Skip to main content
Log in

Adaptive bidirectional diffusion for image restoration

  • Research Papers
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

A large number of applications in image processing and computer vision depend on image quality. In this paper, combining the forward diffusion with the backward diffusion by different weights, we present an adaptive bidirectional diffusion method for image denoising and deblurring simultaneously. Further, we introduce a gradient factor into the data fidelity term, which forms a spatially varying constraint and allows a better restoration of image edges and fine details. In order to obtain a stable solution, we develop a numerically stable scheme and give its theoretical analysis. Finally, we show advantages of this method in deblurring edges, denoising and restoring fine details of image compared with other related methods in experiments.

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.

Similar content being viewed by others

References

  1. Zhang Y D, Wu L N. Improved image filter based on SPCNN. Sci China Ser F-Inf Sci, 2008, 51: 2115–2125

    Article  Google Scholar 

  2. Chan T F, Shen J. Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods. Philadelphia: the Society for Industrial and Applied Mathematics, 2005

    MATH  Google Scholar 

  3. Tikhonov A N, Arsenin V Y. Solutions of Ill-posed Problems. Washington DC: Winston & Sons Incorporation, 1977

    MATH  Google Scholar 

  4. Nordstrom K N. Biased anisotropic diffusion—a unified regularization and diffusion approach to edge detection. Imag Vision Comput, 1990, 8: 318–327

    Article  Google Scholar 

  5. Witkin A P. Scale-space filtering. In: Proceedings of the International Joint Conference on Artificial Intelligence, Karlsruhe, West Germany, 1983. 1019–1021

  6. Koenderink J J. The structure of images. Bio Cybern, 1984, 50: 363–370

    Article  MATH  MathSciNet  Google Scholar 

  7. Perona P, Malik J. Scale-space and edge detection using anisotropic diffusion. IEEE Trans Patt Anal Mach Intell, 1990, 12: 629–639

    Article  Google Scholar 

  8. Alvarez L, Lions P L, Morel J M. Image selective smoothing and edge detection by nonlinear diffusion II. SIAM J Num Anal, 1992, 29: 845–866

    Article  MATH  MathSciNet  Google Scholar 

  9. Kornprobst P, Deriche R, Aubert G. Image coupling, restoration and enhancement via pde’s. In: Proceedings of the IEEE International Conference on Image Processing, Washington, DC, 1997. 458–461

  10. Keeling S L, Stollberger R. Nonlinear anisotropic diffusion filtering for multiscale edge enhancement. Inverse Problems, 2002, 18: 175–190

    Article  MATH  MathSciNet  Google Scholar 

  11. Gilboa G, Sochen N, Zeevi Y Y. Forward-and-backward diffusion processes for adaptive image enhancement and denoising. IEEE Trans Image Process, 2002, 11: 689–703

    Article  Google Scholar 

  12. Fu S, Ruan Q, Geng Y, et al. Feature-oriented coupled bidirectional flow for image denoising and edge sharpening. In: Proceedings of the IEEE International Region 10 Conference (Tencon 2005), Melbourne, Qld, 2006. 1–5

  13. Aubert G, Kornprobst P. Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations. 2nd ed. New York: Springer-Verlag, 2006

    MATH  Google Scholar 

  14. Liu F. Diffusion filtering in image processing based on wavelet transform. Sci China Ser F-Inf Sci, 2006, 49: 494–503

    Article  MATH  Google Scholar 

  15. Fu S, Ruan Q, Wang W, et al. A feature-dependent fuzzy bidirectional flow for adaptive image sharpening. Neurocomputing, 2007, 70: 883–895

    Google Scholar 

  16. Fu S, Ruan Q, Mu C, et al. Feature preserving coupled bidirectional flow for edge sharpening and image enhancement. Chin J Comput, 2008, 31: 529–535

    Article  MathSciNet  Google Scholar 

  17. Gabor D. Information theory in electron microscopy. Lab Invest, 1965, 14: 801–807

    Google Scholar 

  18. Hummel R A, Kimia B, Zucker SW. Deblurring Gaussian blur. Comput Vision Graph Image Process, 1987, 38: 66–80

    Article  Google Scholar 

  19. Kuijper A. Geometrical pdes based on second-order derivatives of gauge coordinates in image processing. Image Vision Comput, 2009, 27: 1023–1034

    Article  Google Scholar 

  20. Kovasznay L S G, Joseph H M. Image processing. Proc Instit Radio Eng, 1955, 43: 560–570

    Google Scholar 

  21. Wang W W, Wang Z M, Yuan Z Y, et al. A fast and adaptive method for complex-valued sar image denoising based on lk norm regularization. Sci China Ser F-Inf Sci, 2009, 52: 138–148

    Article  MATH  MathSciNet  Google Scholar 

  22. Yang J Y, Peng Y G, Xu W L, et al. Ways to sparse representation: an overview. Sci China Ser F-Inf Sci, 2009, 52: 695–703

    Article  MATH  MathSciNet  Google Scholar 

  23. Fu S, Zhang C. Adaptive non-convex total variation regularisation for image restoration. IET Electr Lett, 2010, 46: 907–908

    Article  Google Scholar 

  24. Lindenbaum M, Fischer M, Bruckstein A. On Gabor’s contribution to image enhancement. Patt Recog, 1994, 27: 1–8

    Article  Google Scholar 

  25. Buades A, Coll B, Morel J M. Image enhancement by non-local reverse heat equation. Technical report, Centre de Mathématiques et de Leurs Applications (CMLA), France, 2006

  26. Gilboa G, Sochen N, Zeevi Y Y. Variational denoising of partly textured images by spatially varying constraints. IEEE Trans Image Process, 2006, 15: 2281–2289

    Article  Google Scholar 

  27. Osher S, Paragios N. Geometric Level Set Methods in Imaging, Vision, and Graphics. New York: Springer-Verlag, 2003

    MATH  Google Scholar 

  28. Osher S, Fedkiw R P. Level Set Methods and Dynamic Implicit Surfaces. New York: Springer-Verlag, 2002

    Google Scholar 

  29. Weickert J, Romeny B, Viergever M A. Efficient and reliable schemes for nonlinear diffusion filtering. IEEE Trans Image Process, 1998, 7: 398–410

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to ShuJun Fu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fu, S., Zhang, C. Adaptive bidirectional diffusion for image restoration. Sci. China Inf. Sci. 53, 2452–2460 (2010). https://doi.org/10.1007/s11432-010-4108-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-010-4108-4

Keywords

Navigation