RX architectures for real-time anomaly detection in hyperspectral images

In the field of hyperspectral image processing, anomaly detection (AD) is a deeply investigated task whose goal is to find objects in the image that are anomalous with respect to the background. In many operational scenarios, detection, classification and identification of anomalous spectral pixels have to be performed in real time to quickly furnish information for decision-making. In this framework, many studies concern the design of computationally efficient AD algorithms for hyperspectral images in order to assure real-time or nearly real-time processing. In this work, a sub-class of anomaly detection algorithms is considered, i.e., those algorithms aimed at detecting small rare objects that are anomalous with respect to their local background. Among such techniques, one of the most established is the Reed-Xiaoli (RX) algorithm, which is based on a local Gaussian assumption for background clutter and locally estimates its parameters by means of the pixels inside a window around the pixel under test (PUT). In the literature, the RX decision rule has been employed to develop computationally efficient algorithms tested in real-time systems. Initially, a recursive block-based parameter estimation procedure was adopted that makes the RX processing and the detection performance differ from those of the original RX. More recently, an update strategy has been proposed which relies on a line-by-line processing without altering the RX detection statistic. In this work, the above-mentioned RX real-time oriented techniques have been improved using a linear algebra-based strategy to efficiently update the inverse covariance matrix thus avoiding its computation and inversion for each pixel of the hyperspectral image. The proposed strategy has been deeply discussed pointing out the benefits introduced on the two analyzed architectures in terms of overall number of elementary operations required. The results show the benefits of the new strategy with respect to the original architectures.