Generalized likelihood ratio test for finite mixture model of K-distributed random variables

In this paper a new detection method for sonar imagery is developed for K-distributed background clutter using a finite mixture model (FMM) of K-distributions. The method for estimation of the parameters of the FMM and a generalized log-likelihood ratio test is derived. The detector is compared to the corresponding counterparts derived for the standard K-, Gaussian, and Rayleigh distributions. Test results of the proposed method on a data set of synthetic aperture sonar (SAS) images is also presented. This database contains images with synthetically generated targets of different shapes inserted into real SAS background imagery. Results illustrating the effectiveness of the FMMK-distributed detector are presented in terms of probability of detection, false alarm rates, and receiver operating characteristic (ROC) curves for various bottom clutter conditions.