Stable estimation of pulses of unknown shape from multiple snapshots via ESPRIT

TL;DR

This paper develops a new perturbation analysis for ESPRIT that enables stable pulse estimation from noisy multi-snapshot data without strict model assumptions, applicable to various array configurations and practical scenarios.

Contribution

It introduces a novel, less restrictive perturbation analysis for ESPRIT, extending its theoretical guarantees to more realistic conditions and diverse array designs.

Findings

Quantifies snapshot requirements for stable recovery with many Fourier measurements

Proposes compressive blind array calibration using random sub-arrays

Empirical results validate the theoretical analysis

Abstract

We consider the problem of resolving overlapping pulses from noisy multi-snapshot measurements, which has been a problem central to various applications including medical imaging and array signal processing. ESPRIT algorithm has been used to estimate the pulse locations. However, existing theoretical analysis is restricted to ideal assumptions on signal and measurement models. We present a novel perturbation analysis that overcomes the previous theoretical limitation, which is derived without a stringent assumption on the signal model. Our unifying analysis applies to various sub-array designs of the ESPRIT algorithm. We demonstrate the usefulness of the perturbation analysis by specifying the result in two practical scenarios. In the first scenario, we quantify how the number of snapshots for stable recovery scales when the number of Fourier measurements per snapshot is sufficiently large. In the second scenario, we propose compressive blind array calibration by ESPRIT with random sub-arrays and provide the corresponding non-asymptotic error bound. Furthermore, we demonstrate that the empirical performance of ESPRIT corroborates the theoretical analysis through extensive numerical results.