Generalized likelihood ratio test for modified replacement model in hyperspectral imaging detection

Abstract The replacement model, which assumes that the abundances sum up to one, is often advocated for subpixel target detection in hyperspectral imaging, and various detection schemes based on this model have been developed in the literature. However, in practical situations, this unitary constraint may be too strong due to possible attenuation of the target bidirectional reflectance distribution function, signature mismatches or impediments in the radiometric corrections. The aim of this paper is to improve the replacement-model detection algorithms by relaxing this unitary constraint. To this end, we propose to consider a modified replacement model. One step and two steps generalized likelihood ratio tests are developed for this new model and compared to standard solutions through numerical simulations. An application to real data shows the improvement offered by the proposed approach.