Robust Recovery of Stream of Pulses using Convex Optimization

TL;DR

This paper demonstrates that delays and amplitudes in a stream of pulses can be accurately recovered using convex optimization, even in noisy conditions, under certain separation criteria, with applications in ultrasound and radar.

Contribution

It introduces a convex optimization framework for robust recovery of pulse streams, extending applicability to univariate and bivariate cases with noise tolerance.

Findings

Recovery is possible with arbitrary accuracy under separation conditions.

The method is robust to additive noise and model mismatch.

Applicable to ultrasound and radar signal processing.

Abstract

This paper considers the problem of recovering the delays and amplitudes of a weighted superposition of pulses. This problem is motivated by a variety of applications such as ultrasound and radar. We show that for univariate and bivariate stream of pulses, one can recover the delays and weights to any desired accuracy by solving a tractable convex optimization problem, provided that a pulse-dependent separation condition is satisfied. The main result of this paper states that the recovery is robust to additive noise or model mismatch.