论文标题
用于组同步的展开算法
Unrolled algorithms for group synchronization
论文作者
论文摘要
小组同步问题涉及估算其成对比率嘈杂测量的组元素的收集。此任务是许多计算问题中的关键组成部分，包括单粒子冷冻电子显微镜（Cryo-EM）中的分子重建问题。估计组元素的标准方法是基于迭代应用线性和非线性操作员的基础，不一定是最佳的。我们采用与深神经网络的结构相似性的动机，我们采用了算法展开的概念，其中训练数据用于优化算法。我们为多种组同步实例设计了展开的算法，包括3-D旋转组的同步：Cryo-EM中的同步问题。我们还将类似的方法应用于多参考对准问题。我们通过数值实验表明，展开策略在各种情况下都优于现有的同步算法。
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.
