Bayesian vs generalized likelihood ratio detection of solid sub-pixel targets

Numerical experiments compare Bayesian and non-Bayesian Generalized Likelihood Ratio Test (GLRT) detection algorithms for opaque sub-pixel hyperspectral targets of unknown abundance. A simplified problem is identified, which allows the full range of Bayesian priors to be explored. When one seeks to minimize the false alarm rate at a fixed detection rate, one finds that GLRT detection outperforms Bayesian detection for any choice of prior. By contrast, when the criterion is detection rate at fixed false alarm rate, Bayesian detection is better. The results hold over a wide range of parameters, and appear to contradict known optimality results for Bayesian detectors. The apparent discrepancy is explained, and a case is made for the practical use of GLRT-based detection statistics.