Fourier-domain beamforming: the path to compressed ultrasound imaging.

Sonography techniques use multiple transducer elements for tissue visualization. Signals received at each element are sampled before digital beamforming. The sampling rates required to perform high-resolution digital beamforming are significantly higher than the Nyquist rate of the signal and result in considerable amount of data that must be stored and processed. A recently developed technique, compressed beamforming, based on the finite rate of innovation model, compressed sensing (CS), and Xampling ideas, allows a reduction in the number of samples needed to reconstruct an image comprised of strong reflectors. A drawback of this method is its inability to treat speckle, which is of significant importance in medical imaging. Here, we build on previous work and extend it to a general concept of beamforming in frequency. This allows exploitation of the low bandwidth of the ultrasound signal and bypassing of the oversampling dictated by digital implementation of beamforming in time. By using beamforming in frequency, the same image quality is obtained from far fewer samples. We next present a CS technique that allows for further rate reduction, using only a portion of the beamformed signal's bandwidth. We demonstrate our methods on in vivo cardiac data and show that reductions up to 1/28 of the standard beamforming rates are possible. Finally, we present an implementation on an ultrasound machine using sub-Nyquist sampling and processing. Our results prove that the concept of sub-Nyquist processing is feasible for medical ultrasound, leading to the potential of considerable reduction in future ultrasound machines' size, power consumption, and cost.