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Compressed-sensing methodology typically employs random projections simultaneously with signal acquisition to accomplish dimensionality reduction within a sensor device. The effect of such random projections on the preservation of anomalous data is investigated. The popular RX anomaly detector is derived for the case in which global anomalies are to be identified directly in the random-projection domain, and it is determined via both random simulation, as well as empirical observation that strongly anomalous vectors are likely to be identifiable by the projection-domain RX detector even in low-dimensional projections. Finally, a reconstruction procedure for hyperspectral imagery is developed wherein projection-domain anomaly detection is employed to partition the data set, permitting anomaly and normal pixel classes to be separately reconstructed in order to improve the representation of the anomaly pixels.