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Divergence-based tests for the bivariate gamma distribution applied to polarimetric synthetic aperture radar

Author

Listed:
  • Abraão Nascimento

    (Universidade Federal de Pernambuco)

  • Jodavid Ferreira

    (Universidade Federal da Paraíba)

  • Alisson Silva

    (Universidade Federal de Pernambuco)

Abstract

The use of polarimetric synthetic aperture radar (PolSAR) is one of the most successful tools for solving remote sensing problems. The multidimensional speckle noise encountered in the acquisition of these images is the main challenge for PolSAR users. Therefore, tailored processing of PolSAR images is required, especially for the use of hypothesis testing in change detection. In this paper, we use McKay’s bivariate gamma distribution (MBG) to describe a joint distribution resulting from two components of the total scattering power image (SPAN). We derive closed form expressions for the MBG Kullback–Leibler and Rényi divergences between SPAN-based random pairs. We provide new two-sample divergence-based hypothesis tests and evaluate their performance using Monte Carlo experiments. Finally, we apply the new tests to real PolSAR images to evaluate the changes caused by urbanization processes in the Los Angeles and California regions. The results show that our proposals are able to detect changes in PolSAR images.

Suggested Citation

  • Abraão Nascimento & Jodavid Ferreira & Alisson Silva, 2023. "Divergence-based tests for the bivariate gamma distribution applied to polarimetric synthetic aperture radar," Statistical Papers, Springer, vol. 64(5), pages 1439-1463, October.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:5:d:10.1007_s00362-022-01354-4
    DOI: 10.1007/s00362-022-01354-4
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    References listed on IDEAS

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    1. Saralees Nadarajah, 2005. "Reliability for some bivariate gamma distributions," Mathematical Problems in Engineering, Hindawi, vol. 2005, pages 1-13, January.
    2. Hagedorn, M. & Smith, P.J. & Bones, P.J. & Millane, R.P. & Pairman, D., 2006. "A trivariate chi-squared distribution derived from the complex Wishart distribution," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 655-674, March.
    3. Salicru, M. & Morales, D. & Menendez, M. L. & Pardo, L., 1994. "On the Applications of Divergence Type Measures in Testing Statistical Hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 372-391, November.
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