Robust RX anomaly detector without covariance matrix estimation

We explore the problem of anomaly detection based on several one-dimensional projections. The main advantage of the proposed approach is that it does not require any covariance matrix estimation, allowing to compute spatial adaptive anomaly detection in small neighborhoods. Although this is contrary to common sense, theoretical results support the consistence of our approach when a large number of univariate random projection is considered. The theoretical convergence to the popular RX anomaly detector is derived.