# Super-resolution multi-reference alignment

arXiv: https://arxiv.org/abs/2006.15354 · HTML: https://mlsanity.com/paper/2006.15354/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2020.

## Built on by (most cited first, 2 of 2)

- [Multi-target detection with rotations](https://mlsanity.com/paper/2101.07709/) (2021)
- [An accelerated expectation-maximization algorithm for multi-reference alignment](https://mlsanity.com/paper/2105.07372/) (2021)

## Abstract (arXiv)

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 ℝM 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(√M)). Phrased more informally, one can square the resolution. This result holds if the number of observations is proportional to at least 1/SNR3. 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.