Adaptive Model-Free Tsallis Entropy Estimation for Detecting Non-Fully Developed Speckle

Detecting departures from the fully developed speckle hypothesis in synthetic aperture radar (SAR) imagery is essential for reliable interpretation in remote sensing applications. To address this challenge, this article proposes a statistical test based on a nonparametric estimator of Tsallis entropy, a nonadditive generalization of Shannon entropy that provides enhanced sensitivity to heavy-Tailed distributions characteristic of textured SAR data. The estimator incorporates bootstrap correction to improve accuracy with small sample sizes. The test is integrated within an adaptive windowing strategy that locally selects the optimal window size based on regional homogeneity: larger windows in homogeneous regions to stabilize estimation and smaller windows in heterogeneous areas to preserve structural details. This combination yields an unsupervised statistical framework that generates per-pixel {p}-value maps for detecting departures from fully developed speckle. Experimental validation using both simulated data and SAR imagery confirms the method's precision in detecting texture variability and discriminating between homogeneous and heterogeneous regions. The proposed approach offers an interpretable tool for automated SAR image analysis without requiring training data or explicit parametric texture estimation.