TY - JOUR
T1 - Super-resolution multi-reference alignment
AU - Bendory, Tamir
AU - Jaffe, Ariel
AU - Leeb, William
AU - Sharon, Nir
AU - Singer, Amit
N1 - Publisher Copyright:
© 2021 The Author(s) 2021. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
PY - 2022/6/1
Y1 - 2022/6/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85133602726&partnerID=8YFLogxK
U2 - 10.1093/imaiai/iaab003
DO - 10.1093/imaiai/iaab003
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C2 - 35966813
AN - SCOPUS:85133602726
SN - 2049-8772
VL - 11
SP - 533
EP - 555
JO - Information and Inference
JF - Information and Inference
IS - 2
ER -