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The use of solid cavities around electromagnetic sources has been recently reported as a mechanism to provide enhanced images at microwave frequencies. These cavities are used as measurement randomizers; and they compress the wave fields at the physical layer. As a result of this compression, the amount of information collected by the sensing array through the different excited modes inside the resonant cavity is increased when compared to that obtained by no-cavity approaches. In this work, a two-dimensional cavity, having multiple openings, is used to perform such a compression for ultrasound imaging. Moreover, compressive sensing techniques are used for sparse signal retrieval with a limited number of operating transceivers. As a proof-of-concept of this theoretical investigation, two point-like targets located in a uniform background medium are imaged in the presence and the absence of the cavity. In addition, an analysis of the sensing capacity and the shape of the point spread function is also carried out for the aforementioned cases. The cavity is designed to have the maximum sensing capacity given different materials and opening sizes. It is demonstrated that the use of a cavity, whether it is made of plastic or metal, can significantly enhance the sensing capacity and the point spread function of a focused beam. The imaging performance is also improved in terms cross-range resolution when compared to the no-cavity case.