The Generalized Method of Moments for Multi-Reference Alignment

Asaf Abas; Tamir Bendory; Nir Sharon

doi:10.1109/TSP.2022.3157483

The Generalized Method of Moments for Multi-Reference Alignment

Asaf Abas, Tamir Bendory^*, Nir Sharon

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English
Pages (from-to)	1377-1388
Number of pages	12
Journal	IEEE Transactions on Signal Processing
Volume	70
DOIs	https://doi.org/10.1109/TSP.2022.3157483
State	Published - 2022

Funding

Funders	Funder number
NSF-BSF	2019752
Zimin Institute for Engineering Solutions Advancing Better Lives
United States-Israel Binational Science Foundation	2018230, 2020159
Israel Science Foundation	1924/21

Keywords

Generalized method of moments
multi-reference alignment
orbit recovery problem
single-particle cryo-electron microscopy

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10.1109/TSP.2022.3157483

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title = "The Generalized Method of Moments for Multi-Reference Alignment",

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.",

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AU - Bendory, Tamir

AU - Sharon, Nir

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N2 - 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.

AB - 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.

KW - Generalized method of moments

KW - multi-reference alignment

KW - orbit recovery problem

KW - single-particle cryo-electron microscopy

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JO - IEEE Transactions on Signal Processing

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The Generalized Method of Moments for Multi-Reference Alignment

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