FRI-based Sub-Nyquist Sampling and Beamforming in Ultrasound and Radar

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 two applications, ultrasound imaging and radar, where the FRI signal structure allows to reduce both sampling and processing rates. Furthermore, we show how the FRI framework inspires new processing techniques, such as beamforming in the frequency domain and Doppler focusing. In both applications a pulse of a known shape or a stream of such pulses is transmitted into the respective medium, and the received echoes are sampled and digitally processed in a way referred to as beamforming. Applied either spatially or temporally, beamforming allows to improve signal-to-noise ratio. In radar applications it also allows for target Doppler frequency estimation. Using FRI modeling both for detected and beamformed signals, we are able to reduce sampling rates and to perform digital beamforming directly on the low-rate samples.