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Detection of a target with known spectral signature when this target mayoccupy only a fraction of the pixel is an important issue in hyperspectralimaging. We recently derived the generalized likelihood ratio test (GLRT) forsuch sub-pixel targets, either for the so-called replacement model where thepresence of a target induces a decrease of the background power, due to the sumof abundances equal to one, or for a mixed model which alleviates some of thelimitations of the replacement model. In both cases, the background was assumedto be Gaussian distributed. The aim of this short communication is to extendthese detectors to the broader class of elliptically contoured distributions,more precisely matrix-variate $t$-distributions with unknown mean andcovariance matrix. We show that the generalized likelihood ratio tests in the$t$-distributed case coincide with their Gaussian counterparts, which confersthe latter an increased generality for application. The performance as well asthe robustness of these detectors are evaluated through numerical simulations.

Sub-pixel detection in hyperspectral imaging with elliptically contoured $t$-distributed background