Analytic Expressions for Stochastic Distances Between Relaxed Complex Wishart Distributions

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.Comment: Accepted for publication in the IEEE Transactions on Geoscience and Remote Sensing journa

Improvement of PolSAR Decomposition Scattering Powers Using a Relative Decorrelation Measure

In this letter, a methodology is proposed to improve the scattering powers obtained from model-based decomposition using Polarimetric Synthetic Aperture Radar (PolSAR) data. The novelty of this approach lies in utilizing the intrinsic information in the off-diagonal elements of the 3$\times$3 coherency matrix $\mathbf{T}$ represented in the form of complex correlation coefficients. Two complex correlation coefficients are computed between co-polarization and cross-polarization components of the Pauli scattering vector. The difference between modulus of complex correlation coefficients corresponding to $\mathbf{T}^{\mathrm{opt}}$ (i.e. the degree of polarization (DOP) optimized coherency matrix), and $\mathbf{T}$ (original) matrices is obtained. Then a suitable scaling is performed using fractions \emph{i.e.,} $(T_{ii}^{\mathrm{opt}}/\sum\limits_{i=1}^{3}T_{ii}^{\mathrm{opt}})$ obtained from the diagonal elements of the $\mathbf{T}^{\mathrm{opt}}$ matrix. Thereafter, these new quantities are used in modifying the Yamaguchi 4-component scattering powers obtained from $\mathbf{T}^{\mathrm{opt}}$. To corroborate the fact that these quantities have physical relevance, a quantitative analysis of these for the L-band AIRSAR San Francisco and the L-band Kyoto images is illustrated. Finally, the scattering powers obtained from the proposed methodology are compared with the corresponding powers obtained from the Yamaguchi \emph{et. al.,} 4-component (Y4O) decomposition and the Yamaguchi \emph{et. al.,} 4-component Rotated (Y4R) decomposition for the same data sets. The proportion of negative power pixels is also computed. The results show an improvement on all these attributes by using the proposed methodology.Comment: Accepted for publication in Remote Sensing Letter