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Anisotropic diffusion equation with a new diffusion coefficient for image denoising

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Abstract

This paper presents a new anisotropic diffusion model which is based on a new diffusion coefficient for image denoising. In the proposed model, a new diffusion coefficient and a method of automatically set gradient threshold parameter are introduced into an anisotropic diffusion model, which weakens the staircasing effect and preserves fine edges in a processed image. Comparative experiments show that the new model achieves the more satisfied denoising results than the other existing models.

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References

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

    Article  Google Scholar 

  2. Qiao NS, Zou BJ (2013) Nonlocal orientation diffusion partial differential equation model for optics image denoising. Optik 124:1889–1891

    Article  Google Scholar 

  3. Sun Z, Chen S, Qiao L (2014) A general non-local denoising model using multi-kernel-induced measures. Pattern Recogn 47:1751–1763

    Article  MATH  Google Scholar 

  4. Maleki A, Narayan M, Baraniuk RG (2013) Anisotropic nonlocal means denoising. Appl Comput Harmon Anal 35:452–482

    Article  MathSciNet  MATH  Google Scholar 

  5. Chen S, Liu M, Zhang W, Liu J (2013) Edge preserving image denoising with a closed form solution. Pattern Recogn 46:976–988

    Article  MATH  Google Scholar 

  6. Wang X, Yang H, Fu Z (2013) Edge structure preserving image denoising using OAGSM/NC statistical model. Digit Signal Process 23:200–212

    Article  MathSciNet  Google Scholar 

  7. Jin J, Yang B, Liang K, Wang X (2014) General image denoising framework based on compressive sensing theory. Comput Graph 38:382–391

    Article  Google Scholar 

  8. Oh S, Woo H, Yun S, Kang M (2013) Non-convex hybrid total variation for image denoising. J Vis Commun Image R 24:332–344

    Article  Google Scholar 

  9. Bao L, Robini M, Liu W, Zhu Y (2013) Structure adaptive sparse denoising for diffusion tensor MRI. Med Image Anal 17:442–457

    Article  Google Scholar 

  10. Liu X, Huang L (2014) A new nonlocal total variation regularization algorithm for image denoising. Math Comput Simul 97:224–233

    Article  MathSciNet  Google Scholar 

  11. Yang M, Liang J et al (2013) Non-local means theory based Perona–Malik model for image denosing. Neurocomputing 120:262–267

    Article  Google Scholar 

  12. Rousseeuw PJ, Leroy AM (1987) Robust regression and outlier detection. Wiley, New York

    Book  MATH  Google Scholar 

  13. Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13:600–612

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  15. Arian M, Manjari N, Richard B (2013) Anisotropic nonlocal means denoising. Appl Comput Harmon Anal 35:452–482

    Article  MathSciNet  MATH  Google Scholar 

  16. Wang Y, Ren W, Wang H (2013) Anisotropic second and fourth order diffusion models based on convolutional virtual electric field for image denoising. Comput Math Appl 66:1729–1742

    Article  MathSciNet  MATH  Google Scholar 

  17. Chang SG, Yu B, Vetterli M (2000) Adaptive wavelet thresholding for image denoising and compression. IEEE Trans Image Process 9(9):1532–1546

    Article  MathSciNet  MATH  Google Scholar 

  18. Somnath M, Mandal JK (2013) Wavelet based denoising of medical images using sub-band adaptive thresholding through genetic algorithm. Proc Technol 10:680–689

    Article  Google Scholar 

  19. Elad M (2002) On the origin of the bilateral filter and ways to improve it. IEEE Trans Image Process 11:1141–1151

    Article  MathSciNet  Google Scholar 

  20. Yang HY, Wang XY, Qu TX, Fu ZK (2011) Image denoising using bilateral filter and Gaussian scale mixtures in shiftable complex directional pyramid domain. Comput Elect Eng 37(5):656–668

    Article  MATH  Google Scholar 

  21. Buades A, Coll B, Morel J (2005) A non-local algorithm for image denoising. In: Proceedings of IEEE international conference on computer vision

  22. Hu J, Luo YP (2013) Non-local means algorithm with adaptive patch size and bandwidth. Optik 124:5639–5645

    Article  Google Scholar 

  23. Yang M, Liang J, Zhang J, Gao H, Meng F, Li X, Song S (2013) Non-local means theory based Perona–Malik model for image denosing. Neurocomputing 120:262–267

    Article  Google Scholar 

  24. Jidesh P (2014) A convex regularization model for image restoration. Comput Elect Eng 40:66–78

    Article  Google Scholar 

  25. Hashemi S, Beheshti S, Cobbold R, Paul N (2015) Adaptive updating of regularization parameters. Signal Process 113:228–233

    Article  Google Scholar 

  26. Liu X (2015) Efficient algorithms for hybrid regularizers based image denoising and deblurring. Comput Math Appl 69:675–687

    Article  MathSciNet  Google Scholar 

  27. Chen D, Chen Y, Xue D (2015) Fractional-order total variation image denoising based on proximity algorithm. Appl Math Comput 257:537–545

    MathSciNet  MATH  Google Scholar 

  28. Bigun J, Grandlund GH, (1987) Optimal orientation detection of linear symmetry, Proceedings 1st IEEE ICCV, London, June

  29. Goldstein T, Osher S (2009) The split Bregman method for \(L_1\)-regularized problems. SIAM J Imag Sci 2(2):323–343

    Article  MATH  Google Scholar 

  30. Liu K, Tan J, Su B (2014) An adaptive image denoising model based on Tikhonov and TV regularizations. Adv Multimed. doi:10.1155/2014/934834

    Google Scholar 

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

    Article  MATH  Google Scholar 

  32. Li ZC, Liu J, Tang J, Lu H (2015) Robust structured subspace learning for data representation. IEEE Trans Patt Anal Mach Intell 37(10):2085–2098

    Article  Google Scholar 

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Acknowledgements

The authors are grateful to the anonymous reviewers and the associate editor for their valuable comments, which have greatly helped us to improve this work. This work has been supported by the Transformation Project of High-Tech Result of CQEC KJZH14207.

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Correspondence to Jianjun Yuan.

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Xu, Y., Yuan, J. Anisotropic diffusion equation with a new diffusion coefficient for image denoising. Pattern Anal Applic 20, 579–586 (2017). https://doi.org/10.1007/s10044-016-0590-7

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