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Computational and Mathematical Methods in Medicine
Volume 2012, Article ID 481923, 25 pages
http://dx.doi.org/10.1155/2012/481923
Research Article

A Generalized Gamma Mixture Model for Ultrasonic Tissue Characterization

Laboratorio de Procesado de Imagen, ETSI Telecomunicación Edificio de las Nuevas Tecnologías, Campus Miguel Delibes s/n, Universidad de Valladolid, 47011 Valladolid, Spain

Received 1 June 2012; Revised 20 August 2012; Accepted 31 August 2012

Academic Editor: Huafeng Liu

Copyright © 2012 Gonzalo Vegas-Sanchez-Ferrero et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. W. Goodman, “Some fundamental properties of laser speckle,” in Laser Speckle and Related Phenomena, vol. 9–75 of Topics in Applied Physics, chapter, pp. 1145–1150, Springer, Heidelberg, Germany, 1975. View at Google Scholar
  2. T. Eltoft, “Modeling the amplitude statistics of ultrasonic images,” IEEE Transactions on Medical Imaging, vol. 25, no. 2, pp. 229–240, 2006. View at Publisher · View at Google Scholar · View at Scopus
  3. F. Destrempes, J. Meunier, M.-F. Giroux, G. Soulez, and G. Cloutier, “Segmentation in ultrasonic B-mode images of healthy carotid arteries using mixtures of Nakagami distributions and stochastic optimization,” IEEE Transactions on Medical Imaging, vol. 28, no. 2, pp. 215–229, 2009. View at Publisher · View at Google Scholar · View at Scopus
  4. J. C. Seabra, F. Ciompi, O. Pujol, J. Mauri, P. Radeva, and J. Sanches, “Rayleigh mixture model for plaque characterization in intravascular ultrasound,” IEEE Transactions on Biomedical Engineering, vol. 58, no. 5, pp. 1314–1324, 2011. View at Publisher · View at Google Scholar · View at Scopus
  5. Y. Yu and S. T. Acton, “Speckle reducing anisotropic diffusion,” IEEE Transactions on Image Processing, vol. 11, no. 11, pp. 1260–1270, 2002. View at Publisher · View at Google Scholar · View at Scopus
  6. S. Aja-Fernández and C. Alberola-López, “On the estimation of the coefficient of variation for anisotropic diffusion speckle filtering,” IEEE Transactions on Image Processing, vol. 15, no. 9, pp. 2694–2701, 2006. View at Publisher · View at Google Scholar · View at Scopus
  7. K. Krissian, C.-F. Westin, R. Kikinis, and K. G. Vosburgh, “Oriented speckle reducing anisotropic diffusion,” IEEE Transactions on Image Processing, vol. 16, no. 5, pp. 1412–1424, 2007. View at Publisher · View at Google Scholar · View at Scopus
  8. G. Vegas-Sánchez-Ferrero, S. Aja-Fernández, M. Martín-Fernández, A. F. Frangi, and C. Palencia, “Probabilistic-driven oriented speckle reducing anisotropic diffusion with application to cardiac ultrasonic images,” in Proceedings of the 13th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part I, pp. 518–525, 2010.
  9. G. Vegas-Sánchez-Ferrero, D. Martíin-Martíinez, S. Aja-Fernández, and C. Palencia, “On the influence of interpolation on probabilistic models for ultrasonic images,” in Proceedings of the 7th IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI '10), pp. 292–295, April 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. Z. Tao, H. D. Tagare, and J. D. Beaty, “Evaluation of four probability distribution models for speckle in clinical cardiac ultrasound images,” IEEE Transactions on Medical Imaging, vol. 25, no. 11, pp. 1483–1491, 2006. View at Publisher · View at Google Scholar · View at Scopus
  11. M. M. Nillesen, R. G. P. Lopata, I. H. Gerrits, L. Kapusta, J. M. Thijssen, and C. L. de Korte, “Modeling envelope statistics of blood and myocardium for segmentation of echocardiographic images,” Ultrasound in Medicine and Biology, vol. 34, no. 4, pp. 674–680, 2008. View at Publisher · View at Google Scholar · View at Scopus
  12. P. M. Shankar, “A general statistical model for ultrasonic backscattering from tissues,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 47, no. 3, pp. 727–736, 2000. View at Google Scholar · View at Scopus
  13. P. M. Shankar, “Ultrasonic tissue characterization using a generalized Nakagami model,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 48, no. 6, pp. 1716–1720, 2001. View at Publisher · View at Google Scholar · View at Scopus
  14. E. W. Stacy and G. A. Mihram, “Parameter estimation for a generalized gamma distribution,” Technometrics, vol. 7, no. 3, pp. 349–358, 1965. View at Google Scholar
  15. T. K. Moon, “The expectation-maximization algorithm,” IEEE Signal Processing Magazine, vol. 13, no. 6, pp. 47–60, 1996. View at Google Scholar
  16. O. Gomes, C. Combes, and A. Dussauchoy, “Parameter estimation of the generalized gamma distribution,” Mathematics and Computers in Simulation, vol. 79, no. 4, pp. 955–963, 2008. View at Publisher · View at Google Scholar · View at Scopus
  17. A. Noufaily and M. Jones, “On maximization of the likelihood for the generalized gamma distribution,” Computational Statistics. In press.
  18. R. F. Wagner, S. W. Smith, J. M. Sandrik, and H. Lopez, “Statistics of speckle in ultrasound B-scans,” IEEE Transactions on Sonics and Ultrasonics, vol. 30, no. 3, pp. 156–163, 1983. View at Google Scholar · View at Scopus
  19. V. Dutt and J. F. Greenleaf, “Ultrasound echo envelope analysis using a homodyned K distribution signal model,” Ultrasonic Imaging, vol. 16, no. 4, pp. 265–287, 1994. View at Publisher · View at Google Scholar · View at Scopus
  20. D. R. Wingo, “Computing maximum-likelihood parameter estimates of the generalized gamma distribution by numerical root isolation,” IEEE Transactions on Reliability, vol. 36, no. 5, pp. 586–590, 1987. View at Google Scholar · View at Scopus
  21. H. W. Hager and L. J. Bain, “Inferential procedures for the generalized gamma distribution,” Journal of the American Statistical Association, vol. 65, no. 332, pp. 1601–1609, 1970. View at Google Scholar
  22. B. Jones, W. G. Waller, and A. Feldman, “Root isolation using function values,” BIT Numerical Mathematics, vol. 18, no. 3, pp. 311–319, 1978. View at Publisher · View at Google Scholar · View at Scopus
  23. J. F. Lawless, “Inference in the generalized gamma and log gamma distributions,” Technometrics, vol. 22, no. 3, pp. 409–419, 1980. View at Google Scholar · View at Scopus
  24. J. A. Nelder and R. Mead, “A simplex method for function minimization,” The Computer Journal, vol. 7, no. 4, pp. 308–313, 1965. View at Google Scholar
  25. R. P. Brent, Algorithms for Minimization without Derivatives, Prentice Hall, Upper Saddle River, NJ, USA, 1973.
  26. M. E.-S. Waheed, O. A. Mohamed, and M. E. Abd El-Aziz, “Mixture of generalized gamma density-based score function for fastica,” Mathematical Problems in Engineering, vol. 2011, Article ID 150294, 14 pages, 2011. View at Publisher · View at Google Scholar · View at Scopus
  27. M. A. T. Figueiredo and A. K. Jain, “Unsupervised learning of finite mixture models,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 3, pp. 381–396, 2002. View at Publisher · View at Google Scholar · View at Scopus
  28. H. Alzer, “On some inequalities for the gamma and psi functions,” Mathematics of Computation, vol. 66, no. 217, pp. 373–389, 1997. View at Google Scholar · View at Scopus
  29. G. Marsaglia and W. W. Tsang, “A simple method for generating gamma variables,” ACM Transactions on Mathematical Software, vol. 26, no. 3, pp. 363–372, 2000. View at Google Scholar · View at Scopus
  30. R. M. Dudley, Uniform Central Limit Theorems, Cambridge University Press, Cambridge, UK, 1st edition, 1999.
  31. J. A. Jensen, “Field: a program for simulating ultrasound systems,” in Proceedings of the 10th Nordicbaltic Conference on Biomedical Imaging, vol. 4, supplement 1, part 1, pp. 351–353, 1996.
  32. A. R. Webb, “Gamma mixture models for target recognition,” Pattern Recognition, vol. 33, no. 12, pp. 2045–2054, 2000. View at Google Scholar · View at Scopus
  33. K. Copsey and A. Webb, “Bayesian gamma mixture model approach to radar target recognition,” IEEE Transactions on Aerospace and Electronic Systems, vol. 39, no. 4, pp. 1201–1217, 2003. View at Publisher · View at Google Scholar · View at Scopus
  34. J. Pearl, “Reverend Bayes on inference engines: a distributed hierarchical approach,” in Proceedings of the American Association of Artificial Intelligence National Conference on AI, pp. 133–136, 1982.
  35. F. R. Kschischang, B. J. Frey, and H. A. Loeliger, “Factor graphs and the sum-product algorithm,” IEEE Transactions on Information Theory, vol. 47, no. 2, pp. 498–519, 2001. View at Publisher · View at Google Scholar · View at Scopus