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Improving estimation in speckled imagery

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Abstract

We propose an analytical bias correction for the maximum likelihood estimators of the \(\mathcal{G}_{I}^{0}\) distribution. This distribution is a very powerful tool for speckled imagery analysis, since it is capable of describing a wide range of target roughness. We compare the performance of the corrected estimators with the corresponding original version using Monte Carlo simulation. This second-order bias correction leads to estimators which are better from both the bias and mean square error criteria.

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References

  • Bustos, O. H., Lucini, M. M. & Frery, A. C. (2002), ‘M-estimators of roughness and scale for GAO-modelled SAR imagery’,EURASIP Journal on Applied Signal Processing 2002(1), 105–114.

    MATH  Google Scholar 

  • Cordeiro, G. & Vasconcellos, K. (1999), ‘Second-order biases of the maximum likelihood estimates in von-Mises regression models’,Australian and New Zealand Journal of Statistics 41, 901–910.

    Article  MathSciNet  Google Scholar 

  • Cox, D. R. & Snell, E. J. (1968), ‘A general definition of residuals (with discussion)’,Journal of the Royal Statistical Society B30, 248–275.

    MATH  Google Scholar 

  • Cribari-Neto, F. & Vasconcellos, K. L. P. (2002), ‘Nearly unbiased maximum likelihood estimation for the beta distribution’,Journal of Statistical Computing and Simulation 72(2), 107–118.

    Article  MathSciNet  Google Scholar 

  • Cribari-Neto, F., Frery, A. C. & Silva, M. F. (2002), ‘Improved estimation of clutter properties in speckled imagery’,Computational Statistics and Data Analysis 40(4), 801–824.

    Article  MathSciNet  Google Scholar 

  • Doornik, J. A. (2001),Ox: an object-oriented matrix programming language, 4 edn, Timberlake Consultants & Oxford, London.

    Google Scholar 

  • Firth, D. (1993), ‘Bias reduction of maximum likelihood estimates’,Biometrika 80, 27–38.

    Article  MathSciNet  Google Scholar 

  • Freitas, C. C., Frery, A. C. & Correia, A. H. (in press), ‘The polarimetric G distribution for SAR data analysis’,Environmetrics.

  • Frery, A. C., Cribari-Neto, F. & Souza, M. O. (in press), ‘Analysis of minute features in speckled imagery with maximum likelihood estima-tion’,EURASIP Journal on Applied Signal Processing.

  • Frery, A. C., Müller, H.-J., Yanasse, C. C. F. & Sant’Anna, S. J. S. (1997a), ‘A model for extremely heterogeneous clutter’,IEEE Transactions on Geoscience and Remote Sensing 35(3), 648–659.

    Article  Google Scholar 

  • Frery, A. C., Sant’Anna, S. J. S., Mascarenhas, N. D. A. & Bustos, O. H. (1997b), ‘Robust inference techniques for speckle noise reduction in 1-look amplitude SAR images’,Applied Signal Processing 4, 61–76.

    Google Scholar 

  • Goodman, J. W. (1976), ‘Some fundamental properties of speckle’,Journal of the Optical Society of America 66, 1145–1150.

    Article  Google Scholar 

  • Goodman, N. R. (1963), ‘Statistical analysis based on a certain complex Gaussian distribution (an introduction)’,Annals of Mathematical Statistics 34, 152–177.

    Article  MathSciNet  Google Scholar 

  • Gradshteyn, I. S. & Ryzhik, I. M. (1980),Table of Integrals, Series and Products, Academic Press, New York.

    MATH  Google Scholar 

  • Jørgensen, B. (1982),Statistical Properties of the Generalized Inverse Gaussian Distribution, Vol. 9 ofLecture Notes in Statistics, Springer-Verlag, New York.

    Google Scholar 

  • Mejail, M. E., Frery, A. C., Jacobo-Berlles, J. & Bustos, O. H. (2001), ‘Ap-proximation of distributions for SAR images: proposal, evaluation and practical consequences’,Latin American Applied Research 31, 83–92.

    Google Scholar 

  • Mejail, M. E., Jacobo-Berlles, J., Frery, A. C. & Bustos, O. H. (2000), ‘Parametric roughness estimation in amplitude SAR images under the multiplicative model’,Revista de Teledetección 13, 37–49.

    Google Scholar 

  • Mejail, M. E., Jacobo-Berlles, J., Frery, A. C. & Bustos, O. H. (2003), ‘Clas-sification of SAR images using a general and tractable multiplicative model’,International Journal of Remote Sensing 24(18), 3565–3582.

    Article  Google Scholar 

  • Oliver, C. & Quegan, S. (1998),Understanding Synthetic Aperture Radar Images, Artech House, Boston.

    Google Scholar 

  • Pike, M., Hill, A. & Smith, P. (1980), ‘Bias and efficiency in logistic analysis of stratified case-control studies’,International Journal of Epidemiology 9, 89–95.

    Article  Google Scholar 

  • Seshadri, V. (1993),The Inverse Gaussian Distribution: A Case Study in Exponential Families, Claredon Press, Oxford.

    Google Scholar 

  • Young, D. & Bakir, S. (1987), ‘Bias correction for a generalized log-gamma regression model’,Technometrics 29, 183–191.

    Article  MathSciNet  Google Scholar 

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Acknowledgements

We gratefully acknowledge partial financial support from CNPq, Brazil.

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Vasconcellos, K.L.P., Frery, A.C. & Silva, L.B. Improving estimation in speckled imagery. Computational Statistics 20, 503–519 (2005). https://doi.org/10.1007/BF02741311

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