Stable Support Recovery of Stream of Pulses with Application to Ultrasound Imaging
arXiv:1507.07256 · doi:10.1109/TSP.2016.2552500
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.
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