Hankel low-rank matrix approximation for gravitational-wave data analysis

TL;DR

This paper investigates Hankel low-rank matrix approximation techniques for denoising and extracting signals from complex gravitational-wave data, demonstrating near-optimal performance and validating with numerical relativity waveforms.

Contribution

It benchmarks three Hankel-based algorithms for GW signal extraction, showing their effectiveness and efficiency in realistic synthetic and numerical data scenarios.

Findings

All algorithms achieve near-optimal performance.

Mismatch scales inversely with the square of SNR.

Successful extraction of quasinormal modes from waveforms.

Abstract

Next-generation gravitational-wave (GW) detectors, such as the Laser Interferometer Space Antenna (LISA), will observe vast numbers of overlapping signals. Disentangling these signals from instrumental noise and from one another constitutes a significant data analysis challenge. We explore a denoising technique based on embedding time series into Hankel matrices: a superposition of $n$ (damped) sinusoids corresponds to a matrix of rank $2n$. Thus, the problem of signal extraction is reduced to a structured low-rank approximation problem. Using synthetic data tailored to GW applications, we benchmark three Hankel-based algorithms: ESPRIT, Cadzow iterations, and iteratively reweighted least squares (IRLS). Our test scenarios include isolated and multi-component monochromatic signals, the resolution of sources with closely spaced frequencies, and the recovery of black hole quasinormal modes (QNM). All three algorithms achieve near-optimal performance consistent with Fisher matrix bounds, evidenced by an inverse-square scaling of the mismatch with the signal-to-noise ratio. Furthermore, a proof-of-concept application to numerical relativity waveforms validates the ability of these algorithms to extract QNM frequencies from ringdown signals. Hankel low-rank approximation therefore offers a transparent, computationally efficient avenue for preprocessing GW time series.