Cryo-electron microscopy (cryo-EM) is a powerful imaging technique for reconstructing three-dimensional molecular structures from noisy tomographic projection images of randomly oriented particles. We introduce a new data fusion framework, termed the method of double moments (MoDM), which reconstructs molecular structures from two instances of the second-order moment of projection images obtained under distinct orientation distributions: one uniform, the other non-uniform and unknown. We prove that these moments generically uniquely determine the underlying structure, up to a global rotation and reflection, and we develop a convex-relaxation-based algorithm that achieves accurate recovery using only second-order statistics. Our results demonstrate the advantage of collecting and modeling multiple datasets under different experimental conditions, illustrating that leveraging dataset diversity can substantially enhance reconstruction quality in computational imaging tasks.

翻译：冷冻电镜（cryo-EM）是一种强大的成像技术，能从随机取向粒子的噪声断层投影图像中重建三维分子结构。我们提出了一种新的数据融合框架，称为双矩方法（MoDM），该方法利用在两种不同取向分布（一种均匀分布，另一种非均匀且未知分布）下获取的投影图像的二阶矩实例来重建分子结构。我们证明这些矩在一般情况下能唯一确定底层结构（除全局旋转和反射外），并开发了一种基于凸松弛的算法，仅使用二阶统计量即可实现精确重建。我们的结果展示了在不同实验条件下收集和建模多个数据集的好处，表明利用数据集多样性可以显著提升计算成像任务中的重建质量。