Exploiting FRI signal structure for sub-Nyquist sampling and processing in medical ultrasound

Signals consisting of short pulses are present in many applications including ultrawideband communication, object detection and navigation (radar, sonar) and medical imaging. The structure of such signals, effectively captured within the finite rate of innovation (FRI) framework, allows for significant reduction in sampling rates, required for perfect reconstruction. In this work we consider ultrasound imaging, where the FRI signal structure allows to reduce both sampling and processing rates. We show that beamforming, a crucial processing step in image generation that generally requires oversampling, can be implemented directly on reduced rate samples. This is obtained by replacing the standard time-domain processing by a frequency domain approach and relying on FRI sampling techniques in frequency. Using this approach we achieve significant rate reduction while retaining adequate image quality for both 2D and 3D imaging setups using data obtained by commercial imaging system.