Kernel-based subpixel target detection in hyperspectral images

In this paper we present a nonlinear realization of a signal detection approach that uses the generalized likelihood ratio tests (GLRTs). It is based on converting the linear mixture subspace model, so called matched subspace detector (MSD) into its corresponding nonlinear subspace model. The linear model for the GLRT of MSD is first extended to a high dimensional feature space (equivalent to a non-linear space in the input domain) and then the corresponding nonlinear GLRT expression is obtained. In order to address the intractability of the GLRT in the feature space we kernelize the nonlinear GLRT using kernel eigenvector representations as well as the kernel trick where dot products in the 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.