  Signals comprised of a stream of short pulses appear in many applications
including bio-imaging and radar. The recent finite rate of innovation
framework, has paved the way to low rate sampling of such pulses by noticing
that only a small number of parameters per unit time are needed to fully
describe these signals. Unfortunately, for high rates of innovation, existing
sampling schemes 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 from the minimal number of samples.
We then design a compactly supported class of filters, satisfying this
condition. The periodic solution is extended to finite and infinite streams,
and is shown to be numerically stable even for a large number of pulses. High
noise robustness is also demonstrated when the delays are sufficiently
separated. Finally, we process ultrasound imaging data using our techniques,
and show that substantial rate reduction with respect to traditional ultrasound
sampling schemes can be achieved.
