Stable Support Recovery of Stream of Pulses with Application to Ultrasound Imaging

TL;DR

This paper presents a convex optimization approach for accurately estimating pulse delays in noisy environments, with applications demonstrated in ultrasound imaging, achieving low localization error and false detection amplitudes.

Contribution

It introduces a novel convex optimization method for stream of pulses delay estimation with provable error bounds and practical ultrasound imaging applications.

Findings

Localization error proportional to square root of noise level

False detections have small amplitudes

Method validated through numerical and ultrasound experiments

Abstract

This paper considers the problem of estimating the delays of a weighted superposition of pulses, called stream of pulses, in a noisy environment. We show that the delays can be estimated using a tractable convex optimization problem with a localization error proportional to the square root of the noise level. Furthermore, all false detections produced by the algorithm have small amplitudes. Numerical and in-vitro ultrasound experiments corroborate the theoretical results and demonstrate their applicability for the ultrasound imaging signal processing.