Robust Recovery of Positive Stream of Pulses

TL;DR

This paper introduces a convex optimization method for accurately recovering the delays and amplitudes of positive pulse streams, demonstrating robustness to noise and dependence on pulse density and localization.

Contribution

It proposes a novel convex program for positive pulse stream recovery that is robust to noise and provides theoretical error bounds.

Findings

Recovery error is proportional to noise level.

Error increases exponentially with pulse density.

Method is effective in noisy conditions.

Abstract

The problem of estimating the delays and amplitudes of a positive stream of pulses appears in many applications, such as single-molecule microscopy. This paper suggests estimating the delays and amplitudes using a convex program, which is robust in the presence of noise (or model mismatch). Particularly, the recovery error is proportional to the noise level. We further show that the error grows exponentially with the density of the delays and also depends on the localization properties of the pulse.