Extending the RX anomaly detection algorithm to continuous spectral and spatial domains

The RX anomaly detection algorithm is a statistical method for detecting pixels in hyperspectral imagery that are significantly different from the other pixels in their locale. The RX algorithm is based upon the assumption of an existing uniform discrete sampling in both space and spectrum. In this report, we give consideration to extending the RX algorithm to continuous spatial and spectral domains so that future optical devices may be optimally constructed for anomaly detection. This report gives a heuristic outline for the extension of the RX algorithm to continuous spatial and spectral domains, explores new concepts in functional statistics necessary to make the algorithm rigorous, and suggests directions for the continuation of this research in the future.