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- Title
Super-resolution multi-reference alignment.
- Authors
Bendory, Tamir; Jaffe, Ariel; Leeb, William; Sharon, Nir; Singer, Amit
- Abstract
We study super-resolution multi-reference alignment, the problem of estimating a signal from many circularly shifted, down-sampled and noisy observations. We focus on the low SNR regime, and show that a signal in |${\mathbb{R}}^M$| is uniquely determined when the number |$L$| of samples per observation is of the order of the square root of the signal's length (|$L=O(\sqrt{M})$|). Phrased more informally, one can square the resolution. This result holds if the number of observations is proportional to |$1/\textrm{SNR}^3$|. In contrast, with fewer observations recovery is impossible even when the observations are not down-sampled (|$L=M$|). The analysis combines tools from statistical signal processing and invariant theory. We design an expectation-maximization algorithm and demonstrate that it can super-resolve the signal in challenging SNR regimes.
- Subjects
EXPECTATION-maximization algorithms; SIGNAL processing; SQUARE root
- Publication
Information & Inference: A Journal of the IMA, 2022, Vol 11, Issue 2, p533
- ISSN
2049-8764
- Publication type
Article
- DOI
10.1093/imaiai/iaab003