A New Algorithm for Robust Estimation of the Signal Subspace in Hyperspectral Images in the Presence of Rare Signal Components
Recently, anomaly detection has been one of the most interesting researches in hyperspectral images (HSIs) applications. Generally, anomalies in HSIs are rare pixels. The Reed–Xiaoli (RX) algorithm is a benchmark anomaly detector for HSIs, which uses the local Gaussian model generally . But for RX algorithm there are two issues to be considered. First it requires the estimation of model parameters, which the estimation accuracy will decrease because the high dimensionality of HSIs. The second is the computational load for the need to estimate the inverse of large covariance matrices. Hence, dimensionality reduction plays an important role as a preprocessing step to improve the detection performance . As anomaly detection is concerned, the key of the dimensionality reduction for HSIs is how to take a good estimation of the anomalous signal subspace which implies anomalous information and suitable for anomalies detection has been a fundamental issue for the hyperspectral processing. So in this paper, we focus on dimensionality reduction through estimating the anomalous signal subspace with the preservation of rare vectors. A number of methods have proposed for dimensionality reduction such as principal component analysis (PCA) the discrete Karhunen–Loève transform (DKLT). These methods are both based on second-order statistics, because the data variance is mainly influenced by the background but the rare signals which are not suitable for detection application for HSIs. Gu et al. proposed a SKPCA method which is nonlinear based on KPCA and highorder statistics to select the anomalous signal component for detection . Oleg et al. proposed maximum orthogonal complement algorithm (MOCA) which take into account the preservation of rare vectors . Recently N. Acito et al. have improved the MOCA by simplifying the iterative procedure to lighten the computational load and proposed a new method to estimate the rank of the rare signal subspace. But they both not take much attention to look for the subspace that suitable for anomaly detection using HSIs .