Abstract-Signals comprised of a stream of short pulses appear in many applications including bio-imaging, radar, and ultrawideband communication. Recently, a new framework, referred to as finite rate of innovation, has paved the way to low rate sampling of such pulses by exploiting the fact that only a small number of parameters per unit time are needed to fully describe these signals. Unfortunately, for high rates of innovation, existing approaches are numerically unstable. In this paper we propose a general sampling approach which leads to stable recovery even in the presence of many pulses. We begin by deriving a condition on the sampling kernel which allows perfect reconstruction of periodic streams of pulses from a minimal number of samples. This extends previous work which assumes that the sampling kernel is an ideal low-pass filter. A compactly supported class of filters, satisfying the mathematical condition, is then introduced, leading to a sampling framework based on compactly supported kernels. We then extend our periodic solution to finite and infinite streams, and show that our method is numerically stable even for a large number of pulses per unit time. High noise robustness is demonstrated as well when the time delays are sufficiently separated. Finally, we apply our results to ultrasound imaging data, and show that our techniques result in substantial rate reduction with respect to traditional ultrasound sampling schemes. Index Terms-Analog-to-digital conversion, annihilating filters, finite rate of innovation, generalized sampling, perfect reconstruction, ultrasound imaging.
To explore the relation of our method to REF , we first focus on periodic streams of pulses with period T .
1 Low Rate Sampling of Pulse Streams with Application to Ultrasound Imaging
Computer Science