Compressive sensing (CS) theory states that, if certain conditions are met, a signal can be retrieved at a sampling rate that is lower than what Nyquist theorem requires. Among these conditions are the sparsity of the signal and the incoherence of the sensing matrix, which is constructed based on how the sensing system is designed. One effective method to render the sensing matrix incoherent is to use random processes in its construction. Diverse approaches have been proposed to randomize the sensing matrix including transmission at random transmitter positions and spectral coding with the use of a physical structure that responds very differently at disparate frequencies. In this work, a holey cavity with various frequency modes is used to spectrally code the ultrasound wave fields. Then, with the use of CS theory and simulations, it is shown that the sensing system that is equipped with such a cavity performs meaningfully better than a regular system in terms of sensing capacity, beam focusing, and imaging. What is more, the validity of Born approximation is investigated in this work to show its extent of applicability in imaging relatively small targets. Due to computational limitations, the simulation domain has been selected to be comparatively small; yet, the achieved results evidently show the concept and warrant further studies on holey cavities in ultrasound imaging, including their fabrication and experimental corroboration. The decrease in the number of measurements necessary for correct image reconstruction can make ultrasound sensing systems more efficient in size and scan time in a variety of applications including medical diagnosis, non-destructive testing, and monitoring.

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