Constrained Total Variation Based Three-Dimension Single Particle Reconstruction in Cryogenic Electron Microscopy


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.

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    \(\mathrm {RD} = \frac{\Vert \mathbf{v}^{(k+1)}-\mathbf{v}^{(k)}\Vert _2}{\max (\Vert \mathbf{v}^{(k)}\Vert _2,10^{-4})}\).


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Correspondence to You-Wei Wen.

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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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Pan, H., Wen, YW. & Zeng, T. Constrained Total Variation Based Three-Dimension Single Particle Reconstruction in Cryogenic Electron Microscopy. J Sci Comput 85, 37 (2020).

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  • Cryogenic electron microscopy (cryo-EM)
  • Single particle reconstruction
  • Micrographs
  • Total variation
  • Primal-dual