Entropy-based Statistical Analysis of PolSAR Data

TL;DR

This paper derives entropy measures for PolSAR data modeled by the scaled Wishart distribution, analyzes their properties, and proposes new hypothesis tests for contrast detection, validated with simulated and real data.

Contribution

It provides analytic expressions for Shannon, Rényi, and Tsallis entropies under the scaled Wishart model and introduces new hypothesis tests based on these measures.

Findings

Shannon entropy-based test outperforms Rényi-based test.

Derived confidence intervals for entropy measures.

Validated methods with simulated and real PolSAR data.

Abstract

Images obtained from coherent illumination processes are contaminated with speckle noise, with polarimetric synthetic aperture radar (PolSAR) imagery as a prominent example. With an adequacy widely attested in the literature, the scaled complex Wishart distribution is an acceptable model for PolSAR data. In this perspective, we derive analytic expressions for the Shannon, R\'enyi, and restricted Tsallis entropies under this model. Relationships between the derived measures and the parameters of the scaled Wishart law (i.e., the equivalent number of looks and the covariance matrix) are discussed. In addition, we obtain the asymptotic variances of the Shannon and R\'enyi entropies when replacing distribution parameters by maximum likelihood estimators. As a consequence, confidence intervals based on these two entropies are also derived and proposed as new ways of capturing contrast. New hypothesis tests are additionally proposed using these results, and their performance is assessed using simulated and real data. In general terms, the test based on the Shannon entropy outperforms those based on R\'enyi's.