Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 309418, 10 pages
http://dx.doi.org/10.1155/2013/309418
Research Article

HPM-Based Dynamic Wavelet Transform and Its Application in Image Denoising

College of Information and Electrical Engineering, China Agricultural University, Postbox 53, East Campus, 17 Qinghua Donglu Road, Haidian District, Beijing 100083, China

Received 26 April 2013; Revised 10 August 2013; Accepted 25 August 2013

Academic Editor: Claudio R. Fuerte-Esquivel

Copyright © 2013 Shu-Li Mei. 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. P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 7, pp. 629–639, 1990. View at Publisher · View at Google Scholar · View at Scopus
  2. Z. Guo, J. Sun, D. Zhang, and B. Wu, “Adaptive Perona-Malik model based on the variable exponent for image denoising,” IEEE Transactions on Image Processing, vol. 21, no. 3, pp. 958–967, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  3. X. Zhang and X. Feng, “Texture preserving Perona-Malik model,” in Proceedings of the 4th International Congress on Image and Signal Processing (CISP '11), vol. 2, pp. 812–815, October 2011. View at Publisher · View at Google Scholar · View at Scopus
  4. C. Lopez-Molina, B. de Baets, J. Cerron et al., “A generalization of the Perona-Malik anisotropic diffusion method using restricted dissimilarity functions,” International Journal of Computational Intelligence Systems, vol. 6, no. 1, pp. 14–28, 2013. View at Google Scholar
  5. I. Daubechies and G. Teschke, “Variational image restoration by means of wavelets: simultaneous decomposition, deblurring, and denoising,” Applied and Computational Harmonic Analysis, vol. 19, no. 1, pp. 1–16, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. I. Daubechies and G. Teschke, “Wavelet based image decomposition by variational functionals,” in Wavelet Applications in Industrial Processing, vol. 5266 of Proceedings of SPIE, pp. 94–105, October 2003. View at Publisher · View at Google Scholar · View at Scopus
  7. S. L. Mei, Q. S. Lu, S. W. Zhang, and L. Jin, “Adaptive interval wavelet precise integration method for partial differential equations,” Applied Mathematics and Mechanics, vol. 26, no. 3, pp. 333–340, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. S.-L. Mei, Q.-S. Lu, and S.-W. Zhang, “Adaptive wavelet precise integration method for partial differential equations,” Chinese Journal of Computational Physics, vol. 21, no. 6, pp. 523–530, 2004. View at Google Scholar · View at Scopus
  9. S. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, CRC Press, 2004. View at MathSciNet
  10. S. Liao, “Notes on the homotopy analysis method: some definitions and theorems,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 983–997, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. S.-J. Liao and K. F. Cheung, “Homotopy analysis of nonlinear progressive waves in deep water,” Journal of Engineering Mathematics, vol. 45, no. 2, pp. 105–116, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. Y. Zhao, Z. Lin, Z. Liu, and S. Liao, “The improved homotopy analysis method for the Thomas-Fermi equation,” Applied Mathematics and Computation, vol. 218, no. 17, pp. 8363–8369, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. O. Martin, “On the homotopy analysis method for solving a particle transport equation,” Applied Mathematical Modelling, vol. 37, no. 6, pp. 3959–3967, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. G. Domairry, A. Mohsenzadeh, and M. Famouri, “The application of homotopy analysis method to solve nonlinear differential equation governing Jeffery-Hamel flow,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 1, pp. 85–95, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. J.-H. He, “The homotopy perturbation method nonlinear oscillators with discontinuities,” Applied Mathematics and Computation, vol. 151, no. 1, pp. 287–292, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. J.-H. He, “Homotopy perturbation method for bifurcation of nonlinear problems,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 6, no. 2, pp. 207–208, 2005. View at Google Scholar · View at Scopus
  17. J.-H. He, “Asymptotic methods for solitary solutions and compactons,” Abstract and Applied Analysis, vol. 2012, Article ID 916793, 130 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. J.-H. He, “Addendum: new interpretation of homotopy perturbation method,” International Journal of Modern Physics B, vol. 20, no. 18, pp. 2561–2568, 2006. View at Publisher · View at Google Scholar · View at Scopus
  19. L. Cveticanin, “Homotopy-perturbation method for pure nonlinear differential equation,” Chaos, Solitons and Fractals, vol. 30, no. 5, pp. 1221–1230, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  20. S. Abbasbandy, “Application of He's homotopy perturbation method for Laplace transform,” Chaos, Solitons and Fractals, vol. 30, no. 5, pp. 1206–1212, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  21. M. Rafei and D. D. Ganji, “Explicit solutions of Helmholtz equation and fifth-order KdV equation using homotopy perturbation method,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 3, pp. 321–328, 2006. View at Google Scholar · View at Scopus
  22. A. M. Siddiqui, R. Mahmood, and Q. K. Ghori, “Thin film flow of a third grade fluid on a moving belt by he's homotopy perturbation method,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 1, pp. 7–14, 2006. View at Google Scholar · View at Scopus
  23. A. R. Ghotbi, H. Bararnia, G. Domairry, and A. Barari, “Investigation of a powerful analytical method into natural convection boundary layer flow,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 5, pp. 2222–2228, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  24. S. H. Hosein Nia, A. N. Ranjbar, D. D. Ganji, H. Soltani, and J. Ghasemi, “Maintaining the stability of nonlinear differential equations by the enhancement of HPM,” Physics Letters A, vol. 372, no. 16, pp. 2855–2861, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  25. M. Esmaeilpour and D. D. Ganji, “Application of He's homotopy perturbation method to boundary layer flow and convection heat transfer over a flat plate,” Physics Letters A, vol. 372, no. 1, pp. 33–38, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. H. Yan, “Adaptive wavelet precise integration method for nonlinear Black-Scholes model based on variational iteration method,” Abstract and Applied Analysis, vol. 2013, Article ID 735919, 6 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  27. R. Y. Xing, “Wavelet-based homotopy analysis method for nonlinear matrix system and its application in burgers equation,” Mathematical Problems in Engineering, vol. 2013, Article ID 982810, 7 pages, 2013. View at Publisher · View at Google Scholar
  28. D. C. Wan and G. W. Wei, “The study of quasi wavelets based numerical method applied to Burgers' equations,” Applied Mathematics and Mechanics, vol. 21, no. 10, pp. 991–1001, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. G. W. Wei, “Quasi wavelets and quasi interpolating wavelets,” Chemical Physics Letters, vol. 296, no. 3-4, pp. 253–258, 1998. View at Publisher · View at Google Scholar · View at Scopus
  30. S.-L. Mei, “Construction of target controllable image segmentation model based on homotopy perturbation technology,” Abstract and Applied Analysis, vol. 2013, Article ID 131207, 8 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. S.-L. Mei, C.-J. Du, and S.-W. Zhang, “Asymptotic numerical method for multi-degree-of-freedom nonlinear dynamic systems,” Chaos, Solitons and Fractals, vol. 35, no. 3, pp. 536–542, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  32. S. Mei, S. Zhang, and Q. Lu, “Wavelet precise integration method for burgers equations based on homotopy technique,” Chinese Journal of Computational Physics, vol. 24, no. 1, pp. 54–58, 2007. View at Google Scholar · View at Scopus