Improved covariance matrix estimation: interpretation and experimental analysis of different approaches for anomaly detection applications

The benchmark anomaly detection algorithm for hyperspectral images is the Reed-Xiaoli (RX) Detector, which is based on the Local Multivariate Normality of background. RX algorithm, along with its many modified versions, has been widely explored, and the main concerns identified are related to local background covariance matrix estimation. Besides the well-known small-sample size problem, other limitations have been found affecting covariance matrix estimation, e.g. local background non-homogeneity and contamination from adjacent targets. These critical aspects are deeply different in nature, like the situations from which they arise, and hence they have been typically discussed within different frameworks, disregarding possible existing links while developing different approaches to solution. Nevertheless, these critical aspects may occur together in reality, and all of them have to be taken into consideration when approaching anomaly detection, since they may strongly affect detection performance. Therefore, an analysis of the possible existing connections seems crucial in order to asses if existing algorithms, maybe designed ad-hoc to solve a specific problem, can handle more complex situations. In this work, the aforementioned limitations have been investigated from an anomaly detection perspective, and the corresponding approaches to improved covariance matrix estimation have been analyzed by using real hyperspectral data.