Directionally constrained or constrained energy minimization adaptive matched filter: theory and practice

The constrained energy minimization (CEM) algorithm and the closely related matched filter processor have been widely used for target detection in hyperspectral data exploitation applications. In this paper, we look at the key assumptions underlying the derivation of each algorithm and the effect these assumptions have upon their performance. To illuminate and better understand their operation, we compare both algorithms to Fisher's linear discriminant and the quadratic Bayes classifier. Bayes classifier reduces to Fisher's linear discriminant when the target and background covariances are equal. Furthermore, Fisher's linear discriminant is reduced to the matched filter, when we look for low probability targets. These interrelations can be used to justify the use of the matched filter, which has been developed for the detection of known signals in additive noise, for hyperspectral target which are not corrupted by additive noise. Finally, we investigate under what conditions the output of the matched filter follows a normal distribution.