@article{4cb5aa5e98844e93933fd102ce1eb842,
title = "Denoising and covariance estimation of single particle cryo-EM images",
abstract = "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 {\textquoteleft}phase flipping{\textquoteright}, 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 {\textquoteleft}Covariance Wiener Filtering{\textquoteright} (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.",
keywords = "CTF correction, Steerable PCA, Wiener filtering",
author = "Tejal Bhamre and Teng Zhang and Amit Singer",
note = "Funding Information: We are thankful to Maofu Liao, Sjors Scheres, Irina Serysheva and Joachim Frank for generously providing us with the experimental datasets. We thank Xiaochen Bai for answering our questions about the 80S dataset. We are grateful to Yoel Shkolniskly and Zhizhen Zhao for help with the code. We also thank Zhizhen Zhao for reviewing earlier versions of this manuscript, and for numerically expressing isotropic linear operators such as the CTF in the Fourier–Bessel basis. We thank Fred Sigworth and Joakim And{\'e}n for many helpful discussions about this work. We also thank Joakim And{\'e}n for pointing out the symmetrization required for the linear system to be solved by conjugate gradient. We are grateful to both reviewers and the editor for their helpful comments. The authors were partially supported by Award Number R01GM090200 from the NIGMS, FA9550-12-1-0317 and FA9550-13-1-0076 from AFOSR, LTR DTD 06-05-2012 from the Simons Foundation, and the Moore Foundation Data-Driven Discovery Investigator Award. Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",
year = "2016",
month = jul,
day = "1",
doi = "10.1016/j.jsb.2016.04.013",
language = "English (US)",
volume = "195",
pages = "72--81",
journal = "Journal of Structural Biology",
issn = "1047-8477",
publisher = "Academic Press Inc.",
number = "1",
}