The problem of detecting and locating multiple scatterers in multibaseline Synthetic Aperture Radar (SAR) tomography, starting from compressive measurements and applying support detection techniques, is addressed. Different approaches based on the detection of the support set of the unknown sparse vector, that is, of the position of the nonzero elements in the unknown sparse vector, are analyzed. Support detection techniques have already proved to allow a reduction in the number of measurements required for obtaining a reliable solution. In this paper, a support detection method, based on a Generalized Likelihood Ratio Test (Sup-GLRT), is proposed and compared with the SequOMP method, in terms of probability of detection achievable with a given probability of false alarm and for different numbers of measurements.