Nonlocal Total Variation Based Speckle Denoising Model

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 221)

Abstract

A large range of methods covering various fields of mathematics are available for denoising an image. The initial denoising models are derived from energy minimization using nonlinear partial differential equations (PDEs). The filtering models based on smoothing operators have also been used for denoising. Among them the recently developed nonlocal means method proposed by Buades, Coll and Morel in 2005 is quite successful. Though the method is very accurate, it is very slow and hence quite impractical. In 2008, Gilboa and Osher extended some known PDE and variational techniques in image processing to the nonlocal framework and proposed the nonlocal total variation method for Gaussian noise. We used this idea to develop a nonlocal model for speckle noise. Here we have extended the speckle model introduced by Krissian et al. in 2005 to the nonlocal framework. The Split Bregman scheme is used solve this new model.

Keywords

Image denoising Speckle denoising models Nonlocal means Nonlocal PDE Nonlocal TV 

References

  1. 1.
    Bresson X (2009) A short note for nonlocal tv minimization. Technical reportGoogle Scholar
  2. 2.
    Buades A, Coll B, Morel JM (2005) A non-local algorithm for image denoising. In: IEEE computer society conference on computer vision and pattern recognition, CVPR 2005, vol 2, pp 60–65. doi: 10.1109/CVPR.2005.38
  3. 3.
    Gilboa G, Osher S (2008) Nonlocal operators with applications to image processing. Multiscale Model Simul 7(3):1005–1028. http://dblp.uni-trier.de/db/journals/mmas/mmas7.html#GilboaO08
  4. 4.
    Goldstein T, Osher S (2009) The split bregman method for l1-regularized problems. SIAM J Imaging Sci 2:323–343. doi: 10.1137/080725891, http://portal.acm.org/citation.cfm?id=1658384.1658386 Google Scholar
  5. 5.
    Kim S, Lim H (2007) A non-convex diffusion model for simultaneous image denoising and edge enhancement. Electron J Differ Equ Conference 15:175–192MathSciNetGoogle Scholar
  6. 6.
    Krissian K, Kikinis R, Westin CF, Vosburgh K (2005) Speckle-constrained filtering of ultrasound images. In: CVPR ’05: Proceedings of the 2005 IEEE computer society conference on computer vision and pattern recognition (CVPR’05), vol 2. IEEE Computer Society, Washington, DC, pp 547–552. doi: 10.1109/CVPR.2005.331
  7. 7.
    Li C (2003) An efficient algorithm for total variation regularization with applications to the single pixel camera and compressive sensing. Master’s thesis, Rice University, Houston, TexasGoogle Scholar
  8. 8.
    Rudin LI, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenom 60(1–4):259–268. doi: 10.1016/0167-2789(92)90242-F MATHCrossRefGoogle Scholar
  9. 9.
    Wang Y, Yin W, Zhang Y (2007) A fast algorithm for image deblurring with total variation regularization. Technical report, Department of Computational and Applied Mathematics, Rice University, Houston, TexasGoogle Scholar
  10. 10.
    Zhou D, Schlkopf B (2004) A regularization framework for learning from graph data. In: ICML workshop on statistical relational learning, pp 132–137Google Scholar
  11. 11.
    Zhou D, Schlkopf B (2005) Regularization on discrete spaces. In: Pattern recognition. Springer, Heidelberg, pp 361–368Google Scholar

Copyright information

© Springer India 2013

Authors and Affiliations

  1. 1.Department of Mathematical SciencesSaginaw Valley State UniversityUniversity CenterUSA
  2. 2.Department of Mathematics and StatisticsMississippi State UniversityMississippiUSA

Personalised recommendations