Closed-form non-parametric GLRT detector for sub-pixel targets in hyperspectral images

The generalized likelihood ratio test (GLRT) is here combined with the non-parametric approach to derive a new adaptive detector for sub-pixel 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 sub-pixel 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.