Statistical and Neural Approaches for Estimating Parameters of a Speckle Model Based on the Nakagami Distribution

  • Mark P. Wachowiak
  • Renata Smolíková
  • Mariofanna G. Milanova
  • Adel S. Elmaghraby
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2123)


The Nakagami distribution is a model for the backscattered ultrasound echo from tissues. The Nakagami shape parameter m has been shown to be useful in tissue characterization. Many approaches to estimating this parameter have been reported. In this paper, a maximum likelihood estimator (MLE) is derived, and a solution method is proposed. It is also shown that a neural network can be trained to recognize parameters directly from data. Accuracy and consistency of these new estimators are compared to those of the inverse normalized variance, Tolparev-Polyakov, and Lorenz estimators.


Maximum Likelihood Estimation Speckle Noise Neural Learning General Statistical Model Neural Approach 
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  1. 1.
    Abdi, A., Kaveh, M.: Performance Comparison of Three Different Estimators for the Nakagami m Parameter Using Monte Carlo Simulation. IEEE Communications Letters 4 (2000) 119–121CrossRefGoogle Scholar
  2. 2.
    Alzer, H.: On Some Inequalities for the Gamma and Psi Functions. Math. Comp. 66 (1997) 373–389zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Clifford, L., Fitzgerald, P., James, D.: Non-Rayleigh First-Order Statistics of Ultrasonic Backscatter from Normal Myocardum. Ultrasound in Med. and Biol. 19 (1993) 487–495CrossRefGoogle Scholar
  4. 4.
    Iskander, D. R., Zoubir, A. M., Boashash, B.: A Method for Estimating the Parameters of the K Distribution. IEEE Trans. Sig. Proc. 47 (1991) 1147–1151CrossRefGoogle Scholar
  5. 5.
    Liu, M. C., Kuo, W., Sastri, T.: An Exploratory Study of a Neural Network Approach for Reliability Data. Analysis Quality and Reliability Eng. Intl. 11 (1995) 107–112CrossRefGoogle Scholar
  6. 6.
    Nakagami, M.: The m-distribution: A general formula of intensity distribution of rapid fading. in Statistical Methods in Radio Wave Propagation W. C. Hoffman, Ed. New York: Pergamon (1960) 3–36Google Scholar
  7. 7.
    Shankar, P. M.: A General Statistical Model for Ultrasonic Backscattering from Tissues. IEEE Trans. on Ultrasonics, Ferroelectrics and Frequency Control 47 (2000) 727–736CrossRefGoogle Scholar
  8. 8.
    Smolýková, R., Wachowiak, M. P., Elmaghraby, A. S., Zurada, J. M.: A Neuro-Statistical Approach to Ultrasound Speckle Modeling. Proc. ISCA 13th Intl. Conf., Honolulu, HI (2000) 94–97Google Scholar
  9. 9.
    Wachowiak, M. P., Smolýková, R., Zurada, J. M., Elmaghraby, A. S.: A Neural Approach to Speckle Noise Modeling. Intelligent Engineering System Through Artificial Neural Networks: Smart Engineering System Design: Neural Networks, Fuzzy Logic, Evolutionary Programming, Data Mining and Complex Systems 10 ASME Press, New York (2000) 837–842Google Scholar
  10. 10.
    Wachowiak, M. P., Smolýková, R., Elmaghraby, A. S., Zurada, J. M.: Classification and Estimation of Ultrasound Speckle Noise With Neural Networks. Proc. on IEEE International Symposium on Bio-Informatics and Biomedical Engineering. Arlington, Virginia (2000) 245–252Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Mark P. Wachowiak
    • 1
  • Renata Smolíková
    • 1
    • 2
  • Mariofanna G. Milanova
    • 1
    • 3
  • Adel S. Elmaghraby
    • 1
  1. 1.Department of Computer Engineering and Computer ScienceUniversity of LouisvilleLouisvilleUSA
  2. 2.Institute for Research and Applications of Fuzzy ModelingUniversity of OstravaCzech Republic
  3. 3.ICSRBulgarian Academy of ScienceBulgaria

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