Skip to main content
SpringerLink
Log in

A blending method based on partial differential equations for image denoising

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

In this paper we proposed a new de-noising technique based on combination of isotropic diffusion model, anisotropic diffusion (PM) model, and total variation model. The proposed model is able to be adaptive in each region depending on the information of the image. More precisely, the model performs more diffusion in the flat areas of the image, and less diffusion in the edges of the image. And so we can get rid of the noise, and preserve the edges of the image simultaneously. To verify that, we did several experiments, which showed that our algorithm is the best method for edge preserving and noise removing, compared with the isotropic diffusion, anisotropic diffusion, and total variation methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Andreu F, Mazón JM, Moll JS (2005) The total variation flow with nonlinear boundary conditions. Asymptotic Anal 43(1–2):9–46

    MATH  Google Scholar 

  2. Aubert G, Kornprobst P (2006) Mathematical Problems in Image Processing PDEs and the Calculus of Variations, 2nd edn. Springer, New York

    Google Scholar 

  3. Beck A, Teboulle M (2009) Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE T Image Process 18(11):2419–2434

    Article  MathSciNet  Google Scholar 

  4. Bijaoui A (2002) wavelets, gaussian mixtures and wiener filtering. Signal Process 82(4):709–712

    Article  MATH  Google Scholar 

  5. Catté F, Lions P-L, Morel J-M, Coll T (1992) Image selective smoothing and edge detection by nonlinear diffusion. SIAM J Numer Anal 29(1):182–193

    Article  MATH  MathSciNet  Google Scholar 

  6. Chang SG, Yu B, Vetterli M (2000) Spatially adaptive wavelet thresholding with context modeling for image denoising. IEEE T Image Process 9(9):1522–1531

    Article  MATH  MathSciNet  Google Scholar 

  7. Chatterjee P, Milanfar P (2010) Is denoising dead? IEEE T Image Process 19(4):895–911

    Article  MathSciNet  Google Scholar 

  8. Gallouët T, Herbin R (2004) Convergence of linear finite elements for diffusion equations with measure data. Comptes Rendus Mathematique 338(1):81–84

    Article  MATH  MathSciNet  Google Scholar 

  9. Garamendi JF, Gaspar FJ, Malpica N, Schiavi E (2013) Box relaxation schemes in staggered discretizations for the dual formulation of total variation minimization. IEEE T Image Process 22(5):2030–2043

    Article  MathSciNet  Google Scholar 

  10. Gilboa G, Sochen N, Zeevi YY (2002) Forward-and-backward diffusion processes for adaptive image enhancement and denoising. IEEE T Image Process 11(7):689–703

    Article  Google Scholar 

  11. Guo Z, Sun J, Zhang D, Wu B (2012) Adaptive Perona-Malik model based on the variable exponent for image denoising. IEEE T Image Process 21(3):958–967

    Article  MathSciNet  Google Scholar 

  12. Kannan K, Perumal SA, Arulmozhi K (2010) Optimal decomposition level of discrete, stationary and dual tree complex wavelet transform for pixel based fusion of multi-focused Images. Serbian J Elec Eng 7(1):81–93

    Article  Google Scholar 

  13. Li F, Gao F, Cai N (2011) A new algorithm for removing salt and pepper noise from images. J Inform Comput Sci 8(16):3819–3825

    Google Scholar 

  14. Liu J, Gao F, Li Z (2011) A model of image denoising based on partial differential equations. The Proceedings of IEEE International Conference on Multimedia Technology (ICMT), China, 26–28 July 2011. pp 1892–1896

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

    Article  MATH  Google Scholar 

  16. Lysaker M, Osher S, Tai X-C (2004) Noise removalusing smoothed normals and surface fitting. IEEE T Image Process 13(10):1345–1357

    Article  MATH  MathSciNet  Google Scholar 

  17. Lysaker M, Tai X-C (2006) Iterative image restoration combining total variation minimization and a second-order functional. Int J Comput Vision 66(1):5–18

    Article  MATH  Google Scholar 

  18. Mendrik AM, Vonken EJ, Rutten A, Viergever MA, Ginneken B (2009) Noise reduction in computed tomography scans using 3-D anisotropic hybrid diffusion with continuous switch. IEEE T Med Imaging 28(10):1585–1594

    Article  Google Scholar 

  19. Perona P, Malik J (1987) Scale space and edge detection using anisotropic diffusion. Proc. IEEE Comp. Soc. Workshop on Computer Vision (Miami Beach, Nov. 30–Dec. 2, 1987), IEEE Computer Society Press. Washington, pp 16–22

    Google Scholar 

  20. Perona P, Malik J (1988) A network for multiscale image segmentation, Proc. IEEE Int. Symp. Circuits and Systems (ISCAS-88, Espoo, June 7–9 1988), pp 2565–2568

  21. Perona P, Malik J (1990) Scale space and edge detection using anisotropic diffusion. IEEE T Pattern Anal 12(7):629–639

    Article  Google Scholar 

  22. Portilla J, Strela V, Wainwright MJ, Simoncelli EP (2003) Image denoising using scale mixtures of gaussians in the wavelet domain. IEEE T Image Process 12(11):1338–1351

    Article  MATH  MathSciNet  Google Scholar 

  23. Ram I, Elad M, Cohen I (2011) Generalized Ttree-based wavelet transform. IEEE T Signal Proces 59(9):4199–4209

    Article  MathSciNet  Google Scholar 

  24. Rudin L, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Phisica D 60(1–4):259–268

    Article  MATH  Google Scholar 

  25. Scherzer O, Weickert J (2000) Relations between regularization and diffusion filter. J Math Imaging Vis 12(1):43–63

    Article  MATH  MathSciNet  Google Scholar 

  26. Sorzanoa COS, Ortiza E, Lóezc M, Rodrigod J (2006) Improved bayesian image denoising based on wavelets with applications to electron microscopy. Pattern Recogn 39(6):1205–1213

    Article  Google Scholar 

  27. Tikhonov AN, Arsenin VY (1977) Solutions of Ill-Posed problem. Winston and Sons, Washington, D.C.

    Google Scholar 

  28. Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE T Image Process 13(4):1–14

    Article  Google Scholar 

  29. Weickert J (1998) Anisotropic Diffusion in Image Processing, University of Copenhagen Denmark Press

  30. Witkin AP (1983) Scale-space filtering. 8th International Joint Conference on Artificial Intelligence, vol 2. Karlsruhe, West Germany, pp 1019–1022

  31. Yahya AA, Tan J (2012) A novel partial differential equation method based on image features and its applications in denoising. In: The Proceedings of the Fourth IEEE International Conference on Digital Home (ICDH), Guangzhou, China, 23–25 Nov 2012, pp 46–51

  32. Zhang X, Wang R, Jiao LC (2011) Partial differential equation model method based on image feature for denoising. In: The Proceedings of IEEE International Workshop on Multi-Platform/Multi-Sensor Remote Sensing and Mapping (M2RSM), China, pp 1–4

Download references

Author information

Authors and Affiliations

  1. School of Computer and Information, Hefei University of Technology, Hefei, 230009, China

    Ali Abdullah Yahya, Jieqing Tan & Min Hu

Authors
  1. Ali Abdullah Yahya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jieqing Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Min Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ali Abdullah Yahya.

Additional information

This work is supported by the NSFC-Guangdong Joint Foundation (Key Project) under Grant No. U1135003 and the National Natural Science Foundation of China under Grant No. 61070227.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yahya, A.A., Tan, J. & Hu, M. A blending method based on partial differential equations for image denoising. Multimed Tools Appl 73, 1843–1862 (2014). https://doi.org/10.1007/s11042-013-1586-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-013-1586-6

Keywords

Search

Navigation