Published in

Oxford University Press, Information and Inference: a Journal of the IMA, 2(11), p. 533-555, 2021

DOI: 10.1093/imaiai/iaab003

Links

Tools

Export citation

Search in Google Scholar

Super-resolution multi-reference alignment

Journal article published in 2021 by Tamir Bendory, Ariel Jaffe, William Leeb, Nir Sharon, Amit Singer
Distributing this paper is prohibited by the publisher
Distributing this paper is prohibited by the publisher

Full text: Unavailable

Green circle
Preprint: archiving allowed
Orange circle
Postprint: archiving restricted
Red circle
Published version: archiving forbidden
Data provided by SHERPA/RoMEO

Abstract

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 ${ℝ}^M$ 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.