Super-resolution multi-reference alignment
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Feb 18, 2021
- Source ID
- 10.1093/imaiai/iaab003
Entities
People
- Amit Singer
- Ariel Jaffe
- Nir Sharon
- Tamir Bendory
- William Leeb
Organizations
- Air Force Office of Scientific Research
- Bonfils-Stanton Foundation
- National Institute of General Medical Sciences
- National Institutes of Health
- National Science Foundation
- Princeton University
- Tel Aviv University
- University of Minnesota
- Yale University