Method of moments for 3D single particle ab initio modeling with non-uniform distribution of viewing angles
Method of moments for 3D single particle ab initio modeling with non-uniform distribution of viewing angles
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DOI：
10.1088/1361-6420/ab6139
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发表时间：
2019-07
期刊：
影响因子：
2.1
通讯作者：
N. Sharon;J. Kileel;Y. Khoo;Boris Landa;A. Singer
中科院分区：
文献类型：
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作者：
N. Sharon;J. Kileel;Y. Khoo;Boris Landa;A. Singer
冷冻电子显微镜（cryo-EM）中的单粒子重建是一种越来越流行的技术，用于从在未知视角拍摄的几个嘈杂的2D投影图像中确定分子的3D结构。大多数重建算法需要对3D结构进行低分辨率初始化，这是从头算建模的目标。由Zvi Kam在1980年提出，矩量法（MoM）提供了一种方法，其中计算2D图像的低阶统计，并且通过求解多项式方程组来估计3D结构。不幸的是，Kam的方法受到限制性假设的影响，最明显的是视角应该均匀分布。通常不切实际，均匀性需要计算高阶相关性，因为在这种情况下，一阶和二阶矩无法确定3D结构。在本文中，我们删除这个假设，允许一个未知的，非均匀分布的视角在矩量法。也许令人惊讶的是，我们表明，这种情况下是统计上更容易比均匀的情况下，因为现在的第一和第二时刻一般足以确定低分辨率的分子膨胀。在一个已知的，非均匀分布的理想化设置中，我们找到了一个有效的可证明的算法反转的第一和第二时刻。对于未知的非均匀分布，我们使用非凸优化方法来求解分子和分布。
Single-particle reconstruction in cryo-electron microscopy (cryo-EM) is an increasingly popular technique for determining the 3D structure of a molecule from several noisy 2D projections images taken at unknown viewing angles. Most reconstruction algorithms require a low-resolution initialization for the 3D structure, which is the goal of ab initio modeling. Suggested by Zvi Kam in 1980, the method of moments (MoM) offers one approach, wherein low-order statistics of the 2D images are computed and a 3D structure is estimated by solving a system of polynomial equations. Unfortunately, Kam’s method suffers from restrictive assumptions, most notably that viewing angles should be distributed uniformly. Often unrealistic, uniformity entails the computation of higher-order correlations, as in this case first and second moments fail to determine the 3D structure. In the present paper, we remove this hypothesis, by permitting an unknown, non-uniform distribution of viewing angles in MoM. Perhaps surprisingly, we show that this case is statistically easier than the uniform case, as now first and second moments generically suffice to determine low-resolution expansions of the molecule. In the idealized setting of a known, non-uniform distribution, we find an efficient provable algorithm inverting first and second moments. For unknown, non-uniform distributions, we use non-convex optimization methods to solve for both the molecule and distribution.