On the method of logarithmic cumulants for parametric probability density function estimation

IEEE Transactions on Image Processing

Volumn 22, Issue 10, 2013, Pages 3791-3806

  Krylov, Vladimir A ^a   Moser, Gabriele ^b   Serpico, Sebastiano B ^b   Zerubia, Josiane ^c  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF GENOA   (Italy)

^c INRIA   (France)

Author keywords

generalized gamma distribution; image classification; K distribution; parameter estimation; Probability density function; strong consistency

Indexed keywords

GENERALIZED GAMMA DISTRIBUTION; K-DISTRIBUTION; METHOD OF MOMENTS (MOM); PROBABILITY DENSITY FUNCTION ESTIMATIONS; STATISTICAL ESTIMATORS; STRONG CONSISTENCY; SUPERVISED IMAGE CLASSIFICATIONS; SYNTHETIC AND REAL DATA;

EXPERIMENTS; IMAGE CLASSIFICATION; IMAGE PROCESSING; METHOD OF MOMENTS; PARAMETER ESTIMATION; PROBABILITY DENSITY FUNCTION;

SYNTHETIC APERTURE RADAR;

ALGORITHM; COMPUTER SIMULATION; ECHOGRAPHY; HUMAN; IMAGE PROCESSING; PROCEDURES; STATISTICAL MODEL; TELECOMMUNICATION; ARTICLE; METHODOLOGY;

ALGORITHMS; COMPUTER SIMULATION; HUMANS; IMAGE PROCESSING, COMPUTER-ASSISTED; MODELS, STATISTICAL; RADAR; ULTRASONOGRAPHY;

EID: 84883337089     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2013.2262285     Document Type: Article

References (37)

1. C. M. Bishop, Pattern Recognition and Machine Learning. New York, NY, USA: Springer-Verlag, 2006.
2. A. Stuart and J. Keith, Kendall's Advanced Theory of Statistics, 6th ed. New York, NY, USA: Wiley, 2008.
3. K. Song, "Globally convergent algorithms for estimating generalized gamma distributions in fast signal and image processing, " IEEE Trans. Image Process., vol. 17, no. 8, pp. 1233-1250, Aug. 2008.
4. G. Moser, J. Zerubia, and S. B. Serpico, "SAR amplitude probability density function estimation based on a generalized Gaussian model, " IEEE Trans. Image Process., vol. 15, no. 6, pp. 1429-1442, Jun. 2006.
5. C. Tison, J.-M. Nicolas, F. Tupin, and H. Maitre, "A new statistical model for Markovian classification of urban areas in high-resolution SAR images, " IEEE Trans. Geosci. Remote Sens., vol. 42, no. 10, pp. 2046-2057, Oct. 2004.
6. D. A. Abraham and A. P. Lyons, "Reliable methods for estimating the K-distribution shape parameter, " IEEE J. Ocean. Eng., vol. 35, no. 2, pp. 288-302, Apr. 2010.
7. R. A. Redner and H. F. Walker, "Mixture densities, maximum likelihood, and the EM algorithm, " SIAM Rev., vol. 26, no. 2, pp. 195-239, 1984.
8. J.-M. Nicolas, "Introduction aux statistiques de deuxieme espece: Applications des logs-moments et des logs-cumulants a l'analyse des lois d'images radar, " Traitement Signal (French), vol. 19, no. 3, pp. 139-167, 2002.
9. H. Cramer, Mathematical Methods of Statistics. Princeton, NJ, USA: Princeton Univ. Press, 1946.
10. B. Epstein, "Some applications of the Mellin transform in statistics, " Ann. Math. Stat., vol. 19, no. 3, pp. 370-379, 1948.
11. E. E. Kuruoglu and J. Zerubia, "Modelling SAR images with a generalization of the Rayleigh distribution, " IEEE Trans. Image Process., vol. 13, no. 4, pp. 527-533, Apr. 2004.
12. E. W. Stacy, "A generalization of the gamma distribution, " Ann. Math. Statist., vol. 33, no. 3, pp. 1187-1192, 1962.
13. E. Jakeman and P. N. Pusey, "A model for non-Rayleigh sea echo, " IEEE Trans. Antennas Propag., vol. 24, no. 6, pp. 806-814, Nov. 1976.
14. C. Oliver and S. Quegan, Understanding Synthetic Aperture Radar Images, 2nd ed. Raleigh, NC, USA: SciTech, 2004.
15. J. W. Shin, J. H. Chang, and N. S. Kim, "Statistical modeling of speech signals based on generalized gamma distribution, " IEEE Signal Process. Lett., vol. 12, no. 3, pp. 258-261, Mar. 2005.
16. J. H. Chang, J. W. Shin, N. S. Kim, and S. K. Mitra, "Image probability distribution based on generalized gamma function, " IEEE Signal Process. Lett., vol. 12, no. 4, pp. 325-328, Apr. 2005.
17. V. A. Krylov, G. Moser, S. B. Serpico, and J. Zerubia, "Enhanced dictionary-based SAR amplitude distribution estimation and its validation with very high-resolution data, " IEEE Geosci. Remote Sens. Lett., vol. 8, no. 1, pp. 148-152, Jan. 2011.
18. H.-C. Li, W. Hong, Y.-R. Wu, and P.-Z. Fan, "On the empirical-statistical modeling of SAR images with generalized gamma distribution, " IEEE J. Sel. Top. Signal Process., vol. 5, no. 3, pp. 386-397, Jun. 2011.
19. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions. New York, NY, USA: Dover, 1964.
20. F. Galland, J.-M. Nicolas, H. Sportouche, M. Roche, F. Tupin, and P. Refregier, "Unsupervised synthetic aperture radar image segmentation using Fisher distributions, " IEEE Trans. Geosci. Remote Sens., vol. 47, no. 8, pp. 2966-2972, Aug. 2009.
21. S. N. Anfinsen and T. Eltoft, "Application of the matrix-variate Mellin transform to analysis of polarimetric radar images, " IEEE Trans. Geosci. Remote Sens., vol. 49, no. 6, pp. 2281-2295, Jun. 2011.
22. T. Eltoft, "Modeling the amplitude statistics of ultrasonic images, " IEEE Trans. Med. Imag., vol. 25, no. 2, pp. 229-240, Feb. 2006.
23. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. New York, NY, USA: McGraw-Hill, 1991.
24. V. A. Krylov, G. Moser, S. B. Serpico, and J. Zerubia, "Supervised high-resolution dual-polarization SAR image classification by finite mixtures and copulas, " IEEE J. Sel. Topics Signal Process., vol. 5, no. 3, pp. 554-566, Jun. 2011.
25. J. F. Lawless, "Inference in the generalized gamma and log gamma distribution, " Technometrics, vol. 22, no. 3, pp. 409-419, 1980.
26. D. R. Wingo, "Computing maximum-likelihood parameter estimates of the generalized gamma distribution by numerical root isolation, " IEEE Trans. Rel., vol. 36, no. 5, pp. 586-590, Dec. 1987.
27. H. W. Hager and L. J. Bain, "Inferential procedures for the generalized gamma distribution, " J. Amer. Stat. Assoc., vol. 65, no. 332, pp. 1601-1609, 1970.
28. A. C. Cohen and B. J. Whitten, Parameter Estimation in Reliability and Life Span Models. New York, NY, USA: Marcel Dekker, 1988.
29. H. Hirose, "Maximum likelihood parameter estimation by model augmentation with applications to the extended four-parameter generalized gamma distribution, " Math. Comput. Simul., vol. 54, nos. 1-3, pp. 81-97, 2000.
30. F. Ashkar, B. Bobee, D. Leroux, and D. Morisette, "The generalized method of moments as applied to the generalized gamma distribution, " Stochastic Hydrol. Hydraul., vol. 2, no. 3, pp. 161-174, 1988.
31. W. J. J. Roberts and S. Furui, "Maximum likelihood estimation of K-distribution parameters via the expectation-maximization algorithm, " IEEE Trans. Signal Process., vol. 48, no. 12, pp. 3303-3306, Dec. 2000.
32. D. R. Iskander, A. M. Zoubir, and B. Boashash, "A method for estimating the parameters of the k-distribution, " IEEE Trans. Signal Process., vol. 47, no. 4, pp. 1147-1151, Apr. 1999.
33. S. Z. Li, Markov Random Field Modeling in Image Analysis, 3rd ed. New York, NY, USA: Springer-Verlag, 2009.
34. Y. Boykov, O. Veksler, and R. Zabih, "Efficient approximate energy minimization via graph cuts, " IEEE Trans. Pattern Anal. Mach. Intell., vol. 20, no. 12, pp. 1222-1239, Nov. 2001.
35. Y. Boykov and V. Kolmogorov, "An experimental comparison of mincut/ max-flow algorithms for energy minimization in vision, " IEEE Trans. Pattern Anal. Mach. Intell., vol. 26, no. 9, pp. 1124-1137, Sep. 2004.
36. W. Rudin, Principles of mathematical analysis, 3rd ed. New York, NY, USA: McGraw-Hill, 1976.
37. N. Batir, "On some properties of digamma and polygamma functions, " J. Math. Anal. Appl., vol. 328, no. 1, pp. 452-465, 2007.