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Mathematical Problems in Engineering
Volume 2015, Article ID 636295, 12 pages
http://dx.doi.org/10.1155/2015/636295
Research Article

Patch Similarity Modulus and Difference Curvature Based Fourth-Order Partial Differential Equation for Image Denoising

National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China

Received 15 October 2014; Revised 16 June 2015; Accepted 25 June 2015

Academic Editor: Ivanka Stamova

Copyright © 2015 Yunjiao Bai 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. R. D. da Silva, R. Minetto, W. R. Schwartz, and H. Pedrini, “Adaptive edge-preserving image denoising using wavelet transforms,” Pattern Analysis and Applications, vol. 16, no. 4, pp. 567–580, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. H. Zhong, C. Yang, and X. Zhang, “A new weight for nonlocal means denoising using method noise,” IEEE Signal Processing Letters, vol. 19, no. 8, pp. 535–538, 2012. View at Publisher · View at Google Scholar
  3. 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 · View at Scopus
  4. A. A. Yahya, J. Tan, and M. Hu, “A blending method based on partial differential equations for image denoising,” Multimedia Tools and Applications, vol. 73, no. 3, pp. 1843–1862, 2014. View at Publisher · View at Google Scholar · View at Scopus
  5. E. Nadernejad, S. Sharifzadeh, and S. Forchhammer, “Using anisotropic diffusion equations in pixon domain for image de-noising,” Signal, Image and Video Processing, vol. 7, no. 6, pp. 1113–1124, 2013. View at Publisher · View at Google Scholar · View at Scopus
  6. Q. Yuan, L. Zhang, and H. Shen, “Regional spatially adaptive total variation super-resolution with spatial information filtering and clustering,” IEEE Transactions on Image Processing, vol. 22, no. 6, pp. 2327–2342, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. 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
  8. F. Catt{\'e}, P.-L. Lions, J.-M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM Journal on Numerical Analysis, vol. 29, no. 1, pp. 182–193, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. S.-M. Chao and D.-M. Tsai, “An improved anisotropic diffusion model for detail-and edge-preserving smoothing,” Pattern Recognition Letters, vol. 31, no. 13, pp. 2012–2023, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. D. Zhao, C.-J. He, and Q. Chen, “Anisotropic diffusion model combined with local entropy,” Pattern Recognition and Artificial Intelligence, vol. 25, no. 4, pp. 642–647, 2012. View at Google Scholar · View at Scopus
  11. Q. Chen, P. Montesinos, Q. S. Sun, and D. S. Xia, “Ramp preserving Perona-Malik model,” Signal Processing, vol. 90, no. 6, pp. 1963–1975, 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. Y.-L. You and M. Kaveh, “Fourth-order partial differential equations for noise removal,” IEEE Transactions on Image Processing, vol. 9, no. 10, pp. 1723–1730, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. J. Rajan, K. Kannan, and M. R. Kaimal, “An improved hybrid model for molecular image denoising,” Journal of Mathematical Imaging and Vision, vol. 31, no. 1, pp. 73–79, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. X. Liu, L. Huang, and Z. Guo, “Adaptive fourth-order partial differential equation filter for image denoising,” Applied Mathematics Letters, vol. 24, no. 8, pp. 1282–1288, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. P. Guidotti and K. Longo, “Two enhanced fourth order diffusion models for image denoising,” Journal of Mathematical Imaging and Vision, vol. 40, no. 2, pp. 188–198, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. P. Jidesh and S. George, “Fourth-order gauss curvature driven diffusion for image denoising,” International Journal of Computer & Electrical Engineering, vol. 4, no. 3, pp. 350–354, 2012. View at Publisher · View at Google Scholar
  17. T. Liu and Z. Xiang, “Image restoration combining the second-order and fourth-order PDEs,” Mathematical Problems in Engineering, vol. 2013, Article ID 743891, 7 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  18. M. R. Hajiaboli, “A self-governing fourth-order nonlinear diffusion filter for image noise removal,” IPSJ Transactions on Computer Vision and Applications, vol. 2, pp. 94–103, 2010. View at Publisher · View at Google Scholar
  19. M. R. Hajiaboli, “An anisotropic fourth-order diffusion filter for image noise removal,” International Journal of Computer Vision, vol. 92, no. 2, pp. 177–191, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  20. Q. Chen, Y. Zheng, Q. Sun, and D. Xia, “Patch similarity based anisotropic diffusion for image denoising,” Journal of Computer Research and Development, vol. 47, no. 1, pp. 33–42, 2010. View at Google Scholar · View at Scopus
  21. Q. Chen, P. Montesinos, Q. S. Sun, P. A. Heng, and D. S. Xia, “Adaptive total variation denoising based on difference curvature,” Image and Vision Computing, vol. 28, no. 3, pp. 298–306, 2010. View at Publisher · View at Google Scholar · View at Scopus
  22. S.-H. Lee and J. K. Seo, “Noise removal with Gauss curvature-driven diffusion,” IEEE Transactions on Image Processing, vol. 14, no. 7, pp. 904–909, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Transactions on Image Processing, vol. 13, no. 4, pp. 600–612, 2004. View at Publisher · View at Google Scholar · View at Scopus
  24. L.-C. Chang, E. El-Araby, V. Q. Dang, and L. H. Dao, “GPU acceleration of nonlinear diffusion tensor estimation using CUDA and MPI,” Neurocomputing, vol. 135, pp. 328–338, 2014. View at Publisher · View at Google Scholar · View at Scopus