Polarimetric SAR Image Classification Using Geodesic Distances and Composite Kernels

The covariance/coherence matrices are the most common way of representing polarimetric information in the polarimetric synthetic aperture radar (PolSAR) data and have been extensively used in PolSAR classification. Since PolSAR covariance and coherence matrices are Hermitian positive-definite, they form a nonlinear manifold, rather than Euclidean space. Though the geodesic distance measures defined on a manifold are suitable for describing similarities of PolSAR matrix data, the nonlinearity of the manifold often makes the involved optimization problems awkward. To address this problem, we propose to embed the manifold-based PolSAR data into a high (infinite)-dimensional reproducing kernel Hilbert space by Stein kernel and log-Euclidean kernel. Besides, we introduce the composite kernel into the sparse representation classification in order to exploit the spatial context information of PolSAR data. The proposed method is assessed using different PolSAR datasets. Experimental results demonstrate the superior performance compared with the methods without the use of contextual information.