# Image recovery from rotational and translational invariants

arXiv: https://arxiv.org/abs/1910.10006 · HTML: https://mlsanity.com/paper/1910.10006/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2019.

## Built on by (most cited first, 3 of 3)

- [Multi-target detection with rotations](https://mlsanity.com/paper/2101.07709/) (2021)
- [Score-based diffusion priors for multi-target detection](https://mlsanity.com/paper/2312.08500/) (2023)
- [Robust single-particle cryo-EM image denoising and restoration](https://mlsanity.com/paper/2401.01097/) (2024)

## Abstract (arXiv)

We introduce a framework for recovering an image from its rotationally and translationally invariant features based on autocorrelation analysis. This work is an instance of the multi-target detection statistical model, which is mainly used to study the mathematical and computational properties of single-particle reconstruction using cryo-electron microscopy (cryo-EM) at low signal-to-noise ratios. We demonstrate with synthetic numerical experiments that an image can be reconstructed from rotationally and translationally invariant features and show that the reconstruction is robust to noise. These results constitute an important step towards the goal of structure determination of small biomolecules using cryo-EM.