Table of Contents Author Guidelines Submit a Manuscript
Advances in Multimedia
Volume 2014, Article ID 934834, 10 pages
http://dx.doi.org/10.1155/2014/934834
Research Article

An Adaptive Image Denoising Model Based on Tikhonov and TV Regularizations

1School of Computer and Information, Hefei University of Technology, Hefei 23009, China
2School of Computer and Information, Anqing Normal University, Anqing 246011, China

Received 23 January 2014; Revised 11 July 2014; Accepted 14 July 2014; Published 4 August 2014

Academic Editor: Jianping Fan

Copyright © 2014 Kui Liu 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. P. Chatterjee and P. Milanfar, “Is denoising dead?” IEEE Transactions on Image Processing, vol. 19, no. 4, pp. 895–911, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. A. Buades, B. Coll, and J. M. Morel, “A review of image denoising algorithms, with a new one,” Multiscale Modeling and Simulation, vol. 4, no. 2, pp. 490–530, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  3. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Transactions on Image Processing, vol. 16, no. 8, pp. 2080–2095, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. 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
  5. D. Chen, Y. Chen, and D. Xue, “Three fractional-order TV-L2 models for image denoising,” Journal of Computational Information Systems, vol. 9, no. 12, pp. 4773–4780, 2013. View at Publisher · View at Google Scholar · View at Scopus
  6. 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 MathSciNet · View at Scopus
  7. L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D: Nonlinear Phenomena, vol. 60, no. 1–4, pp. 259–268, 1992. View at Publisher · View at Google Scholar · View at Scopus
  8. P. Blomgren, T. F. Chan, and P. Mulet, “Extensions to total variation denoising,” in Advanced Signal Processing: Algorithms, Architectures and Implementations VII, Proceedings of SPIE, pp. 367–375, San Diego, Calif, USA, July 1997. View at Publisher · View at Google Scholar · View at Scopus
  9. M. Lysaker, A. Lundervold, and X. C. Tai, “Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time,” IEEE Transactions on Image Processing, vol. 12, no. 12, pp. 1579–1589, 2003. View at Publisher · View at Google Scholar · View at Scopus
  10. A. S. Khare, R. Mohan, and S. Sharma, “An efficient image denoising method based on fourth-order partial differential equations,” International Journal of Advanced Computer Research, vol. 3, no. 9, pp. 126–131, 2013. View at Google Scholar
  11. 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
  12. S. Zheng, Z. Pan, G. Wang, and X. Yan, “A variational model of image restoration based on first and second order derivatives and its split Bregman algorithm,” in Proceedings of the 3rd IEEE/IET International Conference on Audio, Language and Image Processing (ICALIP '12), pp. 860–865, Shanghai, China, July 2012. View at Publisher · View at Google Scholar · View at Scopus
  13. S. Oh, H. Woo, S. Yun, and M. Kang, “Non-convex hybrid total variation for image denoising,” Journal of Visual Communication and Image Representation, vol. 24, no. 3, pp. 332–344, 2013. View at Publisher · View at Google Scholar · View at Scopus
  14. A. Gholami and S. M. Hosseini, “A balanced combination of Tikhonov and total variation regularizations for reconstruction of piecewise-smooth signals,” Signal Processing, vol. 93, no. 7, pp. 1945–1960, 2013. View at Publisher · View at Google Scholar · View at Scopus
  15. W. Stefan, R. A. Renaut, and A. Gelb, “Improved total variation-type regularization using higher order edge detectors,” SIAM Journal on Imaging Sciences, vol. 3, no. 2, pp. 232–251, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. R. W. Liu, L. Shi, W. Huang, J. Xu, S. C. H. Yu, and D. Wang, “Generalized total variation-based MRI Rician denoising model with spatially adaptive regularization parameters,” Magnetic Resonance Imaging, vol. 32, no. 6, pp. 702–720, 2014. View at Publisher · View at Google Scholar
  17. E. J. Candès and F. Guo, “New multiscale transforms, minimum total variation synthesis: applications to edge-preserving image reconstruction,” Signal Processing, vol. 82, no. 11, pp. 1519–1543, 2002. View at Publisher · View at Google Scholar · View at Scopus
  18. A. Gholami and H. R. Siahkoohi, “Regularization of linear and non-linear geophysical ill-posed problems with joint sparsity constraints,” Geophysical Journal International, vol. 180, no. 2, pp. 871–882, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. A. N. Tikhonov, A. S. Leonov, and A. G. Yagola, “Nonlinear ill-posed problems,” in World Congress of Nonlinear Analysts '92, Vol. I–IV (Tampa, FL, 1992), pp. 505–511, de Gruyter, Berlin, Germany, 1996. View at Google Scholar · View at MathSciNet
  20. C. Pschl, Tikhonov regularization with general residual term [Ph.D. thesis], Leopold-Franzens-Universität, Innsbruck, Austria, 2008.
  21. S. Esedoǵlu and S. J. Osher, “Decomposition of images by the anisotropic Rudin-Osher-Fatemi model,” Communications on Pure and Applied Mathematics, vol. 57, no. 12, pp. 1609–1626, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. J. S. Moll, “The anisotropic total variation flow,” Mathematische Annalen, vol. 332, no. 1, pp. 177–218, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  23. T. Goldstein and S. Osher, “The split Bregman method for L1-regularized problems,” SIAM Journal on Imaging Sciences, vol. 2, no. 2, pp. 323–343, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  24. 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
  25. Y. Wang, W. Chen, S. Zhou, T. Yu, and Y. Zhang, “MTV: modified total variation model for image noise removal,” Electronics Letters, vol. 47, no. 10, pp. 592–594, 2011. View at Publisher · View at Google Scholar · View at Scopus