One-Step Generalized Likelihood Ratio Test for Subpixel Target Detection in Hyperspectral Imaging

One of the main objectives of hyperspectral image processing is to detect a given target among an unknown background. The standard data to conduct such detection is a reflectance map, where the spectral signatures of each pixel's components, known as endmembers, are associated with their abundances in the pixel. Due to the low spatial resolution of most hyperspectral sensors, such a target occupies a fraction of the pixel. A widely used model in the case of subpixel targets is the replacement model. Among the vast number of possible detectors, algorithms matched to the replacement model are quite rare. One of the few examples is the finite target matched filter (MF), which is an adjustment of the well-known MF. In this article, we derive the exact generalized likelihood ratio test for this model. This new detector can be used both with a local covariance estimation window or a global one. It is shown to outperform the standard target detectors on real data, especially for small covariance estimation windows.