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.