Compressive Spectral Estimation with Single-Snapshot ESPRIT: Stability and Resolution

TL;DR

This paper develops a single-snapshot ESPRIT method for spectral estimation, providing stability and resolution guarantees, with exact reconstruction in noise-free cases and explicit error bounds under noise.

Contribution

It introduces a stability and resolution analysis for single-snapshot ESPRIT with performance guarantees, including explicit error bounds and conditions for exact recovery.

Findings

Exact reconstruction guaranteed with enough data in noise-free case

Explicit error bounds under noise with frequency separation

Favorable separation and sparsity conditions compared to compressed sensing

Abstract

In this paper Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) is developed for spectral estimation with single-snapshot measurement. Stability and resolution analysis with performance guarantee for Single-Snapshot ESPRIT (SS-ESPRIT) is the main focus. In the noise-free case, exact reconstruction is guaranteed for any arbitrary set of frequencies as long as the number of measurement data is at least twice the number of distinct frequencies to be recovered. In the presence of noise and under the assumption that the true frequencies are separated by at least two times Rayleigh's Resolution Length, an explicit error bound for frequency reconstruction is given in terms of the dynamic range and the separation of the frequencies. The separation and sparsity constraint compares favorably with those of the leading approaches to compressed sensing in the continuum.