Innovation Rate Sampling of Pulse Streams with Application to Ultrasound Imaging

TL;DR

This paper introduces a stable, low-rate sampling method for pulse streams, applicable to ultrasound imaging, that overcomes numerical instability issues in high-rate scenarios and demonstrates significant rate reduction in practical applications.

Contribution

The authors develop a stable sampling approach for pulse streams that extends finite rate of innovation theory, enabling efficient ultrasound imaging with reduced sampling rates.

Findings

Stable recovery of pulse streams with many pulses.

Effective rate reduction in ultrasound imaging.

Robustness to noise with well-separated pulses.

Abstract

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.