Applicability of robust unconstrained linear unmixing (RULU) to endmember extraction techniques

This work presents results of applying the robust unconstrained linear unmixing (RULU) in conjunction with well known endmember extraction techniques to identify outliers within the set of extracted endmembers. Endmember extraction techniques that use the convexity of the data cloud to estimate the endmembers do not consider the applicability of the linear model once the endmembers have been extracted. It has to be taken into account that anomalies as well as the purest pixels present in an image might be the extremes of the spread of spectral signatures. In other words, pixels that constitute the vertices of the convex hull of the cloud of data points might be either anomalies or the purest pixels of the dominant classes, and in order to distinguish between those, the applicability of the linear model has to be considered. On the other hand, methods that search for anomalies might wrongly return endmembers as anomalies, since both populations are relatively small. The proposed algorithm allows the distinction between true endmembers that contribute to the majority of mixed pixels in the scene and outliers that do not contribute significantly to the scene and might distort the fitting of the linear model. Here NFINDR, VCA, SGA and ULU are compared with their corresponding robust counterparts.