A PDE-Based Nonlinear Filter Adapted to Rayleigh’s Speckle Noise for De-speckling 2D Ultrasound Images

  • Rajeev Srivastava
  • J. R. P. Gupta
Part of the Communications in Computer and Information Science book series (CCIS, volume 94)


The speckle noise present in the acquired ultrasound image may lead to misinterpretation of medical image during diagnosis and therefore, it must be reduced. The speckle noise in ultrasound image is normally multiplicative in nature and distributed according to Rayleigh’s probability density function (pdf). In this paper, a nonlinear partial-differential equation (PDE) based speckle reduction model adapted to Rayleigh’s noise is proposed in variational framework to reduce the speckle noise from 2D ultrasound (US) images. The initial condition of the PDE is the speckle noised US image and the de-speckled image is obtained after certain iterations of the proposed PDE till its convergence. The performance of the proposed non-linear PDE based filter has been evaluated in terms of mean square error (MSE), peak signal-to-noise ratio (PSNR), correlation parameter (CP) and mean structure similarity index map (MSSIM) for several ultrasound images with varying amount of speckle noise variance. The obtained results justify the applicability of the proposed scheme.


Mean Square Error Ultrasound Image Synthetic Aperture Radar Adaptive Filter Anisotropic Diffusion 
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  1. 1.
    Gonzalez, R.C., Wintz, P.: Digital Image Processing, 2nd edn. Academic Press, New York (1987)Google Scholar
  2. 2.
    Jain, A.K.: Fundamentals of Digital Image Processing. PHI, India (2005)Google Scholar
  3. 3.
    Johan, M.: Thijssen: Ultrasonic speckle formation, analysis and processing applied to tissue characterization. Pattern Recognition Letters 24, 659–675 (2003)CrossRefGoogle Scholar
  4. 4.
    Lee, J.S.: Speckle Analysis and Smoothing of Synthetic Aperture Radar Images. Computer Graphics and Image Processing 17, 24–32 (1981)CrossRefGoogle Scholar
  5. 5.
    Lee, J.S.: Digital Image Smoothing and the Sigma Filter. Computer Vision, Graphics and Image Processing 24, 255–269 (1983)CrossRefGoogle Scholar
  6. 6.
    Frost, V.S., Stiles, J.A., Josephine, A., Shanmugan, K.S., Holtzman, J.C.: A Model for Radar Images and Its Application to Adaptive Digital Filtering of Multiplicative Noise. IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-4 (2), 157–166 (1982)CrossRefGoogle Scholar
  7. 7.
    Lopes, A., Nezry, E., Touzi, R., Laur, H.: Maximum a Posteriori Speckle Filtering and First Order Texture Models in SAR Images. In: International Geoscience and Remote Sensing Symposium (IGARSS), Washingaton DC, USA (1990)Google Scholar
  8. 8.
    Donoho, D.L., Johnstone, I.M.: Ideal spatial adaptation via wavelet shrinkage. Biometrika 81, 425–455 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence 12, 629–639 (1990)CrossRefGoogle Scholar
  10. 10.
    Rudin, L., Osher, S., Fatemi, E.: Non linear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)zbMATHCrossRefGoogle Scholar
  11. 11.
    Beck, A., Teboulle, M.: Fast Gradient-Based Algorithms for Constrained Total Variation Image De-noising and Deblurring Problems. IEEE Transactions on Image Processing 18(11), 2419–2434 (2009)CrossRefGoogle Scholar
  12. 12.
    Chen, Q., Montesinos, P., Sun, Q.S., Heng, P.A., De Xia, S.: Adaptive total variation denoising based on difference curvature. Image and Vision Computing (2009), doi:10.1016/j.imavis.2009.04.012Google Scholar
  13. 13.
    Giloba, G., Sochen, N., Zeevi, Y.Y.: Image enhancement and de-noising by complex diffusion processes. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(8), 1020–1036 (2004)CrossRefGoogle Scholar
  14. 14.
    You, Y.L., Kaveh, M.: Fourth – order partial differential equations for noise Removal. IEEE Transactions on Image Processing 9, 1723–1730 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Witkin, A.P.: Scale-space filtering. In: Proc: Int. Joint Conf. Artificial Intelligence, pp. 1019–1021 (1983)Google Scholar
  16. 16.
    Chambolle, A.: Partial Differential equations and image processing. In: Proc: IEEE Int. Conf. on Image Processing, Austin, TX (November 1994)Google Scholar
  17. 17.
    Caselles, V., Morel, J.M., Sapiro, G.: Introduction to the special issue on partial differential equations and geometry driven diffusions in image processing. IEEE Transactions on Image Processing 7(3), 269–273 (1998)CrossRefGoogle Scholar
  18. 18.
    ter Harr Romeny, B. (ed.): Geometry driven diffusion in computer vision. Kluwer, Boston (1994)Google Scholar
  19. 19.
    Shi, J., Osher, S.: A nonlinear scale space method for a convex multiplicative model. SIAM Journal of Imaging Sciences 1(3), 294–321 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Yu, Y., Acton, S.T.: Speckle Reducing Anisotropic Diffusion. IEEE Transactions on Image Processing 11(11), 1260–1270 (2002)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Mateo, J.L., Fernández-Caballero, A.: Finding out general tendencies in speckle noise reduction in ultrasound images. Expert Systems with Application 36, 7786–7797 (2009)CrossRefGoogle Scholar
  22. 22.
    Kuan, D.T., Sawchuk, A.A.: Adaptive restoration of images with speckle. IEEE Trans. Acoustics, Speech and Signal Processing ASSP-35, 373–383 (1987)CrossRefGoogle Scholar
  23. 23.
    Dewaele, P., Wambacq, P., Oosterlinck, A., Marchand, J.L.: Comparison of some speckle reduction techniques for SAR images. In: Proc: Geoscience and Remote Sensing Symposium, IGARSS 1990, pp. 2417–2422 (1990)Google Scholar
  24. 24.
    Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C: The Art of Scientific Computing, 2nd edn. Cambridge University Press, USA (1992), ISBN 0-521-43108-5Google Scholar
  25. 25.
    Salinas, H.M., Fernandez, D.C.: Comparison of PDE-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography. IEEE Transactions on Medical Imaging 26(6), 761–771 (2007)CrossRefGoogle Scholar
  26. 26.
    Wang, Z., Bovik, A.C., Sheikh, H.R., Simon-celli, E.P.: Image quality assessment- from error visibility to structural similarity. IEEE Transactions on Image Processing 13(4), 1–14 (2004)CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Rajeev Srivastava
    • 1
  • J. R. P. Gupta
    • 2
  1. 1.Department of Computer Engineering, Institute of TechnologyBanaras Hindu University (ITBHU)VaranasiIndia
  2. 2.Department of Instrumentation and Control EngineeringNetaji Subhas Institute of, Technology (Delhi University)New DelhiIndia

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