# Expectation-maximization for structure determination directly from cryo-EM micrographs

arXiv: https://arxiv.org/abs/2303.02157 · HTML: https://mlsanity.com/paper/2303.02157/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2023.

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

- [Score-based diffusion priors for multi-target detection](https://mlsanity.com/paper/2312.08500/) (2023)
- [Solving ill-conditioned polynomial equations using score-based priors with application to multi-target detection](https://mlsanity.com/paper/2509.11397/) (2025)

## Abstract (arXiv)

A single-particle cryo-electron microscopy (cryo-EM) measurement, called a micrograph, consists of multiple two-dimensional tomographic projections of a three-dimensional (3-D) molecular structure at unknown locations, taken under unknown viewing directions. All existing cryo-EM algorithmic pipelines first locate and extract the projection images, and then reconstruct the structure from the extracted images. However, if the molecular structure is small, the signal-to-noise ratio (SNR) of the data is very low, making it challenging to accurately detect projection images within the micrograph. Consequently, all standard techniques fail in low-SNR regimes. To recover molecular structures from measurements of low SNR, and in particular small molecular structures, we devise an approximate expectation-maximization algorithm to estimate the 3-D structure directly from the micrograph, bypassing the need to locate the projection images. We corroborate our computational scheme with numerical experiments and present successful structure recoveries from simulated noisy measurements.