# Ab-initio Contrast Estimation and Denoising of Cryo-EM Images

arXiv: https://arxiv.org/abs/2202.07737 · HTML: https://mlsanity.com/paper/2202.07737/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 40 references that are in the map.
- First posted on arXiv 15 Feb 2022.

## Builds on (most cited first, 10 of 10)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Rotationally Invariant Image Representation for Viewing Direction Classification in Cryo-EM](https://mlsanity.com/paper/1309.7643/) (2013)
- [Fast Steerable Principal Component Analysis](https://mlsanity.com/paper/1412.0781/) (2014)
- [Denoising and Covariance Estimation of Single Particle Cryo-EM Images](https://mlsanity.com/paper/1602.06632/) (2016)
- [Non-unique games over compact groups and orientation estimation in cryo-EM](https://mlsanity.com/paper/1505.03840/) (2015)
- [The steerable graph Laplacian and its application to filtering image data-sets](https://mlsanity.com/paper/1802.01894/) (2018)
- [Cryo-EM reconstruction of continuous heterogeneity by Laplacian spectral volumes](https://mlsanity.com/paper/1907.01898/) (2019)
- [Mahalanobis Distance for Class Averaging of Cryo-EM Images](https://mlsanity.com/paper/1611.03193/) (2016)
- [Bias and variance reduction and denoising for CTF Estimation](https://mlsanity.com/paper/1908.03454/) (2019)
- [Generative Adversarial Networks for Robust Cryo-EM Image Denoising](https://mlsanity.com/paper/2008.07307/) (2020)

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

- [Fast rigid alignment of heterogeneous images in sliced Wasserstein distance](https://mlsanity.com/paper/2503.13756/) (2025)
- [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)

Background and Objective: The contrast of cryo-EM images varies from one to another, primarily due to the uneven thickness of the ice layer. This contrast variation can affect the quality of 2-D class averaging, 3-D ab-initio modeling, and 3-D heterogeneity analysis. Contrast estimation is currently performed during 3-D iterative refinement. As a result, the estimates are not available at the earlier computational stages of class averaging and ab-initio modeling. This paper aims to solve the contrast estimation problem directly from the picked particle images in the ab-initio stage, without estimating the 3-D volume, image rotations, or class averages. Methods: The key observation underlying our analysis is that the 2-D covariance matrix of the raw images is related to the covariance of the underlying clean images, the noise variance, and the contrast variability between images. We show that the contrast variability can be derived from the 2-D covariance matrix and we apply the existing Covariance Wiener Filtering (CWF) framework to estimate it. We also demonstrate a modification of CWF to estimate the contrast of individual images. Results: Our method improves the contrast estimation by a large margin, compared to the previous CWF method. Its estimation accuracy is often comparable to that of an oracle that knows the ground truth covariance of the clean images. The more accurate contrast estimation also improves the quality of image restoration as demonstrated in both synthetic and experimental datasets. Conclusions: This paper proposes an effective method for contrast estimation directly from noisy images without using any 3-D volume information. It enables contrast correction in the earlier stage of single particle analysis, and may improve the accuracy of downstream processing.