Cryogenic Electron Microscopy (cryo-EM) has become an essential technique for studying the structure of biological macromolecules. The goal of cryo-EM is to reconstruct the three-dimensional structure of molecules from their projection images. Although cryo-EM offers the advantage of studying molecules in their native hydrated state, cryo-EM images suffer from extremely low signal-to-noise ratio (SNR). Single particle reconstruction (SPR,) algorithms overcome the low SNR, by grouping and averaging images from similar projection directions. The average images with improved SNR are known as "class means". However, the class means are often compromised by a large number of outliers, including images of particle fragments, ice, dirt and incorrectly grouped particle images from other directions. In order to obtain an accurate reconstruction, there is need for combating the effect of outliers in class means.
Current strategies of dealing with outliers in cryo-EM detect and remove outliers based on cross-correlating individual images with reference images obtained from a model or from manually pre-selected images. Images with correlations below a prescribed threshold are considered as outliers. The performance of such methods is very sensitive to the chosen threshold and the threshold often has to be adjusted for images of different, SNRs.
In contrast to the above methods, we propose a robust estimator for class means in the presence of outliers which eliminates thresholds. The robust estimator is a form of w-estimators where the weight function is designed to downweight cryo-EM outliers in the class mean estimates. We theoretically analyze the Fisher-consistency and the influence function of the estimator. We establish the robustness of the estimator against outliers by showing that its influence function is bounded. By taking into account of the contrast transfer functions (CTFs) of the images, we further extended the estimator to a robust estimator for CTF-corrected class means from images acquired with different CTFs. Fisher-consistency and boundedness of influence function also hold for this estimator.
Exhaustive simulations are provided to compare the performance of the proposed estimator and the conventional method that is based on thresholding the correlation coefficient. Unlike the conventional method, the proposed estimator is shown to be capable of adapting to images of different SNRs and outlier percentages without manual adjustments. Additionally, experiments of applying the robust estimator to real cryo-EM data are also reported. The results show that the estimator is able to significantly downweight the outliers and thus suppress their contributions to the class means in real-world cases.
|Advisor:||Tagare, Helmut. D.|
|School Location:||United States -- Connecticut|
|Source:||DAI-B 77/06(E), Dissertation Abstracts International|
|Keywords:||Class Averaging, Cryo-EM, Electron Microscopy, Robust Estimation, Single Particle Reconstuction, Three-dimensinal Reconstruction|
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