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Compound PDE-Based Image Restoration Algorithm Using Second-Order and Fourth-Order Diffusions

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Neural Information Processing (ICONIP 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9948))

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Abstract

A hybrid nonlinear diffusion-based image restoration technique is proposed in this article. The novel compound PDE denoising model combines nonlinear second-order and fourth-order diffusions to achieve a more effective image enhancement. The weak solution of the combined PDE, representing the restored digital image, is determined by developing a robust explicit numerical approximation scheme using the finite-difference method. The performed denoising tests and method comparison are also described in this paper.

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References

  1. Jain, A.K.: Fundamentals of Digital Image Processing. Prentice Hall, Upper Saddle River (1989)

    MATH  Google Scholar 

  2. Jansen, M.: Noise Reduction by Wavelet Thresholding. Springer, New York (2001)

    Book  MATH  Google Scholar 

  3. Weickert, J.: Anisotropic Diffusion in Image Processing, European Consortium for Mathematics in Industry. B.G. Teubner Stuttgart, Germany (1998)

    Google Scholar 

  4. Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. In: Proceedings of the IEEE Computer Society Workshop on Computer Vision, pp. 16–22, November 1987

    Google Scholar 

  5. Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D: Nonlinear Phenom. 60(1), 259–268 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen, Q., Montesinos, P., Sun, Q., Heng, P., Xia, D.: Adaptive total variation denoising based on difference curvature. Image Vis. Comput. 28(3), 298–306 (2010)

    Article  Google Scholar 

  7. Micchelli, C.A., Shen, L., Xu, Y., Zeng, X.: Proximity algorithms for image models II: L1/TV denosing. Adv. Comput. Math. 38(2), 401–426 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Cai, J.F., Osher, S., Shen, Z.: Split Bregman methods and frame based image restoration. Multiscale Model. Sim. 8(2), 337–369 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Barbu, T., Barbu, V., Biga, V., Coca, D.: A PDE variational approach to image denoising and restorations. Nonlinear Anal. RWA 10, 1351–1361 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Barbu, T., Favini, A.: Rigorous mathematical investigation of a nonlinear anisotropic diffusion-based image restoration model. Electr. J. Diff. Eqn. 129, 1–9 (2014)

    MATH  Google Scholar 

  11. You, Y.L., Kaveh, M.: Fourth-order partial differential equations for noise removal. IEEE Trans. Image Process. 9, 1723–1730 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  12. Lysaker, M., Lundervold, A., Tai, X.C.: Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time. IEEE Trans. Image Process. 12(12), 1579–1590 (2003)

    Article  MATH  Google Scholar 

  13. Barbu, T.: A PDE based Model for Sonar Image and Video Denoising. Analele Științifice ale Universității Ovidius, Constanța, Seria Matematică 19(3), 51–58 (2011)

    MathSciNet  MATH  Google Scholar 

  14. Barbu, T.: Nonlinear fourth-order hyperbolic PDE-based image restoration scheme. In: Proceedings of EHB 2015, Iaşi, Romania, pp. 19–21. IEEE, November 2015

    Google Scholar 

  15. Wang, H., Wang, Y., Ren, W.: Image denoising using anisotropic second and fourth order diffusions based on gradient vector convolution. Comput. Sci. Inf. Syst. 9, 1493–1512 (2012)

    Article  Google Scholar 

  16. Wu, J.Y., Ruan, Q.: Combining adaptive PDE and wavelet shrinkage in image denoising with edge enhancing property. In: Proceedings of the 18th International Conference on Pattern Recognition, vol. 3, pp. 718–721 (2006)

    Google Scholar 

  17. Johnson, P.: Finite Difference for PDEs. School of Mathematics, University of Manchester (2008)

    Google Scholar 

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Acknowledgments

This research is supported by project PN-II-RU-TE-2014-4-0083 (UEFSCDI Romania) and Institute of Computer Science of the Romanian Academy.

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Authors and Affiliations

  1. Institute of Computer Science of the Romanian Academy, Iaşi, Romania

    Tudor Barbu

Authors
  1. Tudor Barbu
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Correspondence to Tudor Barbu .

Editor information

Editors and Affiliations

  1. The University of Tokyo, Tokyo, Japan

    Akira Hirose

  2. Kobe University, Kobe, Japan

    Seiichi Ozawa

  3. Okinawa Institute of Science and Technology Graduate University, Onna, Japan

    Kenji Doya

  4. Nara Institute of Science and Technology, Ikoma, Japan

    Kazushi Ikeda

  5. Kyungpook National University, Daegu, Korea (Republic of)

    Minho Lee

  6. Chinese Academy of Sciences, Beijing, China

    Derong Liu

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Barbu, T. (2016). Compound PDE-Based Image Restoration Algorithm Using Second-Order and Fourth-Order Diffusions. In: Hirose, A., Ozawa, S., Doya, K., Ikeda, K., Lee, M., Liu, D. (eds) Neural Information Processing. ICONIP 2016. Lecture Notes in Computer Science(), vol 9948. Springer, Cham. https://doi.org/10.1007/978-3-319-46672-9_78

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  • DOI: https://doi.org/10.1007/978-3-319-46672-9_78

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46671-2

  • Online ISBN: 978-3-319-46672-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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