Joint hyperspectral subspace detection derived from a Bayesian likelihood ratio test

The standard approach to solving detection problems in which clutter and/or target ditributions are modeled with unknown parameter is to apply the generalized likelihood ratio (GLR) test. This procedure automatically gernerates new estimates of the unknown model parameter for each new feature test value. An alternative approach is to estimate prior distribution for the unknown parameters. The associated Bayesian Likelihood Ratio (BLR) test can be used to generate many standard detectors for example, matched filtering or the GLR as special cases. For the particular problem of Joint Subspace Detection (JSD), several such Bayesian problems often lead to the same test as some GLR problem. Formulating such problems can lend insight into what types of background and target distributions are appropriate for a given GLR test. In addition, the added generality afforded by the new approach, in the form a selectable prior distributions, defines a wider exploratory space fro target detection. JSD can, for example, permit the incorporation of general types of experience gleaned from measurement programs. This paper explores these potentialities by applying several Bayesian formulations of the detection problem to hyperspectral data set.