Abstract-One of the key steps in ultrasound image formation is digital beamforming of signals sampled by several transducer elements placed upon an array. High-resolution digital beamforming introduces the demand for sampling rates significantly higher than the signals' Nyquist rate, which greatly increases the volume of data that must be transmitted from the system's front end. In 3D ultrasound imaging, 2D transducer arrays rather than 1D arrays are used, and more scan-lines are needed. This implies that the amount of sampled data is vastly increased with respect to 2D imaging. In this work we show that a considerable reduction in data rate can be achieved by applying the ideas of Xampling and frequency domain beamforming, leading to a sub-Nyquist sampling rate, which uses only a portion of the bandwidth of the ultrasound signals to reconstruct the image. We extend previous work on frequency domain beamforming for 2D ultrasound imaging to accommodate the geometry imposed by volumetric scanning and a 2D grid of transducer elements. We demonstrate high image quality from low-rate samples by simulation of a phantom image comprised of several small reflectors. We also apply our technique on raw data of a heart ventricle phantom obtained by a commercial 3D ultrasound system. We show that by performing 3D beamforming in the frequency domain, sub-Nyquist sampling and low processing rate are achievable, while maintaining adequate image quality.

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