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. 2022 Sep:224:107018.
doi: 10.1016/j.cmpb.2022.107018. Epub 2022 Jul 15.

Ab-initio contrast estimation and denoising of cryo-EM images

Yunpeng Shi  1 , Amit Singer  2
Affiliations

Ab-initio contrast estimation and denoising of cryo-EM images

Yunpeng Shi et al. Comput Methods Programs Biomed. 2022 Sep.

Abstract

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.

Keywords: Contrast estimation; Image denoising; Wiener filtering.

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Figures

Fig. 1.
Fig. 1.
An example of clean and noisy images with white noise. The defocus value for the CTF of the noisy images in this example is 2.67 μm.
Fig. 2.
Fig. 2.
The estimated variance of contrasts with varying SNR and number of images n. The image noise is white Gaussian. The ground truth value of the y-axis is 1, because the image contrasts are sampled from the uniform distribution on [0.5,1.5].
Fig. 3.
Fig. 3.
Normalized error of covariance estimates by different methods. The image noise is white Gaussian.
Fig. 4.
Fig. 4.
Scatter plots of estimated contrasts v.s. true contrasts. n = 10000, SNR = 1. The image noise is white Gaussian. Ideally each scatter plot should align well with the line y = x.
Fig. 5.
Fig. 5.
Scatter plots of estimated contrasts v.s. true contrasts. n = 10000, SNR = 0.1. The image noise is white Gaussian. Ideally each scatter plot should align well with the line y = x.
Fig. 6.
Fig. 6.
Scatter plots of estimated contrasts v.s. true contrasts. n = 1000, SNR = 0.1. The image noise is white Gaussian. Ideally each scatter plot should align well with the line y = x.
Fig. 7.
Fig. 7.
Contrast estimation error under different SNRs and number of images. The image noise is white Gaussian.
Fig. 8.
Fig. 8.
Clean, noisy and denoised images with SNR = 0.1 and n = 10000. The image noise is white Gaussian.
Fig. 9.
Fig. 9.
NRMSE of the denoised images under different SNRs and the number of images. The image noise is white Gaussian.
Fig. 10.
Fig. 10.
Average error per defocus group of contrast estimation by different methods. n = 10000, SNR = 0.1. The image noise is white Gaussian. The left figure panel uses centered noisy images. In the right panel, we randomly shifted the noisy images by 1–5 pixels in the x and y directions independently. In both panels, the two lines corresponding to CWF-GS and CWF-SDP overlap with each other.
Fig. 11.
Fig. 11.
Average NRMSE of denoised images from different methods, per defocus group (left figure) and per contrast group (right figure). n = 10000, SNR = 0.1. The image noise is white Gaussian. In the right panel, the red and purple lines overlap with each other.
Fig. 12.
Fig. 12.
An example of clean and noisy images with colored noise. The defocus value for the CTF of the noisy images in this example is 2.67 μm.
Fig. 13.
Fig. 13.
The estimated variance of contrasts with varying SNR and n. The image noise is colored Gaussian with decaying PSD. The ground truth of the y-axis is 1.
Fig. 14.
Fig. 14.
Normalized error of covariance estimates by different methods. The image noise is colored Gaussian with decaying PSD. The line of CWF does not appear in the left panel due to its high error. In the right panel, the line of CWF overlaps with the lines of other methods.
Fig. 15.
Fig. 15.
Scatter plots of estimated contrasts v.s. true contrasts. n = 10000, SNR = 1. The image noise is colored Gaussian with decaying PSD.
Fig. 16.
Fig. 16.
Scatter plots of estimated contrasts v.s. true contrasts. n = 10000, SNR = 0.1. The image noise is colored Gaussian with decaying PSD.
Fig. 17.
Fig. 17.
Scatter plots of estimated contrasts v.s. true contrasts. n = 1000, SNR = 0.1. The image noise is colored Gaussian with decaying PSD.
Fig. 18.
Fig. 18.
Contrast estimation error under different SNRs and number of images. The image noise is colored Gaussian with decaying PSD.
Fig. 19.
Fig. 19.
Clean, noisy and denoised images with SNR = 0.1 and n = 10000. The image noise is colored Gaussian with decaying PSD.
Fig. 20.
Fig. 20.
NRMSE of the denoised images under different SNRs and number of images. The image noise is colored Gaussian with decaying PSD.
Fig. 21.
Fig. 21.
Average error per defocus group of contrast estimation by different methods. n = 10000, SNR = 0.1. The image noise is colored Gaussian with decaying PSD. The left panel uses centered noisy images. In the right panel, we randomly shift noisy images by 1–5 pixels in the x and y directions independently. In the right panel, the lines corresponding to CWF-GS and CWF-SDP overlap with each other.
Fig. 22.
Fig. 22.
Average NRMSE of denoised images from different methods, per defocus group (left panel) and per contrast group (right panel). n = 10000, SNR = 0.1. The image noise is colored Gaussian with decaying PSD.
Fig. 23.
Fig. 23.
Demonstration of the relationship between the contrast of picked particle and their locations in the micrographs of EMPIAR-10028. Each dot corresponds to a particle image, whose color represents its estimated contrast.
Fig. 24.
Fig. 24.
Box plot of the oracle contrasts (top) and our estimated contrasts (bottom) in 21 defocus groups of the dataset EMPIAR-10028. The defocus values are sorted in ascending order, ranging from 0.8131 μm to 2.6643 μm.
Fig. 25.
Fig. 25.
The scatter plots of the estimated contrast v.s. the oracle contrast for three defocus groups in the dataset EMPIAR-10028. The dashed line corresponds to the function y = x.
Fig. 26.
Fig. 26.
Denoising results of EMPIAR-10028.
Fig. 27.
Fig. 27.
The average Fourier ring correlation between denoised images and the aligned clean templates over 2015 images from EMPIAR-10028.
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