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Fourth Order Nonlinear Diffusion Filters for Multiplicative Noise Removal

  • Mahipal JettaEmail author
  • Pradeep Nalluri
  • Preetham Dasari
  • Sai Hitesh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10884)

Abstract

The second order partial differential equations based multiplicative noise removal filters produce step edges (staircase artifacts) in the filtered image. This paper proposes two fourth order nonlinear diffusion filters, an isotropic filter and an anisotropic filter, which do not allow these artifacts. Through numerical simulations it is shown that the proposed isotropic filter produces the filtered image in a relatively shorter time, with noticeable improvement in the quality, when compared to a second order filter and the proposed anisotropic diffusion filter.

Keywords

Fourth order partial differential equation Multiplicative noise Speckle removal Staircasing artifacts 

References

  1. 1.
    Lee, J.S.: Digital image enhancement and noise filtering by use of local statistics. IEEE Trans. Pattern Anal. Mach. Intell. 2, 165–168 (1980)CrossRefGoogle Scholar
  2. 2.
    Kuan, D.T., Sawchuk, A.A., Strand, T.C., Chavel, P.: Adaptive noise smoothing filter for images with signal-dependent noise. IEEE Trans. Pattern Anal. Mach. Intell. 2, 165–177 (1985)CrossRefGoogle Scholar
  3. 3.
    Lopes, A., Nezry, E., Touzi, R., Laur, H.: Maximum a posteriori speckle filtering and first order texture models in sar images. In: 10th Annual International Geoscience and Remote Sensing Symposium on Remote Sensing Science for the Nineties, IGARSS 1990, pp. 2409–2412. IEEE (1990)Google Scholar
  4. 4.
    Huang, Y.M., Ng, M.K., Wen, Y.W.: A new total variation method for multiplicative noise removal. SIAM J. Imaging Sci. 2(1), 20–40 (2009)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Zhao, X.L., Wang, F., Ng, M.K.: A new convex optimization model for multiplicative noise and blur removal. SIAM J. Imaging Sci. 7(1), 456–475 (2014)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Coupe, P., Hellier, P., Kervrann, C., Barillot, C.: Nonlocal means-based speckle filtering for ultrasound images. IEEE Trans. Image Process. 18(10), 2221–2229 (2009)MathSciNetCrossRefGoogle Scholar
  7. 7.
    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)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Yu, Y., Acton, S.T.: Speckle reducing anisotropic diffusion. IEEE Trans. Image Process. 11(11), 1260–1270 (2002)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Aja-Fernández, S., Alberola-López, C.: On the estimation of the coefficient of variation for anisotropic diffusion speckle filtering. IEEE Trans. Image Process. 15(9), 2694–2701 (2006)CrossRefGoogle Scholar
  10. 10.
    Krissian, K., Westin, C.F., Kikinis, R., Vosburgh, K.G.: Oriented speckle reducing anisotropic diffusion. IEEE Trans. Image Process. 16(5), 1412–1424 (2007)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Ramos-Llordén, G., Vegas-Sánchez-Ferrero, G., Martin-Fernandez, M., Alberola-López, C., Aja-Fernández, S.: Anisotropic diffusion filter with memory based on speckle statistics for ultrasound images. IEEE Trans. Image Process. 24(1), 345–358 (2015)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990)CrossRefGoogle Scholar
  13. 13.
    Weickert, J.: Anisotropic Diffusion in Image Processing, vol. 1. Teubner Stuttgart (1998)Google Scholar
  14. 14.
    Lysaker, M., Lundervold, A., Tai, X.C.: Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time. IEEE Trans. Image Process. 12(12), 1579–1590 (2003)CrossRefGoogle Scholar
  15. 15.
    Hajiaboli, M., Ahmad, M., Wang, C.: An edge-adapting Laplacian kernel for nonlinear diffusion filters. IEEE Trans. Image Process. 21(4), 1561–1572 (2012)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Pyatykh, S., Hesser, J., Zheng, L.: Image noise level estimation by principal component analysis. IEEE Trans. Image Process. 22(2), 687–699 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Mahipal Jetta
    • 1
    Email author
  • Pradeep Nalluri
    • 1
  • Preetham Dasari
    • 1
  • Sai Hitesh
    • 1
  1. 1.Mahindra École CentraleHyderabadIndia

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