Canonical correlation analysis for assessing the performance of adaptive spectral imagers

A new class of spectrally adaptive infrared detectors has been reported recently that has a pectral response function that can be altered electronically by controlling the bias voltage of the photodetector. Unlike conventional sensors, these new sensors have "bands" that have highly correlated spectral responses. The potential benefit of these sensors is that the number of bands (and their spectral features) used can be adapted to a specific task. The drawback is that there might not be enough spectral diversity to perform detection and classification operations. In this paper we present a new theory that describes the suitability of an arbitrary spectral sensor to perform a specific spectral detection/classification task. This theory is based on the geometric relationships between the sensor space that describes the spectral characteristics of the detector and a scene space that contains the spectra to be observed. We adapt the theory of canonical correlation analysis to provide a rigorous framework for assessing the utility of spectral detectors. We also show that this general theory encompasses traditional band selection methods, but provides much greater flexibility and a more transparent and intuitive explanation of the phenomenology.