The generalized method of moments for multi-reference alignment
arXiv:2103.02215 · doi:10.1109/TSP.2022.3157483
Abstract
This paper studies the application of the generalized method of moments (GMM) to multi-reference alignment (MRA): the problem of estimating a signal from its circularly-translated and noisy copies. We begin by proving that the GMM estimator maintains its asymptotic optimality for statistical models with group symmetry, including MRA. Then, we conduct a comprehensive numerical study and show that the GMM substantially outperforms the classical method of moments, whose application to MRA has been studied thoroughly in the literature. We also formulate the GMM to estimate a three-dimensional molecular structure using cryo-electron microscopy and present numerical results on simulated data.
References in corpus (14)
- Manopt, a Matlab toolbox for optimization on manifolds
- Nonconvex phase synchronization
- Single-particle cryo-electron microscopy: Mathematical theory, computational challenges, and opportunities
- Bispectrum Inversion with Application to Multireference Alignment
- Estimation under group actions: recovering orbits from invariants
- Message-passing algorithms for synchronization problems over compact groups
- Fundamental Limits in Multi-image Alignment
- Method of moments for 3-D single particle ab initio modeling with non-uniform distribution of viewing angles
- Multi-target detection with application to cryo-electron microscopy
- Multi-reference alignment in high dimensions: sample complexity and phase transition
- Multi-target Detection with an Arbitrary Spacing Distribution
- An accelerated expectation-maximization algorithm for multi-reference alignment
- Numerical Algorithms for the Computation of Generalized Prolate Spheroidal Functions
- Optimal Subspace Estimation Using Overidentifying Vectors via Generalized Method of Moments