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Parametric and nonparametric tests for speckled imagery

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Abstract

Synthetic aperture radar (SAR) has a pivotal role as a remote imaging method. Obtained by means of coherent illumination, SAR images are contaminated with speckle noise. The statistical modeling of such contamination is well described according to the multiplicative model and its implied \(\fancyscript{G}^0\) distribution. The understanding of SAR imagery and scene element identification is an important objective in the field. In particular, reliable image contrast tools are sought. Aiming the proposition of new tools for evaluating SAR image contrast, we investigated new methods based on stochastic divergence. We propose several divergence measures specifically tailored for \(\fancyscript{G}^0\) distributed data. We also introduce a nonparametric approach based on the Kolmogorov–Smirnov distance for \(\fancyscript{G}^0\) data. We devised and assessed tests based on such measures, and their performances were quantified according to their test sizes and powers. Using Monte Carlo simulation, we present a robustness analysis of test statistics and of maximum likelihood estimators for several degrees of innovative contamination. It was identified that the proposed tests based on triangular and arithmetic-geometric measures outperformed the Kolmogorov–Smirnov methodology.

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Acknowledgments

Authors are grateful to CNPq and FACEPE for funding this research.

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Authors and Affiliations

  1. Departamento de Estatística, Universidade Federal de Pernambuco, Cidade Universitária, 50740-540, Recife, Pernambuco, Brazil

    Renato J. Cintra

  2. CPMAT & LCCV, Instituto de Computação, Universidade Federal de Alagoas, Maceió, Alagoas, Brazil

    Alejandro C. Frery

  3. Graduate Program in Statistics, Universidade Federal de Pernambuco, Recife, Pernambuco, Brazil

    Abraão D. C. Nascimento

Authors
  1. Renato J. Cintra
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  2. Alejandro C. Frery
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  3. Abraão D. C. Nascimento
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Corresponding author

Correspondence to Renato J. Cintra.

Computational information

Computational information

Simulations of the (h, ϕ)-distance based parametric tests were performed in Ox programming environment [10]; function QAGI was employed for numerical integration. The Kolmogorov–Smirnov test was coded in R and function ks.test was called [35]. The computation time of the triangular and arithmetic-geometric distances took typically less than one and four millisecond, respectively, when performed in a Pentium processor at 3.20 GHz. We used the George Marsaglia’s multiply-with-carry with 52 bits pseudorandom number generator, which has an approximate period of 28222.

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Cintra, R.J., Frery, A.C. & Nascimento, A.D.C. Parametric and nonparametric tests for speckled imagery. Pattern Anal Applic 16, 141–161 (2013). https://doi.org/10.1007/s10044-011-0249-3

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