Constrained Total Variation Based Three-Dimension Single Particle Reconstruction in Cryogenic Electron Microscopy
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Constrained Total Variation Based Three-Dimension Single Particle Reconstruction in Cryogenic Electron Microscopy Huan Pan1,2 · You-Wei Wen1,2
· Tieyong Zeng3
Received: 21 March 2019 / Revised: 19 August 2020 / Accepted: 12 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The single particle reconstruction (SPR) in cryogenic electron microscopy is considered in this paper. This is an emerging technique for determining the three-dimensional (3D) structure of biological specimens from a limited number of the micrographs. Because the micrographs are modulated by contrast transfer functions and corrupted by heavy noise, the number of micrographs might be limited, in general it is a serious ill-posed problem to reconstruct the original particle. In this paper, we propose a constrained total variation (TV) model for single particle reconstruction. The TV norm is represented by the dual formulation that changes the SPR problem into a minimax one. The primal-dual method is applied to find the saddle point of the minimax problem, and the convergence condition is given. Numerical results show that the proposed model is very effective in reconstructing the particle. Keywords Cryogenic electron microscopy (cryo-EM) · Single particle reconstruction · Micrographs · Total variation · Primal-dual
This work is supported by NSFC Grant Nos. 11871210 and 11971215, the Construct Program of the Key Discipline in Hunan Province, the SRF of Hunan Provincial Education Department (No. 17A128), the Hunan Province Graduate Research and Innovation Project (No. CX20190336). The work of Tieyong Zeng was supported by the NSFC under Grant 11671002, in part by the CUHK Start-Up, and in part by the CUHK DAG under Grant Nos. 4053342, 4053405, RGC 14300219, RGC 14302920, and NSFC/RGC N_CUHK 415/19.
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You-Wei Wen [email protected] Tieyong Zeng [email protected]
1
Key Laboratory of Computing and Stochastic Mathematics (LCSM), Ministry of Education of China, Changsha, China
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School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, Hunan, China
3
The Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China 0123456789().: V,-vol
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Journal of Scientific Computing
(2020) 85:37
1 Introduction The Single Particle Reconstruction (SPR) using Cryogenic Electron Microscopy (cryo-EM) is an adavaced imaging technique for determining the three-dimension (3D) structure of biological specimens (such as proteins, protein complexes or viruses), called particles, from their two-dimension projection images at near-atomic resolution [10,13]. The Cryo-EM does not require crystallization, only needs small amounts of sample material, and covers a wide range of sizes of specimens. It has been used successfully to analyze biological structures at high resolution. In Cryo-EM, thousands to millions individual, identical copies of the particles are rapidly frozen into a thin layer of vitreous ice at random unknown orientations, trapping
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