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Inverse problems for cryo electron microscopy of viruses:Randomly oriented projection images of random 3-Dstructures in noise

机译：病毒低温电子显微镜的反问题：噪声中随机3-D结构的随机定向投影图像

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摘要

Instances of biological macromolecular complexes that have identical chemical constituents may not have the same geometry due to, for example, flexibility. Cryo electron microscopy provides one noisy projection image of each of many instances of a complex where the projection directions for the different instances are random. The noise is sufficient severe (SNR 1) that the projection direction for a particular image cannot be easily estimated from the individual image. The goal is to determine the 3-D geometry of the complex (the 3-D distribution of electron scattering intensity) which requires fusing information from these many images of many complexes. In order to describe the geometric heterogeneity of the complexes, the complex is described as a weighted sum of basis functions where the weights are random. In order to get tractable algorithms, the weights are modeled as Gaussian random variables with unknown statistics and the noise is modeled as additive Gaussian random variables with unknown covariance. The statistics of the weights and the statistics of the noise are jointly estimated by maximum likelihood by a generalized expectation maximization algorithm. An example using these ideas on images of Flock House Virus is described.
机译：由于例如柔韧性，具有相同化学组成的生物大分子复合物的实例可能不具有相同的几何形状。低温电子显微镜为复杂区域的许多实例提供了一个嘈杂的投影图像，其中不同实例的投影方向是随机的。噪声非常严重（SNR << 1），以至于无法从单个图像中轻易估计出特定图像的投影方向。目的是确定复合物的3D几何形状（电子散射强度的3D分布），这需要融合来自许多复合物的许多图像的信息。为了描述复合物的几何异质性，将复合物描述为基函数的加权和，其中权重是随机的。为了获得易于处理的算法，将权重建模为统计未知的高斯随机变量，将噪声建模为协方差未知的加性高斯随机变量。权重的统计和噪声的统计是通过广义期望最大化算法通过最大似然联合估计的。描述了在羊群病毒图像上使用这些思想的示例。

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