Images obtained with coherent illumination, as is the case of sonar, ultrasound-B, laser and Synthetic Aperture Radar -SAR, are affected by speckle noise which reduces the ability to extract information from the data. Specialized techniques are required to deal with such imagery, which has been modeled by the G 0 distribution and under which regions with different degrees of roughness and mean brightness can be characterized by two parameters; a third parameter, the number of looks, is related to the overall signal-to-noise ratio. Assessing distances between samples is an important step in image analysis; they provide grounds of the separability and, therefore, of the performance of classification procedures. This work derives and compares eight stochastic distances and assesses the performance of hypothesis tests that employ them and maximum likelihood estimation. We conclude that tests based on the triangular distance have the closest empirical size to the theoretical one, while those based on the arithmetic-geometric distances have the best power. Since the power of tests based on the triangular distance is close to optimum, we conclude that the safest choice is using this distance for hypothesis testing, even when compared with classical distances as Kullback-Leibler and Bhattacharyya.

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The scaled complex Wishart distribution is a widely used model for multilook full polarimetric SAR data whose adequacy has been attested in the literature. Classification, segmentation, and image analysis techniques which depend on this model have been devised, and many of them employ some type of dissimilarity measure. In this paper we derive analytic expressions for four stochastic distances between relaxed scaled complex Wishart distributions in their most general form and in important particular cases. Using these distances, inequalities are obtained which lead to new ways of deriving the Bartlett and revised Wishart distances. The expressiveness of the four analytic distances is assessed with respect to the variation of parameters. Such distances are then used for deriving new tests statistics, which are proved to have asymptotic chi-square distribution. Adopting the test size as a comparison criterion, a sensitivity study is performed by means of Monte Carlo experiments suggesting that the Bhattacharyya statistic outperforms all the others. The power of the tests is also assessed. Applications to actual data illustrate the discrimination and homogeneity identification capabilities of these distances.

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.

Images obtained from coherent illumination processes are contaminated with speckle. A prominent example of such imagery systems is the polarimetric synthetic aperture radar (PolSAR). For such remote sensing tool the speckle interference pattern appears in the form of a positive definite Hermitian matrix, which requires specialized models and makes change detection a hard task. The scaled complex Wishart distribution is a widely used model for PolSAR images. Such distribution is defined by two parameters: the number of looks and the complex covariance matrix.The last parameter contains all the necessary information to characterize the backscattered data and, thus, identifying changes in a sequence of images can be formulated as a problem of verifying whether the complex covariance matrices differ at two or more takes. This paper proposes a comparison between a classical change detection method based on the likelihood ratio and three statistical methods that depend on information-theoretic measures: the Kullback-Leibler distance and two entropies. The performance of these four tests was quantified in terms of their sample test powers and sizes using simulated data. The tests are then applied to actual PolSAR data. The results provide evidence that tests based on entropies may outperform those based on the Kullback-Leibler distance and likelihood ratio statistics. PUBLISHED IN THE IEEE TGRS 2 follow the Gaussian law. Thus, analyzing PolSAR images requires tailored image processing based on the statistical properties of speckled data.PolSAR theory prescribes that the returned (backscattered) signal of distributed targets is adequately represented by its complex covariance matrix. Under the assumption that the complex scattering coefficients are jointly circular Gaussian, the Wishart distribution is the statistical model for multilook PolSAR data. This paper adopts the assumption that a PolSAR image is well described by such distribution.Change detection methods aim at identifying differences in the scene configuration at distinct observation instants. Such procedures have achieved a prominent position in recent decades [2]. Indeed, literature reports several approaches for change detection problems, among them: (i) image ratioing [3]-[6], (ii) multitemporal coherence analysis [7], (iii) spatiotemporal contextual classification [8], [9], (iv) Hotelling-Lawley and likelihood ratio tests [10]-[19] and robust tests [20], (v) combination of image ratioing and the generalized minimum-error method [21], (vi) detection algorithms based on Lagrange optimization [22], (vii) information-theoretic measures for change detection [9], [23]-[30] and (viii) change detection with post-classification [31]. This paper advances points (iv) and (vii) above. The change detection process is theoretically rooted in the hypothesis test theory and the proposal of statistical similarity measures [32]. In particular, hypothesis tests based on the complex covariance matrix have been sought for PolSAR data analysis. Many statistical approaches hav...