Innovation Rate Sampling of Pulse Streams With Application to Ultrasound Imaging

By Ronen Tur, Yonina C. Eldar, Zvi Friedman. IEEE Transactions on Signal Processing, 2010

308 citations recorded by the source corpus.

Signals comprised of a stream of short pulses appear in many applications including bioimaging 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.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/82a9842c6383abb3072de2219f4755e6ad3709b6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computer Vision and Pattern Recognition

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

Structured Compressed Sensing: From Theory to Applications (2011, background): “Theorem 28 [163]: Consider the -periodic stream of pulses of order given by (63).”