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Endmember extraction is usually based on the solution of a system of linear equations that allows the identification of some basic spectra in terms of which the observed mixed spectra may be expressed as linear combinations. In this paper, we propose to close the loop of such an approach by identifying only the basic spectra that reproduce the dominant cover classes of a region as endmembers, and distinguishing them from outlier spectra present in the scene. The latter are often confused by other methods as endmember spectra, whereas in many practical applications, they are treated as anomalies or targets in the scene. Thus, the proposed method identifies endmembers in a robust way, separating them from outliers.