Low Rate Sampling of Pulse Streams with Application to Ultrasound Imaging

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 support...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Ronen Tur, Yonina C. Eldar, Zvi Friedman
• Keywords: Compactly Supported, CORR 2010, Education, General Sampling Approach, Pulses