Dihedral Multi-Reference Alignment
Dihedral Multi-Reference Alignment
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DOI：
10.1109/tit.2022.3146488
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发表时间：
2021-07
影响因子：
2.5
通讯作者：
Tamir Bendory;D. Edidin;W. Leeb;N. Sharon
中科院分区：
文献类型：
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作者：
Tamir Bendory;D. Edidin;W. Leeb;N. Sharon
我们研究二面角多参考对准问题的估计轨道的信号从多个噪声观测的信号，作用于随机元素的二面角群。我们表明，如果组元素是从一个通用的分布，一个通用的信号的轨道是唯一确定的第二时刻的意见。这意味着高噪声状态下的最佳估计速率与噪声方差的平方成比例。这是第一个结果，这种类型的多参考对齐在一个非阿贝尔群与非均匀分布的群元素。从不变的理论和代数几何的工具的基础上，我们还描绘了独特的轨道恢复条件的多参考对齐模型在有限群（即，当二面角群被替换为一个一般的有限群）时，组元素是从一个通用的分布。最后，我们设计并研究了三种基于群同步、期望最大化和矩量法的信号估计计算框架。
We study the dihedral multi-reference alignment problem of estimating the orbit of a signal from multiple noisy observations of the signal, acted on by random elements of the dihedral group. We show that if the group elements are drawn from a generic distribution, the orbit of a generic signal is uniquely determined from the second moment of the observations. This implies that the optimal estimation rate in the high noise regime is proportional to the square of the variance of the noise. This is the first result of this type for multi-reference alignment over a non-abelian group with a non-uniform distribution of group elements. Based on tools from invariant theory and algebraic geometry, we also delineate conditions for unique orbit recovery for multi-reference alignment models over finite groups (namely, when the dihedral group is replaced by a general finite group) when the group elements are drawn from a generic distribution. Finally, we design and study numerically three computational frameworks for estimating the signal based on group synchronization, expectation-maximization, and the method of moments.