Skip to main content
Log in

An Improved Hybrid Model for Molecular Image Denoising

  • Published:
Journal of Mathematical Imaging and Vision Aims and scope Submit manuscript

Abstract

In this paper an improved hybrid method for removing noise from low SNR molecular images is introduced. The method provides an improvement over the one suggested by Jian Ling and Alan C. Bovik (IEEE Trans. Med. Imaging, 21(4), [2002]). The proposed model consists of two stages. The first stage consists of a fourth order PDE and the second stage is a relaxed median filter, which processes the output of fourth order PDE. The model enjoys the benefit of both nonlinear fourth order PDE and relaxed median filter. Apart from the method suggested by Ling and Bovik, the proposed method will not introduce any staircase effect and preserves fine details, sharp corners, curved structures and thin lines. Experiments were done on molecular images (fluorescence microscopic images) and standard test images and the results shows that the proposed model performs better even at higher levels of noise.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Yezzi, A.: Modified curvature motion for image smoothing and enhancement. IEEE Trans. Image Process. 7, 345–352 (1998)

    Article  Google Scholar 

  2. Hero, A., Krim, H.: Mathematical methods in imaging. IEEE Signal Process. Mag. 19, 13–14 (2002)

    Article  Google Scholar 

  3. Hamza, A.B., Krim, H.: Robust environmental image denoising. In: The ISI International Conference on Environmental Statistics and Health (2003)

  4. Hamza, A.B., Krim, H., Unal, G.: Unifying probabilistic and variational estimation. IEEE Signal Process. Mag. 19(5), 37–47 (2002)

    Article  Google Scholar 

  5. Ben Hamza, A., Krim, H., Zerubia, J.: A nonlinear entropic variational model for image filtering. EURASIP J. Appl. Signal Process. 16, 2408–2422 (2004)

    Article  MathSciNet  Google Scholar 

  6. Greer, J.B., Bertozzi, A.L.: Travelling wave solutions of fourth order PDEs for image processing. SIAM J. Math. Anal. 36, 38–68 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intel. 12, 629–639 (1990)

    Article  Google Scholar 

  8. Whitaker, R.T., Prizer, S.M.: A multi scale approach to nonuniform diffusion. CVGIP: Image Underst. 57(1), 99–110 (1993)

    Article  Google Scholar 

  9. Ling, J., Bovik, A.C.: Smoothing low-SNR molecular images via anisotropic median diffusion. IEEE Trans. Med. Imaging 21, 377–384 (2002)

    Article  Google Scholar 

  10. Rajan, J., Kaimal, M.R.: Image denoising using wavelet embedded anisotropic diffusion (WEAD). In: Proceedings of IET International Conference on Visual Information Engineering 2006, pp. 589–593, September 2006

  11. Rajan, J., Kaimal, M.R.: Speckle reduction in images with WEAD & WECD. In: Computer Vision, Graphics and Image Processing. Lecture Notes in Computer Science (LNCS), vol. 4338, pp. 184–193. Springer, New York (2006)

    Chapter  Google Scholar 

  12. Hamza, A.B., Escamilla, P.L., Aroza, J.M., Roldan, R.: Removing noise and preserving details with relaxed median filters. J. Math. Imaging Vis. 11, 161–177 (1999)

    Article  Google Scholar 

  13. Pitas, I., Venetsanopoulos, A.N.: Nonlinear Digital Filters: Principles and Applications. Kluwer Academic, Dordrecht (1990)

    MATH  Google Scholar 

  14. You, Y.L., Kaveh, M.: Fourth-order partial differential equations for noise removal. IEEE Trans. Image Process. 9, 1723–1730 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  15. 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, 1579–1590 (2003)

    Article  Google Scholar 

  16. Wei, G.W.: Generalized Perona-Malik equation for image processing. IEEE Signal Process. Lett. 6, 165–167 (1999)

    Article  Google Scholar 

  17. You, Y.L., Xu, W., Tannenbaum, A., Kaveh, M.: Behavioral analysis of anisotropic diffusion in image processing. IEEE Trans. Image Process. 5, 1539–1553 (1996)

    Article  Google Scholar 

  18. Mrazek, P., Weickert, J., Steidl, G.: Correspondence between wavelet shrinkage and nonlinear diffusion. In: Scale-Space 2003. LNCS, vol. 2695, pp. 101–116. Springer, New York (2003)

    Google Scholar 

  19. Lijima, T.: Basic theory on normalization of pattern. Bull. Electrotech. Lab. 26, 368–388 (1962)

    Google Scholar 

  20. Charbonnier, P., Aubert, G., Feraud, L.B., Barlaud, M.: Two deterministic half-quadratic regularization algorithms for computed imaging. IEEE Int. Conf. Image Process. 2, 168–172 (1994)

    Google Scholar 

  21. Weickert, J.: Anisotropic Diffusion in Image Processing. ECMI Series. Teubner, Stuttgart (1998)

    MATH  Google Scholar 

  22. Andreu, F., Ballester, C., Caselles, V., Mazn, J.M.: Minimizing total variation flow. Differ. Integral Equ. 14, 321–360 (2001)

    MATH  Google Scholar 

  23. Keeling, S.L., Stollberger, R.: Nonlinear anisotropic diffusion filters for wide range edge sharpening. Inverse Probl. 18, 175–190 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  24. Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physics D 60, 259–268 (1992)

    Article  MATH  Google Scholar 

  25. Greer, J.B.: Fourth order diffusion for image processing. Ph.D. dissertation, Dept. of Mathematics, Duke University (2003)

  26. Hamza, A.B., Krim, H.: Image denoising: a nonlinear robust statistical approach. IEEE Trans. Signal Process. 49(12), 3045–3054 (2001)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jeny Rajan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rajan, J., Kannan, K. & Kaimal, M.R. An Improved Hybrid Model for Molecular Image Denoising. J Math Imaging Vis 31, 73–79 (2008). https://doi.org/10.1007/s10851-008-0067-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10851-008-0067-4

Keywords

Navigation