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.

本文考虑了低温电子显微镜中的单粒子重建（SPR）。这是一种从有限数量的显微照片中确定生物样本的三维（3D）结构的新兴技术。由于显微照片是由对比度传递函数调制的，并且会受到重噪声的破坏，因此显微照片的数量可能会受到限制，通常，重建原始粒子是一个严重的不适定问题。在本文中，我们提出了一种用于单粒子重建的约束总变异（TV）模型。电视规范由双重公式表示，该公式将SPR问题变成了minimax。应用原对偶法求出极大极小问题的鞍点，并给出了收敛条件。