In remote sensing, hyperspectral sensors are effectively used for target detection and recognition because of their high
spectral resolution that allows discrimination of different materials in the sensed scene. When a priori information about
the spectrum of the targets of interest is not available, target detection turns into anomaly detection (AD), i.e. searching
for objects that are anomalous with respect to the scene background. In the field of AD, anomalies can be generally
associated to observations that statistically move away from background clutter, being this latter intended as a local
neighborhood surrounding the observed pixel or as a large part of the image. In this context, many efforts have been put
to reduce the computational load of AD algorithms so as to furnish information for real-time decision making.
In this work, a sub-class of AD methods is considered that aim at detecting small rare objects that are anomalous with
respect to their local background. Such techniques not only are characterized by mathematical tractability but also allow
the design of real-time strategies for AD. Within these methods, one of the most-established anomaly detectors is the RX
algorithm which is based on a local Gaussian model for background modeling.
In the literature, the RX decision rule has been employed to develop computationally efficient algorithms implemented
in real-time systems. In this work, a survey of computationally efficient methods to implement the RX detector is
presented where advanced algebraic strategies are exploited to speed up the estimate of the covariance matrix and of its
inverse. The comparison of the overall number of operations required by the different implementations of the RX
algorithms is given and discussed by varying the RX parameters in order to show the computational improvements
achieved with the introduced algebraic strategy.