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Microwave-induced thermal acoustic tomography (MITAT) is an innovative technique to image biomedical tissues based on their electric properties. It has the advantages of both high contrast and high spatial resolution. Image reconstruction method in MITAT is always a critical issue. In this paper, a CS-MITAT (CS: compressive sensing) imaging method is proposed. Compressive sensing (CS) is a recently developed sparse signal representation and analysis framework which handles medical imaging measurements using low sampling rate or increasing imaging quality. The CS-MITAT imaging method applies CS theory to the MITAT for breast tumor imaging. In this method, an over-complete dictionary is established to make sparse measurements in the spatial domain. This treatment greatly saves measurement time. Simulations and experiments with real breast tumor tissues demonstrate the feasibility and effectiveness of the method. Compared with conventional time reversal mirror method which has been used in MITAT research, CS-MITAT provides the same peak signal-to-noise ratio imaging quality by using significantly fewer acoustic sensor positions or scanning times.