Compressed 3D ultrasound imaging with 2D arrays

Contemporary sonography is performed by digitally beamforming signals sampled by several transducer elements placed upon an array. High-resolution digital beamforming introduces the demand for a sampling rate significantly higher than the signal's Nyquist rate, which greatly increases the volume of data that must be processed. In 3D ultrasound imaging, 2D transducer arrays rather than 1D arrays are used, and more scan-lines are needed for volumetric imaging. 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 both in sampling rate and processing time can be achieved by applying the ideas of Xampling and frequency domain beamforming, leading to a sub-Nyquist sampling rate. We extend previous work on frequency domain beamforming for 2D ultrasound imaging to the geometry imposed by 3D tissues and a grid of transducer elements. This method uses only a portion of the bandwidth of the ultrasound signals to reconstruct the image. We demonstrate our results by imaging a phantom comprised of fishing wires, and show that by performing 3D beamforming in the frequency domain, a sub-Nyquist sampling rate and a low processing rate are obtained, while keeping adequate image quality.