Modifying the Yamaguchi Four-Component Decomposition Scattering Powers Using a Stochastic Distance

Model-based decompositions have gained considerable attention after the initial work of Freeman and Durden. This decomposition which assumes the target to be reflection symmetric was later relaxed in the Yamaguchi et al. decomposition with the addition of the helix parameter. Since then many decomposition have been proposed where either the scattering model was modified to fit the data or the coherency matrix representing the second order statistics of the full polarimetric data is rotated to fit the scattering model. In this paper we propose to modify the Yamaguchi four-component decomposition (Y4O) scattering powers using the concept of statistical information theory for matrices. In order to achieve this modification we propose a method to estimate the polarization orientation angle (OA) from full-polarimetric SAR images using the Hellinger distance. In this method, the OA is estimated by maximizing the Hellinger distance between the un-rotated and the rotated $T_{33}$ and the $T_{22}$ components of the coherency matrix $\mathbf{[T]}$. Then, the powers of the Yamaguchi four-component model-based decomposition (Y4O) are modified using the maximum relative stochastic distance between the $T_{33}$ and the $T_{22}$ components of the coherency matrix at the estimated OA. The results show that the overall double-bounce powers over rotated urban areas have significantly improved with the reduction of volume powers. The percentage of pixels with negative powers have also decreased from the Y4O decomposition. The proposed method is both qualitatively and quantitatively compared with the results obtained from the Y4O and the Y4R decompositions for a Radarsat-2 C-band San-Francisco dataset and an UAVSAR L-band Hayward dataset.Comment: Accepted for publication in IEEE J-STARS (IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing

Kronecker Sum Decompositions of Space-Time Data

In this paper we consider the use of the space vs. time Kronecker product decomposition in the estimation of covariance matrices for spatio-temporal data. This decomposition imposes lower dimensional structure on the estimated covariance matrix, thus reducing the number of samples required for estimation. To allow a smooth tradeoff between the reduction in the number of parameters (to reduce estimation variance) and the accuracy of the covariance approximation (affecting estimation bias), we introduce a diagonally loaded modification of the sum of kronecker products representation [1]. We derive a Cramer-Rao bound (CRB) on the minimum attainable mean squared predictor coefficient estimation error for unbiased estimators of Kronecker structured covariance matrices. We illustrate the accuracy of the diagonally loaded Kronecker sum decomposition by applying it to video data of human activity.Comment: 5 pages, 8 figures, accepted to CAMSAP 201