Persistent scatterer interferometry and Synthetic Aperture Radar (SAR) Tomography are powerful tools for the detection and time monitoring of persistent scatterers. They have been proven to be effective in urban scenarios, especially for buildings and infrastructures 3-D reconstruction and monitoring of deformation. In urban areas, occurrence of layover leads to the presence of multiple contributions within the same image pixel from scatterers located at different heights. In the context of SAR Tomography, this problem can be addressed by considering a multiple hypothesis test to detect the presence of feasible multiple scatterers [1][2]. In the present paper, we consider this problem in the framework of the information theory and exploit the theoretical tool, developed in [3], to design a one-stage adaptive architecture for multiple hypothesis testing problems in the context of SAR Tomography. Moreover, we resort to the compressive sensing approach for the estimation of the unknown parameters under each hypothesis. This architecture has been verified on both simulated as well as real data also in comparison with suitable counterparts.