Entropy-based Statistical Analysis of 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, Rényi, 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 Rényi 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 Rényi's.

Accepted for publication on IEEE Transactions on Geoscience and Remote Sensing

References in corpus (7)

• Hypothesis Testing in Speckled Data with Stochastic Distances
• Polarimetric SAR Image Segmentation with B-Splines and a New Statistical Model
• Example of a possible interpretation of Tsallis entropy
• Information Theory and Image Understanding: An Application to Polarimetric SAR Imagery
• Nonparametric Edge Detection in Speckled Imagery
• Parametric and Nonparametric Tests for Speckled Imagery
• Property of Tsallis entropy and principle of entropy increase

Cited by in corpus (6)

• Modifying the Yamaguchi Four-Component Decomposition Scattering Powers Using a Stochastic Distance
• Detecting Changes in Fully Polarimetric SAR Imagery with Statistical Information Theory
• Bias Correction and Modified Profile Likelihood under the Wishart Complex Distribution
• Classification of Complex Wishart Matrices with a Diffusion-Reaction System guided by Stochastic Distances
• Contrast Measures based on the Complex Correlation Coefficient for PolSAR Imagery
• The Geodesic Distance between ${\mathcal{G}}_I^0$ Models and its Application to Region Discrimination