# Denoising and Covariance Estimation of Single Particle Cryo-EM Images

arXiv: https://arxiv.org/abs/1602.06632 · HTML: https://mlsanity.com/paper/1602.06632/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2016.

## Built on by (most cited first, 10 of 10)

- [Matrix Denoising with Doubly Heteroscedastic Noise: Fundamental Limits and Optimal Spectral Methods](https://mlsanity.com/paper/2405.13912/) (2024)
- [Artificial Intelligence Advances for De Novo Molecular Structure Modeling in Cryo-EM](https://mlsanity.com/paper/2102.06125/) (2021)
- [Ab-initio Contrast Estimation and Denoising of Cryo-EM Images](https://mlsanity.com/paper/2202.07737/) (2022)
- [Orthogonal Matrix Retrieval with Spatial Consensus for 3D Unknown-View Tomography](https://mlsanity.com/paper/2207.02985/) (2022)
- [Fast expansion into harmonics on the disk: a steerable basis with fast radial convolutions](https://mlsanity.com/paper/2207.13674/) (2022)
- [Robust single-particle cryo-EM image denoising and restoration](https://mlsanity.com/paper/2401.01097/) (2024)
- [SO(3)-invariant PCA with application to molecular data](https://mlsanity.com/paper/2510.18827/) (2025)
- [Unsupervised Difference Learning for Noisy Rigid Image Alignment](https://mlsanity.com/paper/2205.11829/) (2022)
- [Joint Denoising of Cryo-EM Projection Images using Polar Transformers](https://mlsanity.com/paper/2506.11283/) (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)

The problem of image restoration in cryo-EM entails correcting for the effects of the Contrast Transfer Function (CTF) and noise. Popular methods for image restoration include `phase flipping', which corrects only for the Fourier phases but not amplitudes, and Wiener filtering, which requires the spectral signal to noise ratio. We propose a new image restoration method which we call `Covariance Wiener Filtering' (CWF). In CWF, the covariance matrix of the projection images is used within the classical Wiener filtering framework for solving the image restoration deconvolution problem. Our estimation procedure for the covariance matrix is new and successfully corrects for the CTF. We demonstrate the efficacy of CWF by applying it to restore both simulated and experimental cryo-EM images. Results with experimental datasets demonstrate that CWF provides a good way to evaluate the particle images and to see what the dataset contains even without 2D classification and averaging.