Multispectral detection of dim slightly extended targets in heavy clutter

The spectral signature of a target is typically unknown apriori because of its dependence upon environmental conditions (e.g., sun angle, atmospheric attenuation and scattering), factors effecting the reflectivity and emissivity of the target's surface (dirt, dust, water, paint, etc.) and recent operating history (hot or cold engine, exhaust parts, wheels or tracks, etc.). Because of the high variability of the spectral signature of a target, multispectral detection typically detects spectral anomalies. For example, the canopy of a helicopter hovering in front of tree clutter may glint in the midwave infrared band while the reststrahlen spectral feature of the fuselage paint occurs in the longwave infrared band. Both of these are spectral anomalies relative to the tree clutter. If the target is slightly extended so that it subtends more than one pixel, the spectral anomalies by which the target may be detected will not be spatially collocated. This effectively lowers the ROC (receiver operating characteristic) curve of the detection process. This paper derives the ROC curves for several alternative solutions to this problem. One solution considers all possible spectral n-tuples within a small region. One of these n-tuples would likely contain all of the spectral anomalies of the target. Another solution is to apply a spatial maximum operator to each spectral band prior to the anomaly detector. This also combines all the spectral anomalies from the target into a single n-tuple. These methods have the potential to increase PD but an increase in PFA Will also occur. The ROC curves of these solutions to the problem of detecting slightly extended targets are derived and compared to establish relative levels of performance.