# Centering noisy images with application to cryo-EM

arXiv: https://arxiv.org/abs/2009.04810 · HTML: https://mlsanity.com/paper/2009.04810/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2020.

## Built on by (most cited first, 7 of 7)

- [Alignment of Density Maps in Wasserstein Distance](https://mlsanity.com/paper/2305.12310/) (2023)
- [Fast rigid alignment of heterogeneous images in sliced Wasserstein distance](https://mlsanity.com/paper/2503.13756/) (2025)
- [Orthogonal Matrix Retrieval with Spatial Consensus for 3D Unknown-View Tomography](https://mlsanity.com/paper/2207.02985/) (2022)
- [G-invariant diffusion maps](https://mlsanity.com/paper/2306.07350/) (2023)
- [CRISP: A Framework for Cryo-EM Image Segmentation and Processing with Conditional Random Field](https://mlsanity.com/paper/2502.08287/) (2025)
- [Deep Neural-network Prior for Orbit Recovery from Method of Moments](https://mlsanity.com/paper/2304.14604/) (2023)
- [Two Datasets Are Better Than One: Method of Double Moments for 3-D Reconstruction in Cryo-EM](https://mlsanity.com/paper/2511.07438/) (2025)

## Abstract (arXiv)

We target the problem of estimating the center of mass of noisy 2-D images. We assume that the noise dominates the image, and thus many standard approaches are vulnerable to estimation errors. Our approach uses a surrogate function to the geometric median, which is a robust estimator of the center of mass. We mathematically analyze cases in which the geometric median fails to provide a reasonable estimate of the center of mass, and prove that our surrogate function leads to a successful estimate. One particular application for our method is to improve 3-D reconstruction in single-particle cryo-electron microscopy (cryo-EM). We show how to apply our approach for a better translational alignment of macromolecules picked from experimental data. In this way, we facilitate the succeeding steps of reconstruction and streamline the entire cryo-EM pipeline, saving valuable computational time and supporting resolution enhancement.