Closed-Form Nonparametric GLRT Detector for Subpixel Targets in Hyperspectral Images

The generalized likelihood ratio test (GLRT) is here combined with the nonparametric approach to derive a new adaptive detector for subpixel targets in hyperspectral images. Specifically, a variable bandwidth kernel density estimator (KDE) is employed for estimating the conditional probability density functions composing the GLRT. Although KDE has generally a low mathematical tractability, an approximated closed-form solution is here derived, thanks to an innovative and uncommon choice for the kernel function. Experimental results in subpixel target detection scenarios show that the proposed detector represents not only the natural evolution of but also a successful alternative to both very widely employed and very recently proposed GLRT-based detectors.