  Hyperspectral target detection is a task of primary importance in remote
sensing since it allows identification, location, and discrimination of target
features. To this end, the reflectance maps, which contain the spectral
signatures and related abundances of the materials in the observed scene, are
often used. However, due to the low spatial resolution of most hyperspectral
sensors, targets occupy a fraction of the pixel and, hence, the spectra of
different sub-pixel targets (including the background spectrum) are mixed
together within the same pixel. To solve this issue, in this paper, we adopt a
generalized replacement model accounting for multiple sub-pixel target spectra
and formulate the detection problem at hand as a binary hypothesis test where
under the alternative hypothesis the target is modeled in terms of a linear
combination of endmembers whose coefficients also account for the presence of
the background. Then, we devise detection architectures based upon the
generalized likelihood ratio test where the unknown parameters are suitably
estimated through procedures inspired by the maximum likelihood approach. The
performances of the proposed decision schemes are evaluated by means of both
synthetic as well as real data and compared with an analogous counterpart by
showing the effectiveness of the proposed procedure.
