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Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 914564, 14 pages
http://dx.doi.org/10.1155/2010/914564
Research Article

Determining Neighborhoods of Image Pixels Automatically for Adaptive Image Denoising Using Nonlinear Time Series Analysis

1Key Laboratory of Land Resources Evaluation and Monitoring of Southwest, Sichuan Normal University, Ministry of Education, Chengdu 610068, Sichuan, China
2School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 610054, Sichuan, China
3Institute of Medical Information and Technology, School of Biomedical Engineering, Southern Medical University, Guangzhou 510515, China

Received 30 January 2010; Accepted 20 March 2010

Academic Editor: Ming Li

Copyright © 2010 Zhiwu Liao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. N. Weiner, Extrapolation, Interpolation, and Smoothing of Stationary Time Series, John Wiley & Sons, New York, NY, USA, 1949.
  2. L. Şendur and I. W. Selesnick, “Bivariate shrinkage with local variance estimation,” IEEE Signal Processing Letters, vol. 9, no. 12, pp. 438–441, 2002. View at Publisher · View at Google Scholar · View at Scopus
  3. M. Mignotte, “Image denoising by averaging of piecewise constant simulations of image partitions,” IEEE Transactions on Image Processing, vol. 16, no. 2, pp. 523–533, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  4. Z. Dengwen and C. Wengang, “Image denoising with an optimal threshold and neighbouring window,” Pattern Recognition Letters, vol. 29, no. 11, pp. 1694–1697, 2008. View at Publisher · View at Google Scholar · View at Scopus
  5. D. Coupier, A. Desolneux, and B. Ycart, “Image denoising by statistical area thresholding,” Journal of Mathematical Imaging and Vision, vol. 22, no. 2, pp. 183–197, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  6. C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in Proceedings of the IEEE International Conference on Computer Vision, pp. 839–846, Bombay, India, 1998. View at Scopus
  7. M. Zhang and B. K. Gunturk, “Multiresolution bilateral filtering for image denoising,” IEEE Transactions on Image Processing, vol. 17, no. 12, pp. 2324–2333, 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. H. Yu, L. Zhao, and H. Wang, “Image denoising using trivariate shrinkage filter in the wavelet domain and joint bilateral filter in the spatial domain,” IEEE Transactions on Image Processing, vol. 18, no. 10, pp. 2364–2369, 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. Y.-L. Liu, J. Wang, X. Chen, Y.-W. Guo, and Q.-S. Peng, “A robust and fast non-local means algorithm for image denoising,” Journal of Computer Science and Technology, vol. 23, no. 2, pp. 270–279, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  10. Z. Ji, Q. Chen, Q.-S. Sun, and D.-S. Xia, “A moment-based nonlocal-means algorithm for image denoising,” Information Processing Letters, vol. 109, no. 23-24, pp. 1238–1244, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  11. V. Katkovnik, A. Foi, K. Egiazarian, and J. Astola, “From local kernel to nonlocal multiple-model image denoising,” International Journal of Computer Vision, vol. 86, no. 1, pp. 1–32, 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. X. Wu and N. Memon, “Context-based, adaptive, lossless image code,” IEEE Transactions on Communications, vol. 45, no. 4, pp. 437–444, 1997. View at Publisher · View at Google Scholar · View at Scopus
  13. M. S. Crouse and R. G. Baraniuk, “Contextual hidden Markov models for wavelet-domain signal processing,” in Proceedings of the 31st Asilomar Conference on Signals, Systems and Computers, Pacific Grove, Calif, USA, November 1997.
  14. G. Fan and X.-G. Xia, “Image denoising using a local contextual hidden Markov model in the wavelet domain,” IEEE Signal Processing Letters, vol. 8, no. 5, pp. 125–128, 2001. View at Publisher · View at Google Scholar · View at Scopus
  15. S. G. Chang, B. Yu, and M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Transactions on Image Processing, vol. 9, no. 9, pp. 1522–1531, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. Z. Liao and Y. Y. Tang, “Signal denoising using wavelets and block hidden Markov model,” International Journal of Pattern Recognition and Artificial Intelligence, vol. 19, no. 5, pp. 681–700, 2005. View at Publisher · View at Google Scholar · View at Scopus
  17. A. Buades, B. Coll, and J.-M. Morel, “Nonlocal image and movie denoising,” International Journal of Computer Vision, vol. 76, no. 2, pp. 123–139, 2008, special section: selection of papers for CVPR 2005, Guest Editors: C. Schmid, S. Soatto and C. Tomasi. View at Publisher · View at Google Scholar · View at Scopus
  18. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis, Cambridge University Press, Cambridge, UK, 2nd edition, 2004. View at MathSciNet
  19. M. Li, W.-S. Chen, and L. Han, “Correlation matching method for the weak stationarity test of LRD traffic,” Telecommunication Systems, vol. 43, no. 3-4, pp. 181–195, 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. M. Li and J.-Y. Li, “On the predictability of long-range dependent series,” Mathematical Problems in Engineering, vol. 2010, Article ID 397454, 9 pages, 2010. View at Publisher · View at Google Scholar
  21. M. Li and W. Zhao, “Representation of a stochastic traffic bound,” IEEE Transactions on Parallel and Distributed Systems. In press. View at Publisher · View at Google Scholar
  22. C. Cattani and A. Kudreyko, “Application of periodized harmonic wavelets towards solution of eigenvalue problems for integral equations,” Mathematical Problems in Engineering, vol. 2010, Article ID 570136, 8 pages, 2010. View at Publisher · View at Google Scholar
  23. E. G. Bakhoum and C. Toma, “Mathematical transform of traveling-wave equations and phase aspects of quantum interaction,” Mathematical Problems in Engineering, vol. 2010, Article ID 695208, 15 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  24. C. Keng and H. Bo-Tang, “A survey of state space reconstruction of chaotic time series analysis,” Computer Science, vol. 32, no. 4, pp. 67–70, 2005.
  25. S. Lin, J. Qiao, G. Wang, S. Zhang, and L. Zhi, “Phase space reconstruction of nonlinear time series based on Kernel method,” in Proceedings of the 6th World Congress on Intelligent Control and Automation (WCICA '06), vol. 1, pp. 4364–4368, Dalian, China, 2006. View at Publisher · View at Google Scholar · View at Scopus
  26. M. Casdagli, S. Eubank, J. D. Farmer, and J. Gibson, “State space reconstruction in the presence of noise,” Physica D, vol. 51, no. 1–3, pp. 52–98, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. L. Wang, H. Zhang, H. Meng, and X. Wang, “Nonlinear analysis of individual vehicle behavior in car following,” in Proceedings of the 11th International IEEE Conference on Intelligent Transportation Systems (ITSC '08), pp. 265–268, Beijing, China, October 2008. View at Publisher · View at Google Scholar · View at Scopus
  28. J. B. Dingwell and J. P. Cusumano, “Nonlinear time series analysis of normal and pathological human walking,” Chaos, vol. 10, no. 4, pp. 848–863, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  29. B. Dennis, R. A. Desharnais, J. M. Cushing, S. M. Henson, and R. F. Costantino, “Can noise induce chaos?” Oikos, vol. 102, no. 2, pp. 329–339, 2003. View at Publisher · View at Google Scholar · View at Scopus
  30. R. Poole, “Is it chaos, or is it just noise,” Science, vol. 243, no. 4887, pp. 25–28, 1989.
  31. M. Li, “Fractal time series—a tutorial review,” Mathematical Problems in Engineering, vol. 2010, Article ID 157264, 26 pages, 2010. View at MathSciNet
  32. http://www.hudong.com/wiki/.
  33. V. Guillemin and A. Pollack, Differential Topology, Prentice-Hall, Englewood Cliffs, NJ, USA, 1974. View at MathSciNet
  34. R. C. Kirby and L. C. Siebenmann, Foundational Essays on Topological Manifolds, Smoothings, and Triangulations, Princeton University Press, Princeton, NJ, USA, 1977. View at MathSciNet
  35. Z. Liao, Image Denoising Based on Wavelet Domian Hidden Markov Models, UESTC Press, Chengdu, China, 2006.