title: A Bayesian approach for suppression of limited angular sampling artifacts in single particle 3D reconstruction.
abstract: In the single particle reconstruction, the initial 3D structure often suffers from the limited angular sampling artifact. Selecting 2D class averages of particle images generally improves the accuracy and efficiency of the reference-free 3D angle estimation, but causes an insufficient angular sampling to fill the information of the target object in the 3D frequency space. Similarly, the initial 3D structure by the random-conical tilt reconstruction has the well-known "missing cone" artifact. Here, we attempted to solve the limited angular sampling problem by sequentially applying maximum a posteriori estimate with expectation maximization algorithm (sMAP-EM). Using both simulated and experimental cryo-electron microscope images, the sMAP-EM was compared to the direct Fourier method on the basis of reconstruction error and resolution. To establish selection criteria of the final regularization weight for the sMAP-EM, the effects of noise level and sampling sparseness on the reconstructions were examined with evenly distributed sampling simulations. The frequency information filled in the missing cone of the conical tilt sampling simulations was assessed by developing new quantitative measurements. All the results of visual and numerical evaluations showed the sMAP-EM performed better than the direct Fourier method, regardless of the sampling method, noise level, and sampling sparseness. Furthermore, the frequency domain analysis demonstrated that the sMAP-EM can fill the meaningful information in the unmeasured angular space without detailed a priori knowledge of the objects. The current research demonstrated that the sMAP-EM has a high potential to facilitate the determination of 3D protein structures at near atomic-resolution.
authors.affiliation: Department of Signal Processing, Tampere University of Technology, P.O. Box 553, FI-33101 Tampere, Finland; BioMediTech, Tampere University of Technology, P.O. Box 553, FI-33101 Tampere, Finland. Electronic address: toshio.moriya@mpi-dortmund.mpg.de.
authors.forename: Toshio
authors.initials: T
authors.lastname: Moriya
authors.affiliation: Department of Signal Processing, Tampere University of Technology, P.O. Box 553, FI-33101 Tampere, Finland; BioMediTech, Tampere University of Technology, P.O. Box 553, FI-33101 Tampere, Finland. Electronic address: erman.acar@tut.fi.
authors.forename: Erman
authors.initials: E
authors.lastname: Acar
authors.affiliation: Department of Molecular and Cellular Biology, University of California, Briggs7 (MailCode#0390), Davis, CA 95616, USA. Electronic address: rhch@ucdavis.edu.
authors.forename: R Holland
authors.initials: RH
authors.lastname: Cheng
authors.affiliation: Department of Signal Processing, Tampere University of Technology, P.O. Box 553, FI-33101 Tampere, Finland; BioMediTech, Tampere University of Technology, P.O. Box 553, FI-33101 Tampere, Finland. Electronic address: ulla.ruotsalainen@tut.fi.
authors.forename: Ulla
authors.initials: U
authors.lastname: Ruotsalainen
mesh_terms: D000465:Algorithms; D016477:Artifacts; D001499:Bayes Theorem; D020285:Cryoelectron Microscopy / Q000379:methods*; D007091:Image Processing, Computer-Assisted / Q000379:methods; D021621:Imaging, Three-Dimensional / Q000379:methods*; D011506:Proteins / Q000737:chemistry*
chemical_list: D011506:Proteins
keywords: Cryo-electron microscopy; Maximum a posteriori probability estimation; Median root prior reconstruction; Missing cone; Poisson image formation model; Sparse angular sampling