A novel bivariate distribution and its divergence-based hypothesis inference: an application to the deforestation focus detection

• Published in: International journal of remote sensing Vol. 44; no. 1; pp. 1 - 29
• Main Authors: Silva, A. S., Nascimento, A D.C.
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 02.01.2023; Taylor & Francis Ltd
• Subjects: Bivariate analysis; Bivariate distribution; Change detection; Deforestation; Detectors; Distribution; Hypotheses; Hypothesis testing; information theory; Likelihood ratio; Performance evaluation; PolSAR data; Remote sensing; SAR (radar); Statistical methods; Synthetic aperture radar; Urbanization
• ISSN: 0143-1161; 1366-5901
• DOI: 10.1080/01431161.2022.2155087

The polarimetric synthetic aperture radar (PolSAR) system is one of the most successful tools for solving remote-sensing issues. However, the images produced by this system - which uses coherent illumination - are corrupted by the multidimensional speckle noise that gives PolSAR data a multiplicative character. Therefore, tailored processing of PolSAR images is required, e.g. improved hypothesis testing and change detectors. In this work, we propose a novel bivariate distribution - called McKay bivariate ( MB) - to describe a joint distribution arising from two components of the total scattering power image (SPAN). We derive closed-form expressions for the Kullback-Leibler and Rényi divergences for the MB law. 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. Results show that our proposals to detect changes in PolSAR images outperform the one based on the likelihood ratio.