Joint hyperspectral subspace detection derived from a Bayesian Likelihood Ratio test

The standard approach to solving detection problems in which clutter and/or target distributions are modeled with unknown parameters is to apply the generalized likelihood ratio (GLR) test. This procedure automatically generates new estimates of the unknown model parameters for each new feature test value. An alternative approach is to estimate prior distributions 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 of selectable prior distributions, defines a wider exploratory space for 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 sets.