A central task in recovering the structure of a macromolecule from cryo-electron microscopy (cryo-EM) images is to determine a three-dimensional model of the macromolecule given many of its two-dimensional projection images. The direction from each image taken the images which was is unknown, and are small and extremely noisy. The goal is to determine the direction from which each image was taken and then to combine the images into a three-dimensional model of the molecule. We present an algorithm for determining the viewing direction of all cryo-EM images at once, which is robust to high levels of noise. The algorithm is based on formulating the problem as a synchronization problem; that is, we estimate the relative spatial configuration of pairs of images and then estimate a global assignment of orientations that maximizes the number of satisfied pairwise relations. Information about the spatial relation between pairs of images is extracted from common lines between triplets of images. These noisy pairwise relations are combined into a single consistent assignment of orientations by constructing a matrix whose entries encode the pairwise relations. This matrix is shown to have rank 3, and its nontrivial eigenspace is shown to reveal the projection orientation of each image. In particular, we show that the nontrivial eigenvectors encode the rotation matrix that corresponds to each image.

中文翻译：

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使用同步在 Cryo-EM 中观察方向估计。

从冷冻电子显微镜 (cryo-EM) 图像中恢复大分子结构的核心任务是在给定许多二维投影图像的情况下确定大分子的三维模型。每张图像的方向都是未知的，而且很小而且非常嘈杂。目标是确定拍摄每个图像的方向，然后将这些图像组合成分子的三维模型。我们提出了一种算法，用于一次确定所有冷冻 EM 图像的观察方向，该算法对高水平噪声具有鲁棒性。该算法基于将问题表述为同步问题；那是，我们估计图像对的相对空间配置，然后估计方向的全局分配，使满足的成对关系的数量最大化。从图像三元组之间的公共线中提取有关图像对之间空间关系的信息。这些嘈杂的成对关系通过构造一个矩阵来组合成一个单一的一致的方向分配，该矩阵的条目对成对关系进行编码。该矩阵显示为 3 级，其非平凡特征空间显示每个图像的投影方向。特别是，我们展示了非平凡的特征向量编码对应于每个图像的旋转矩阵。这些嘈杂的成对关系通过构造一个矩阵来组合成一个单一的一致的方向分配，该矩阵的条目对成对关系进行编码。该矩阵显示为 3 级，其非平凡特征空间显示每个图像的投影方向。特别是，我们展示了非平凡的特征向量编码对应于每个图像的旋转矩阵。这些嘈杂的成对关系通过构造一个矩阵来组合成一个单一的一致的方向分配，该矩阵的条目对成对关系进行编码。该矩阵显示为 3 级，其非平凡特征空间显示每个图像的投影方向。特别是，我们展示了非平凡的特征向量编码对应于每个图像的旋转矩阵。