Hyperspectral anomaly detection using kernel RX-algorithm

In this paper we present a nonlinear version of the well-known anomaly detection method, referred to as the RX-algorithm, by extending this algorithm in a feature space associated with the original input space via a certain nonlinear mapping function. An expression for the nonlinear form of the RX-algorithm is derived which is basically intractable mainly due to the high dimensionality of the feature space. We convert the nonlinear RX expression into kernels, which implicitly compute dot products in the nonlinear domain. The proposed kernel RX-algorithm is applied to hyperspectral images for anomaly detection. Improved performance of the kernel RX over the conventional RX is shown for the HYDICE (hyperspectral digital imagery collection experiment) images tested.