Microwave imaging techniques have been widely developed in the last years, exploiting different inversion strategies in several applicative scenarios. Among these, Compressive Sensing (CS) has been recently introduced in the electromagnetic community as an efficient and effective tool for solving inverse scattering problems. Anyway, despite the sensing problem (i.e. the recovering of the information from the measured data) has been deeply investigated and several solution are nowadays available, the sampling problem is still under development. This work aims at introduce a new paradigm, namely Compressive Processing (CP), in which both the sampling and the sensing problems are jointly addressed.