In hyperspectral imaging the replacement model where a target, if present, partly replaces the disturbance is often advocated. In this paper, we consider a somehow more realistic model where only the low-rank background is substituted for the target while a residual noise, which belongs to the orthogonal complement, is unaffected by the presence/absence of the target. A two-step generalized likelkihood ratio test is formulated for such a model. Furthermore we show that the log likelihood can be well approximated by a weighted combination of the log likelihoods of the FTMF and the AMF, and that the dimension of the background subspace is the tuning parameter which enables to balance between these two well-known detectors. A comparison with standard techniques on real hyperspectral data reveals a good performance of the new detectors.