Hyperspectral target detection using kernel matched subspace detector

In this paper we present a nonlinear realization of a subspace signal detection approach based on the generalized likelihood ratio test (GLRT) - so called matched subspace detectors (MSD). The linear model for MSD is first extended to a high, possibly infinite, dimensional feature space and then the corresponding nonlinear GLRT expression is obtained. In order to address the intractability of the GLRT in the nonlinear feature space we kernelize the nonlinear GLRT using kernel eigenvector representations as well as the kernel trick where dot products in the nonlinear feature space are implicitly computed by kernels. The proposed kernel-based nonlinear detector, so called kernel matched subspace detector (KMSD), is applied to a given hyperspectral imagery - HYDICE (hyperspectral digital imagery collection experiment) images - to detect targets of interest. KMSD showed superior detection performance over MSD for the HYDICE images tested in this paper.