RATES OF ESTIMATION FOR HIGH-DIMENSIONAL MULTIREFERENCE ALIGNMENT

• 成果类型: Article
• 署名作者: Dou, Zehao; Fan, Zhou; Zhou, Harrison H.
• 署名单位: Yale University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/23-AOS2346
• 发表日期: 2024
• 页码: 261-284
• 关键词: cryo-em; Sample Complexity; common lines; Synchronization; reconstruction; eigenvectors

摘要

We study the continuous multireference alignment model of estimating a periodic function on the circle from noisy and circularly-rotated observations. Motivated by analogous high-dimensional problems that arise in cryoelectron microscopy, we establish minimax rates for estimating generic signals that are explicit in the dimension K. In a high-noise regime with noise variance sigma 2 >= K, for signals with Fourier coefficients of roughly uniform magnitude, the rate scales as sigma 6 and has no further dependence on the dimension. This rate is achieved by a bispectrum inversion procedure, and our analyses provide new stability bounds for bispectrum inversion that may be of independent interest. In a low-noise regime where sigma 2 <= K/ log K, the rate scales instead as K sigma 2, and we establish this rate by a sharp analysis of the maximum likelihood estimator that marginalizes over latent rotations. A complementary lower bound that interpolates between these two regimes is obtained using Assouad's hypercube lemma. We extend these analyses also to signals whose Fourier coefficients have a slow power law decay.