Robust Spectral Recovery for Dynamical Sampling
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915930325385216 |
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| author | Cai, HanQin Huang, Longxiu Wang, Tianming You, Juntao |
| author_facet | Cai, HanQin Huang, Longxiu Wang, Tianming You, Juntao |
| contents | We study the spectral recovery problem for dynamical sampling on a finite cyclic grid. Given time snapshots obtained from a fixed uniform spatial subsampling of the orbit $x_{\ell}=A^{\ell}f$, we aim to recover the spectrum of the unknown circular convolution operator $A$. However, in the presence of outliers, even in only a few snapshots, existing approaches often struggle to recover the spectrum. We address this challenge by proposing a novel robust spectral recovery model in the presence of time-sparse corruptions. We propose a robust pipeline that lifts the problem to a sequence of robust low-rank Hankel recovery and completion tasks, followed by Prony-type spectral estimation. Numerical experiments confirm the accurate spectral recovery of the proposed approach and exhibit its superior robustness against state-of-the-art under various settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09477 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust Spectral Recovery for Dynamical Sampling Cai, HanQin Huang, Longxiu Wang, Tianming You, Juntao Information Theory Numerical Analysis We study the spectral recovery problem for dynamical sampling on a finite cyclic grid. Given time snapshots obtained from a fixed uniform spatial subsampling of the orbit $x_{\ell}=A^{\ell}f$, we aim to recover the spectrum of the unknown circular convolution operator $A$. However, in the presence of outliers, even in only a few snapshots, existing approaches often struggle to recover the spectrum. We address this challenge by proposing a novel robust spectral recovery model in the presence of time-sparse corruptions. We propose a robust pipeline that lifts the problem to a sequence of robust low-rank Hankel recovery and completion tasks, followed by Prony-type spectral estimation. Numerical experiments confirm the accurate spectral recovery of the proposed approach and exhibit its superior robustness against state-of-the-art under various settings. |
| title | Robust Spectral Recovery for Dynamical Sampling |
| topic | Information Theory Numerical Analysis |
| url | https://arxiv.org/abs/2604.09477 |