing, Department of Electronic and Information Engineering, the Hong Kong Polytechnic University, Hong Kong, China

    Xiaoling Zhang & Kin-Man Lam

Authors
  1. Lei Xu
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  2. Xiaoling Zhang
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  3. Kin-Man Lam
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  4. Jin Xie
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Editor information

Editors and Affiliations

  1. School of Computer Science, University of Nottingham, Jubilee Campus, NG8 1BB, Nottingham, UK

    Guoping Qiu

  2. The Centre for Multimedia Signal Processing, The Hong Kong Polytechnic University, Hong Kong, China

    Kin Man Lam

  3. Faculty of System Design, Tokyo Metropolitan University, 6-6, Asahigaoka, 191-0065, Tokyo, Hino-city

    Hitoshi Kiya

  4. Shanghai Key Laboratory of Intelligent Information Processing, Department of Computer Science & Engineering, Fudan University, Shanghai, China

    Xiang-Yang Xue

  5. Department of Electrical Engineering, University of Southern California, 90089-2564, Los Angeles, CA

    C.-C. Jay Kuo

  6. LIACS Media Lab, Leiden University,  

    Michael S. Lew

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© 2010 Springer-Verlag Berlin Heidelberg

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Xu, L., Zhang, X., Lam, KM., Xie, J. (2010). Image Restoration Based on PDEs and a Non-local Algorithm. In: Qiu, G., Lam, K.M., Kiya, H., Xue, XY., Kuo, CC.J., Lew, M.S. (eds) Advances in Multimedia Information Processing - PCM 2010. PCM 2010. Lecture Notes in Computer Science, vol 6298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15696-0_34

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  • DOI: https://doi.org/10.1007/978-3-642-15696-0_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15695-3

  • Online ISBN: 978-3-642-15696-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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