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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.15740 |
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| _version_ | 1866914399543885824 |
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| author | Geissler, Nicholas Strokov, Vladimir Kümmerle, Christian Kushnarev, Sergey Berti, Emanuele |
| author_facet | Geissler, Nicholas Strokov, Vladimir Kümmerle, Christian Kushnarev, Sergey Berti, Emanuele |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15740 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hankel low-rank matrix approximation for gravitational-wave data analysis Geissler, Nicholas Strokov, Vladimir Kümmerle, Christian Kushnarev, Sergey Berti, Emanuele High Energy Astrophysical Phenomena Instrumentation and Methods for Astrophysics General Relativity and Quantum Cosmology 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. |
| title | Hankel low-rank matrix approximation for gravitational-wave data analysis |
| topic | High Energy Astrophysical Phenomena Instrumentation and Methods for Astrophysics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2603.15740 |