*2.2. L-RXD*

Local anomaly detection is very important since the global RX anomaly detector fails to work when the anomalies are relatively small or only distinct from the local surroundings, but buried in the global background. The most widely used local anomaly detection algorithm is derived from the commonly used RXD, named as local-RX detector (L-RXD). The L-RXD, denoted by *<sup>δ</sup>L*−*RXD*(*r*), is specified by:

$$\delta\_{L-RXD}(\mathbf{r}) = (\mathbf{r} - \mu\_{\mathcal{W}})^T \Sigma\_{\mathcal{W}}{}^{-1} (\mathbf{r} - \mu\_{\mathcal{W}}) \tag{2}$$

where *μW* is the local sample mean of a square window of size *ω* × *ω* pixels, centered at pixel *r* and Σ*W* is the background data sample covariance matrix of the local window *W*.

For L-RXD, a window of the selected size should be chosen firstly. The window size should not be too large or too small to obtain considerable background estimation.
