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.