# Bispectrum Unbiasing for Dilation-Invariant Multi-reference Alignment

arXiv: https://arxiv.org/abs/2402.14276 · HTML: https://mlsanity.com/paper/2402.14276/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2024.

## Built on by (most cited first, 1 of 1)

- [Selective Disk Bispectrum: A Complete and Rotation Invariant Image Descriptor](https://mlsanity.com/paper/2511.19706/) (2025)

## Abstract (arXiv)

Motivated by modern data applications such as cryo-electron microscopy, the goal of classic multi-reference alignment (MRA) is to recover an unknown signal f: ℝ → ℝ from many observations that have been randomly translated and corrupted by additive noise. We consider a generalization of classic MRA where signals are also corrupted by a random scale change, i.e. dilation. We propose a novel data-driven unbiasing procedure which can recover an unbiased estimator of the bispectrum of the unknown signal, given knowledge of the dilation distribution. Lastly, we invert the recovered bispectrum to achieve full signal recovery, and validate our methodology on a set of synthetic signals.