Microwave-induced Thermoacoustics (TA) sensing has the potential to be a breakthrough in subsurface imaging applications. This is because it combines the advantages of high contrast of microwave imaging and high resolution of ultrasound imaging. However, state-of-the-art TA hardware requires that the receiving transducer is scanned in a linear or rotational fashion in order to be able to collect enough orthogonal data needed to produce a TA image possessing high-spatial resolution both in range and cross-range. This process is slow, increases the detection time, and adds an extra complexity to the system. In order to address these problems, a Compressive Sensing (CS) methodology is presented in this paper as a mechanism to reduce the minimum number of data samples required to reconstruct a sparse signal. Furthermore, in order to reduce the mutual information shared by different measurements, a holey cavity structure is proposed to be used to perform 4D coding. In this work, the TA imaging theory is introduced; and the impact that the holey cavity parameters have in the imaging performance is studied. The imaging results in this work are carried out using a distributed Alternating Direction Method of Multipliers (ADMM) algorithm, capable of using norm-1 and norm-2 regularizers; and they reveal the effectiveness of the proposed holey-cavity and CS TA imaging approach.

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