用于组同步的展开算法
Unrolled algorithms for group synchronization
摘要：
群同步问题涉及到估计一个集合的组元素从噪声测量的成对比率。这项任务是许多计算问题的关键组成部分，包括单粒子冷冻电子显微镜（cryo-EM）中的分子重建问题。估计群元素的标准方法基于迭代地应用线性和非线性算子，并且不一定是最优的。由于与深度神经网络的结构相似性，我们采用了算法展开的概念，其中训练数据用于优化算法。我们设计了几个组同步实例，包括同步组的3-D旋转展开算法：在冷冻EM同步问题。我们还将类似的方法应用于多参考对齐问题。我们通过数值实验表明，展开策略优于现有的同步算法在各种各样的情况下。
英文摘要：
The group synchronization problem involves estimating a collection of group elements from noisy measurements of their pairwise ratios. This task is a key component in many computational problems, including the molecular reconstruction problem in single-particle cryo-electron microscopy (cryo-EM). The standard methods to estimate the group elements are based on iteratively applying linear and non-linear operators, and are not necessarily optimal. Motivated by the structural similarity to deep neural networks, we adopt the concept of algorithm unrolling, where training data is used to optimize the algorithm. We design unrolled algorithms for several group synchronization instances, including synchronization over the group of 3-D rotations: the synchronization problem in cryo-EM. We also apply a similar approach to the multi-reference alignment problem. We show by numerical experiments that the unrolling strategy outperforms existing synchronization algorithms in a wide variety of scenarios.
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