Skip to main content
Log in

A statistical learning based image denoising approach

  • Research Article
  • Published:
Frontiers of Computer Science Aims and scope Submit manuscript

Abstract

The image denoising is a very basic but important issue in the field of image procession. Most of the existing methods addressing this issue only show desirable performance when the image complies with their underlying assumptions. Especially, when there is more than one kind of noises, most of the existing methods may fail to dispose the corresponding image. To address this problem, we propose a two-step image denoising method motivated by the statistical learning theory. Under the proposed framework, the type and variance of noise are estimated with support vector machine (SVM) first, and then this information is employed in the proposed denoising algorithm to further improve its denoising performance. Finally, comparative study is constructed to demonstrate the advantages and effectiveness of the proposed method.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Li J, Ge H. New progress in geometric computing for image and video processing. Frontiers of Computer Science, 2012, 6(6): 769–775

    MathSciNet  Google Scholar 

  2. Zhao F, Jiao L, Liu H. Fuzzy c-means clustering with non local spatial information for noisy image segmentation. Frontiers of Computer Science in China, 2011, 5(1): 45–56

    Article  MATH  MathSciNet  Google Scholar 

  3. Horng S J, Hsu L Y, Li T Qiao S, Gong X, Chou H H, Khan M K. Using sorted switching median filter to remove high-density impulse noises. Journal of Visual Communication and Image Representation, 2013, 24(7): 956–967

    Article  Google Scholar 

  4. Om H, Biswas M. An improved image denoising method based on wavelet thresholding. Journal of Signal & Information Processing, 2012, 3(1): 17686–8

    Article  Google Scholar 

  5. Chen G, Qian S E. Denoising of hyperspectral imagery using principal component analysis and wavelet shrinkage. IEEE Transactions on Geoscience and Remote Sensing, 2011, 49(3): 973–980

    Article  Google Scholar 

  6. Kazerouni A, Kamilov U, Bostan E, Unser M. Bayesian denoising: from MAP to MMSE using consistent cycle spinning. IEEE Signal Processing. Letter, 2013, 20(3): 249–252

    Article  Google Scholar 

  7. Kumar V, Kumar A. Simulative analysis for image denoising using wavelet thresholding techniques. International Journal of Advanced Research in Computer Engineering & Technology (IJARCET), 2013, 2(5): 1873–1878

    Google Scholar 

  8. Gramfort A, Poupon C, Descoteaux M. Denoising and fast diffusion imaging with physically constrained sparse dictionary learning. Medical Image Analysis, 2014, 18(1): 36–49

    Article  Google Scholar 

  9. Ataman E, Aatre V K, Wong K M. Some statistical properties of median filters. IEEE Transactions on Acoustics, Speech and Signal Processing, 1981, 29(5): 1073–1075

    Article  Google Scholar 

  10. Daubechies I, Bates B J. Ten lectures on wavelets. Acoustical Society of America Journal, 1993, 93: 1671

    Article  Google Scholar 

  11. Donoho D L, Johnstone JM. Ideal spatial adaptation by wavelet shrinkage. Biometrika, 1994, 81(3): 425–455

    Article  MATH  MathSciNet  Google Scholar 

  12. Donoho D L, Johnstone I M, Kerkyacharian G, Picard D. Wavelet shrinkage: asymptopia? Journal of the Royal Statistical Society. Series B (Methodological), 1995: 301–369

    Google Scholar 

  13. Coifman R R, Donoho D L. Translation-invariant de-noising. New York: Springer, 1995

    Book  Google Scholar 

  14. Chang S G, Yu B, Vetterli M. Adaptive wavelet thresholding for image denoising and compression. IEEE Transactions on Image Processing, 2000, 9(9): 1532–1546

    Article  MATH  MathSciNet  Google Scholar 

  15. Fowler J E. The redundant discrete wavelet transform and additive noise. IEEE Signal Processing Letters, 2005, 12(9): 629–632

    Article  Google Scholar 

  16. Perona P, Malik J. Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1990, 12(7): 629–639

    Article  Google Scholar 

  17. Catté F, Lions P L, Morel J M, Coll T. Image selective smoothing and edge detection by nonlinear diffusion. SIAM Journal on Numerical Analysis, 1992, 29(1): 182–193

    Article  MATH  MathSciNet  Google Scholar 

  18. Rudin L I, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena, 1992, 60(1): 259–268

    Article  MATH  Google Scholar 

  19. Shao Y, Sun F, Li H, Liu Y. Structural similarity-optimal total variation algorithm for image denoising. In: Proceeding of Foundations and Practical Applications of Cognitive Systems and Information Processing. 2014, 833–843

    Chapter  Google Scholar 

  20. Kulkarni S, Harman G. An elementary introduction to statistical learning theory. Wiley, 2011

    Book  MATH  Google Scholar 

  21. Smola A J, Scholkopf B. A tutorial on support vector regression. Statistics and Computing, 2004, 14(3): 199–222

    Article  MathSciNet  Google Scholar 

  22. Abramowit L M, Stegun I A. Htrndbook of mathematical functions. New York: Dover, 1970

    Google Scholar 

  23. Chang C C, Lin C J. Training v-support vector regression: theory and algorithms. Neural Computation, 2002, 14(8): 1959–1977

    Article  MATH  Google Scholar 

  24. Vapnik V. The nature of statistical learning theory. Springer, 2000

    Book  MATH  Google Scholar 

  25. Sheikh H R, Sabir M F, Bovik A C. A statistical evaluation of recent full reference image quality assessment algorithms. IEEE Transactions on Image Processing, 2006, 15(11): 3440–3451

    Article  Google Scholar 

  26. Wang Z, Bovik A C, Sheikh H R, Simoncelli E P. Image quality assessment: from error visibility to structural similarity. IEEE Transactions on Image Processing, 2014, 13(4): 600–612

    Article  Google Scholar 

  27. Hore A, Ziou D. Image quality metrics: PSNR vs. SSIM. In: Proceedings of the 20th International Conference on Pattern Recognition (ICPR). 2010, 2366–2369

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hongbo Li.

Additional information

Ke Tu is now pursuing his PhD in the Department of Computer Science and Technology, Tsinghua University, China. His recent research interests include image denoising, image enhancement and data mining.

Hongbo Li received the PhD from Tsinghua University, China in 2009. He is currently an assistant professor with the Department of Computer Science and Technology, Tsinghua University, China. His research interests include networked control systems and intelligent control.

Fuchun Sun received the PhD in 1998 from the Department of Computer Science and Technology, Tsinghua University, China. Currently, he is a professor in the Department of Computer Science and Technology, Tsinghua University, China. His research interests include intelligent control, neural networks, fuzzy systems, variable structure control, nonlinear systems and robotics.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tu, K., Li, H. & Sun, F. A statistical learning based image denoising approach. Front. Comput. Sci. 9, 713–719 (2015). https://doi.org/10.1007/s11704-015-4224-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11704-015-4224-9

Keywords

Navigation