Kernel-based classification in complex-valued feature spaces for polarimetric SAR data

A kernel-based approach is proposed in this paper to address supervised classification of polarimetric SAR data. Relevant features extracted from such data are generally complex-valued (e.g., scattering coefficients, multilook covariance-matrix entries). First, based on the theory of complex reproducing kernel Hilbert spaces (RKHS´s), a family of admissible kernel functions tailored to the classification of complex-valued features is proposed. Then, a support vector machine (SVM) classifier is developed using this family of kernels and a case-specific interpretation is discussed for the related notion of maximum-margin hyperplane in a complex vector space. Finally, a spatial-contextual classifier is introduced by integrating the proposed family of kernels with a recent combination of SVM and Markov random fields. Case-specific techniques, based on the Powell and Ho-Kashyap numerical algorithms, are incorporated in the proposed methods to automatically optimize their parameters. Experiments with SIR-C data are discussed.