The Generalized Method of Moments for Multi-Reference Alignment

Asaf Abas, Tamir Bendory*, Nir Sharon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)1377-1388
Number of pages12
JournalIEEE Transactions on Signal Processing
Volume70
DOIs
StatePublished - 2022

Funding

FundersFunder number
NSF-BSF2019752
Zimin Institute for Engineering Solutions Advancing Better Lives
United States-Israel Binational Science Foundation2018230, 2020159
Israel Science Foundation1924/21

    Keywords

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

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