Nonlocal Filters for Removing Multiplicative Noise

  • Tanja Teuber
  • Annika Lang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6667)

Abstract

In this paper, we propose nonlocal filters for removing multiplicative noise in images. The considered filters are deduced in a weighted maximum likelihood estimation framework and the occurring weights are defined by a new similarity measure for comparing data corrupted by multiplicative noise. For the deduction of this measure we analyze a probabilistic measure recently proposed for general noise models by Deledalle et al. and study its properties in the presence of additive and multiplicative noise. Since it turns out to have unfavorable properties facing multiplicative noise we propose a new similarity measure consisting of a density specially chosen for this type of noise. The properties of our new measure are examined theoretically as well as by numerical experiments. Afterwards, it is applied to define the weights of our nonlocal filters and different adaptations are proposed to further improve the results. Throughout the paper, our findings are exemplified for multiplicative Gamma noise. Finally, restoration results are presented to demonstrate the good properties of our new filters.

Keywords

Image Patch Multiplicative Noise Additive Gaussian Noise Constant Image Noisy Pixel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aubert, G., Aujol, J.-F.: A variational approach to removing multiplicative noise. SIAM Journal on Applied Mathematics 68(4), 925–946 (2008)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Buades, A., Coll, B., Morel, J.-M.: Online demo: Non-local means denoising, http://www.ipol.im/pub/algo/bcm_non_local_means_denoising
  3. 3.
    Buades, A., Coll, B., Morel, J.-M.: A non-local algorithm for image denoising. In: IEEE Conf. on CVPR, vol. 2, pp. 60–65 (2005)Google Scholar
  4. 4.
    Buades, A., Coll, B., Morel, J.-M.: Image denoising methods. A new nonlocal principle. SIAM Review 52(1), 113–147 (2010)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Coupé, P., Hellier, P., Kervrann, C., Barillot, C.: Nonlocal means-based speckle filtering for ultrasound images. IEEE Trans. Image Process. 18(10), 2221–2229 (2009)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Deledalle, C.-A., Denis, L., Tupin, F.: Iterative weighted maximum likelihood denoising with probabilistic patch-based weights. IEEE Trans. Image Process. 18(12), 2661–2672 (2009)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Deledalle, C.-A., Tupin, F., Denis, L.: Poisson NL means: Unsupervised non local means for Poisson noise. In: Proceedings of IEEE International Conference on Image Processing, pp. 801–804 (2010)Google Scholar
  8. 8.
    Durand, S., Fadili, J., Nikolova, M.: Multiplicative noise removal using L1 fidelity on frame coefficients. J. Math. Imaging Vision 36(3), 201–226 (2010)CrossRefGoogle Scholar
  9. 9.
    Grimmett, G.R., Stirzaker, D.R.: Probability and random processes, 3rd edn. Oxford University Press, Oxford (2001)MATHGoogle Scholar
  10. 10.
    Kervrann, C., Boulanger, J., Coupé, P.: Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal. In: Sgallari, F., Murli, A., Paragios, N. (eds.) SSVM 2007. LNCS, vol. 4485, pp. 520–532. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Matsushita, Y., Lin, S.: A probabilistic intensity similarity measure based on noise distributions. In: IEEE Conf. Computer Vision and Pattern Recognit. (2007)Google Scholar
  12. 12.
    Polzehl, J., Spokoiny, V.: Propagation-separation approach for local likelihood estimation. Probability Theory and Related Fields 135(3), 335–362 (2006)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Rohatgi, V.K.: An Introduction to Probability Theory and Mathematical Statistics. John Wiley & Sons, Inc., Chichester (1976)MATHGoogle Scholar
  14. 14.
    Steidl, G., Teuber, T.: Removing multiplicative noise by Douglas-Rachford splitting methods. J. Math. Imaging Vision 36(2), 168–184 (2010)CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    Teuber, T., Lang, A.: A new similarity measure for nonlocal filtering in the presence of multiplicative noise. University of Kaiserslautern (preprint, 2011)Google Scholar
  16. 16.
    Wiest-Daesslé, N., Prima, S., Coupé, P., Morrissey, S.P., Barillot, C.: Rician noise removal by non-local means filtering for low signal-to-noise ratio MRI: Applications to DT-MRI. In: Metaxas, D., Axel, L., Fichtinger, G., Székely, G. (eds.) MICCAI 2008, Part II. LNCS, vol. 5242, pp. 171–179. Springer, Heidelberg (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Tanja Teuber
    • 1
  • Annika Lang
    • 2
  1. 1.Department of MathematicsUniversity of KaiserslauternGermany
  2. 2.Seminar for Applied MathematicsETH ZurichSwitzerland

Personalised recommendations